Friends, it is a good time to summarize what we have learned in the last lecture. We initiated discussion on the fluidized bed reactor and the objective is to design a fluidized bed reactor. What is a fluidized bed reactor? Fluidized bed reactor is essentially a tube which has a certain catalyst particles and then the gas is flown through this tube and as the velocity of the gas stream increases then the drag force that this fluid stream exerts on the gas particle on the solid catalyst particle that is equal to the weight that is actually gravitational force exerted by these particles because of its natural weight. So, when that equals then the catalyst particle starts raising and that is called the fluidization phenomena. Now, once the fluidization occurs then these gas bubbles are formed and when these gas bubbles are formed there is transport between the transport of the reactants from the gas bubble to the catalyst particle where the reaction occurs in the catalytic sites of the catalyst particle which is already fluidized and then the product which is formed in the sites is actually transported back into the bubbles which is the gas stream and then the bubbles carry these product and leave the reactor. So, this is the process that occurs in a fluidized bed reactor and then we looked at different regimes different fluidization regimes in the fluidized bed reactor. So, if FPR stands for the fluidized bed reactor we looked at different flow regimes. One is the fixed bed regime. In a fixed bed regime the fluid velocity is not significant enough to offset the gravitational force which is exerted by the catalyst particle and as a result the particles they remain packed at the bottom of the reactor where they are sitting on a perforated or a porous plate. Then the second regime is called the minimum fluidization regime, minimum fluidization regime. Now, in this regime the velocity of the fluid is just sufficient to offset the gravitational force that is the drag force that is that the particles experience because of the flow of this gas which is flowing at a certain superficial velocity which is which is being flown into the bed at a certain superficial velocity U0. Then the drag force offsets the or it is just equal to the gravitational force exerted by the catalyst particles then the particles starts raising or they get fluidized and that velocity minimum velocity is called the fluidization velocity and the regime is called the minimum fluidization regime. Typically, the bubbles which are present in the near the minimum fluidization regime they are bubbles are formed near the perforated plate and then the bubble starts travelling through this bed which is being fluidized and the third regime is called the aggressive bubbling regime. So when the velocity with which the gas stream is being flown inside the bubbling significantly increases and so there is aggressive bubbling lots of bubbles are formed which causes tremendous amount of recirculation of the fluid and also the catalyst particles and so that regime is called the aggressive bubbling regime and then the fourth one is called the slugging regime where these velocity is significantly higher that there are channels of these channels are actually created and through these streams the gas stream simply escapes the bed and that is what is called the slugging regime. And the last one is the lean phase where the all the particles are suspended and the density of the porosity is significantly higher and they are all suspended all through the reactor. So that is what is called the lean phase regime. So these are the five different regimes that we described in the last lecture and we initiated the discussion on Cuny-Levenspiel model Cuny-Levenspiel model. So the Cuny-Levenspiel model assumes that all particles are of same size and it also assumes that the solid flow in the emulsion the solid flow in the emulsion phase as though like it is a plug flow and then the emulsion phase exists at a minimum emulsion phase always exists at a minimum fluidization velocity and then it also assumes that the gas void fraction is equal to the void fraction as that of at the minimum fluidization velocity and then it assumes that the solid which is flowing down downwards is actually the concentration of the solids which is present in the emulsion phase is equal to the concentration of the solids which is present in the wakes which are actually formed just below the bubble. Just to recap the bubbles are formed as soon as these fluid actually is going through the bed the bubbles are formed and then the bubbles carry a certain amount of particles and then there is a wake which is formed below the bubble where a lot of particles of high concentration is actually carried along with the bubble around this around the bubbles there is a phase called the cloud phase there is a phase called the cloud phase and in this cloud there are some particles are present in this cloud and then around the cloud is the around the cloud is the phase called the emulsion phase which also contains lots of particles and the emulsion phase is essentially has the same porosity as that of the nearly the porosity of the resting bed and therefore the transport which occurs the mass transport process which occurs is the reactant species are transported from the bubble to the cloud phase. So, this is the cloud phase and this is the emulsion phase and this is the wakes so the mass transport occurs from the bubble phase into the cloud phase and the reactants are transported from the cloud phase into the emulsion phase where the particles are present and the reaction occurs in the particles and then the product is actually transported back into the cloud phase and back into the bubble phase. So, once this happens the bubbles carry the product and then the product leaves the fixed fluid as bed reactor. So, this is the process that occurs in a fluid as bed reactor. So, now we looked at some of the expressions for the there are several parameters that one needs to actually find out before we can model the fluid as bed reactor. So, the velocity with the velocity of gas in emulsion phase is given by u e equal to u m f which is the velocity of the minimum fluidization divided by the porosity at minimum fluidization minus u s where u s is the velocity of solids flowing downwards flowing downwards. Now, the bubble velocity so remember that the one of the important aspects that control the conversion or the performance of the fluid as bed reactor is the time that is spent by the bubble in the fluid as bed reactor because the reactants are carried inside the bubble and the reactants have to get in contact with the solids in order for the catalytic reaction to occur. So, therefore, the amount of time that is spent by the bubble inside the reactor significantly contributes to the performance of the fluid as bed reactor. So, the time that is spent by the bubble inside the reactor is controlled by the velocity with which the bubble is actually raising inside the fluid as bed reactor. So, let us look at how to estimate this velocity of the bubble which is raising inside the fluid as bed reactor. So, the bubble velocity is calculated for a single bubble there are correlations that exist for a single bubbles which is given by u b r and that is equal to 0.71 into gravity into diameter of the bubble to the power of half. So, one needs to know what is the diameter of the bubble in order to estimate what is the single bubble velocity. So now, if many bubbles are present which is typically the case in a fluid as bed reactor then the velocity with which a single bubble is going to raise together with many bubbles is going to be very different because of the presence of other bubbles. So, therefore, in a fluidized state in fluidized state the bubble velocity is given by the bubble there has to be some correction that is associated with the bubble velocity if there were to be just a single bubble. So, therefore, the correction is basically given by u naught minus u m f that is the correction to the single bubble velocity and that tells us what is the velocity of the bubble in a fluidized state where u naught is the superficial velocity with which the gas stream is being flown into the fluidized bed reactor and u m f is the corresponding velocity of at minimum fluidization point minimum fluidization at the minimum fluidization and so, therefore, plugging in the correlation for the for the velocity of a single bubble if we can find that the velocity of the bubble in a fluidized bed reactor in the fluidized state is given by u naught minus u m f plus 0.71 into gravity into diameter of the bubble to the power of half. So, now we need to find out what is the diameter of the bubble what in terms of the other properties of the reactor. So, there are correlations which are actually available. So, one needs to use correlations in order to estimate the diameter of the bubble. So, let us look at what these correlations are. So, the first correlation that you are going to look at is called the Mori-Wen correlation it is the Mori-Wen correlation the correlation is as it goes like this. So, dBm which is the maximum possible bubble diameter minus the diameter of a particular bubble divided by the maximum possible diameter minus the diameter of the bubble when the bubble is just formed that is the initial bubble diameter and that should be equal to exponential of minus 0.3 into h by dt where h is the height at which the particular bubble is being observed and dt is the bed diameter diameter of the bed. And so, now Dbo which is the initial bubble diameter initial bubble diameter that is given by 0.0037 into u naught minus u m f the whole square. If it is a perforated plate if it is a porous plate sorry if it is a porous plate then the correlation that gives an estimate of what is the initial bubble diameter is given by 0.0037 into superficial velocity minus the corresponding fluidization velocity and square of that difference. And that is equal to 0.347 multiplied by the area of cross section into u naught which is the superficial velocity minus the minimum fluidization velocity v m f divided by the number of perforations which is actually present in the perforated plate to the power of 0.4. So, this is the correlation for estimating the initial bubble diameter if the plate which actually holds these particles are actually a it is a perforated plate, if it is a perforated plate then this is the correlation that actually gives an estimate of what is the initial bubble diameter. So, next we need to know what is the maximum possible bubble diameter so the maximum bubble diameter is given by d B m is the maximum bubble diameter and that is given by the correlation 0.652 into the area of cross section of the bed into u naught minus u m f u naught is the superficial velocity with which the gas stream is let inside the fluidized bed reactor and u m f is the minimum fluidization velocity a whole to the power of 0.4. So, that provides an estimate of what is the maximum possible bubble diameter and it is known that the predictions are poor if the bed is very large. So, the d B m prediction by using this correlation is poor for large beds for a large fluidized bed reactor the correlation does not work very well the experimental observation suggests that this correlation does not give a good estimate if the bed is very large. The other correlation which is also available which seems to work over a wide range of fluidized bed reactor is called the Werther correlation the Werther correlation is that the diameter of the bubble is given by 0.853 into 1 plus 0.272 into u naught minus u m f whole to the power of 1 by 3 into 1 minus 0.684 into h which is the height of the bed at that particular instance it to the power of 1.21. So, this correlation is known to give a better prediction of the diameter of the bubble into the fluidized conditions. So, the next estimate that we need to make is the velocity of the solid when it is flowing in the emulsion phase. So, we need to find out what is the solids velocity u s that is what that is the next parameter that needs to be estimated. So, suppose in order to estimate the solids velocity we can perform a very simple material balance this is because of the fact that whatever solid particles which are actually flowing down in the emulsion phase should be equal to what are the solids which are actually being taken up in the wakes which is actually following the bubbles. So, wakes actually have the maximum concentration of the solid particles that are being lifted because of fluidization. So, therefore, the amount of solid particles which are actually flowing upwards in the wake should be equal to the amount of solid particles which are actually transported in the emulsion phase. So, therefore, if we make a material balance across the solids flowing in these 2 phases then we should be able to estimate what should be the relationship for finding the solids velocity. So, let us look at this material balance. So, the solids flowing in emulsion phase that should be equal to flowing down in emulsion phase should be equal to solids flowing solids actually taken upwards in the wakes. So, now putting the corresponding expression solids flowing down in the emulsion is given by area of cross section AC multiplied by the density of the catalyst rho C into 1-delta-alpha into delta into U s where delta is basically the fraction of the total bed that is actually bubbles. So, delta is the fraction of total bed that is bubbles. Now, this excludes the this excludes the wakes that are actually formed this is just the bubbles this is the fraction of the total bed which is basically the bubbles. So, that is delta and then alpha is essentially alpha is the fraction of or the volume of the wake per volume of the bubbles which are actually formed because of fluidization. This is the volume of wakes per volume of the bubbles which are actually formed by fluidization. So, therefore, this quantity 1-delta into alpha delta it actually it actually estimates as to how much what what fraction of the cross sectional area is actually filled with solids is given by 1-delta-alpha into delta. So, therefore, using the this relationship for the solids flowing in emulsion that can be equated to the fraction that contains fraction of volume in a given cross section that is actually filled by wakes is alpha into delta because alpha is the volume of wakes per volume of the bubbles and delta is the fraction of the bed that is actually bubbles multiplied by U b which is the velocity with which the bubble is raising up upwards into multiplied by rho c into ac. So, this material balance of the solids which is flowing down in emulsion and the solids which are actually taken upwards in the wakes can be used to estimate U s and note that the U b is the bubble rising velocity which can be obtained using the correlations that is Mori-Ven or the Werther correlation and alpha and delta are supposedly a known property for a for a particular fluidized bed reactor and we are going to see how to estimate them. So, based on this correlation we can find out that the velocity of the solids U s is actually given by alpha into delta into U b divided by 1-delta-alpha into delta. So, that is the expression for the that is the expression for the velocity with which the solid is flowing. So, the next step is to find out what is this value of delta which is basically the fraction of the of the bed which is actually filled with the bubbles. So, now let us write a simple material balance on the gas flow to find out what is this value of delta which is the fraction of bubbles fraction of the bed which is actually bubbles. So, this we can write a material balance on gas flow to estimate the value of delta. So, that is what we are going to do next. So, the material balance on gas flow basically is just to account for what is the how the gas is being split into different sections and what is the total material balance for the gas flow and that is given by Ac into U naught where U naught is the superficial velocity. So, that is the superficial velocity with which the fluid is actually being pumped into the fluidized bed reactor. So, the total gas that enters the reactor should be equal to the cross section area of the fluidized bed reactor multiplied by the corresponding superficial velocity. So, that should be equal to the gas that is actually carried by the bubbles. So, that will be the cross sectional area into delta which tells you what is the area fractional area that contains that is actually occupied by the bubbles multiplied by the velocity U b tells us what is the flow rate mass flow rate of the of the gas that is actually carried by the bubbles plus some of this gas is now going to go in the wakes. So, that can be estimated as Ac which is the cross sectional area multiplied by the porosity with at the minimum fluidization velocity epsilon mf into alpha into delta into U b. So, alpha is basically the volume of wakes per volume of the bubbles. And then there is another component which is basically the gas that may be present in the emulsion phase. So, that is actually Ac into epsilon mf into 1 minus alpha minus alpha 1 minus delta into alpha into delta into the velocity with which the emulsion is moving. So, this basically tells us what is the material balance for the gas flow. Now, we know that this is the this is the total gas flow, this is the gas flow in the bubbles and this is gas flow in wakes and this is in the emulsion phase that is in the emulsion phase. So, that tells us what is the total amount of material balance on gas flow and we know that the velocity of the emulsion phase is given by U mf divided by epsilon mf minus the velocity of the solids. So, now plugging in these expressions we will be able to find out what is delta.  Now, if U b is significantly larger than U mf that is if the velocity with which the bubbles are actually raising is higher than the minimum fluidization velocity then we can further simplify the expression for the delta which is the fraction of the bed that is actually occupied by the bubbles that is given by U naught minus U mf divided by U b. So, now we have estimated what is delta. So, the next exercise is to characterize the mass transport in fluidized bed reactor characterize the mass transport in fluidized bed. Now, there are two forms of mass transport which actually occurs in the fluidized bed reactor one is there is mass transport between the gas and solids. So, that is very much like the gas solid transport and gas solid reactions. So, gas solid catalytic systems and then the second type of transport is basically between the bubble and the cloud phase between the bubble and the cloud phase and also between the cloud and the emulsion. So, remember that when for the reaction catalytic reaction to occur the reactants which is actually present in the gas stream is carried by the bubbles and this mass transport of the reactants from the bubble phase into the cloud phase and cloud phase into the emulsion phase which actually contains the particles where the reaction occurs and then the products are now transported back. So, therefore, the mass transport process in fluidized bed reactor is slightly different from the slightly in addition to the classical mass transport in the gas solid catalytic systems. So, let us look at what happens here. So, suppose if this is the bubble suppose the bubble is here and then if the cloud is present around here. So, now we may represent W if A is the species, W A B to C is essentially the transport from bubble to the cloud region and this is the emulsion region and then W A C to E is basically the flux of transport or rate of transport from the cloud to the emulsion phase and similarly after the product is formed the W B if B is the product that is formed that is the transport from the emulsion to the cloud phase and then W A W B C to B is the transport of the product from the cloud to the bubble phase. So, this is the in addition to the classical gas solid transport in the catalytic reactors this is an extra transport mechanism which is been observed in which is observed in the fluidized bed reactor. So, let us look at how to characterize the how to find the gas solid mass transport coefficient first and then we will look at the other mode of transport. So, now between gas and single particles there are correlations which is called the Frosling correlation that is the Frosling correlation and that is basically characterizes the mass transport between gas and single particle and that is given by Sherwood number that is equal to 2 plus 0.6 into Reynolds number to the power of half into Schmidt number to the power of 1 by 3 and for emulsion phase for emulsion phase the Cooney and Levenspiel have developed a correlation Cooney and Levenspiel have developed a correlation to estimate the mass transport coefficient in the emulsion phase and that is given by Sherwood number equal to 2 plus 1.5 into Schmidt number to the power of 1 by 3 into 1 minus epsilon into Reynolds number to the power of half and the validity of this correlation is basically between the Reynolds number of 5 and 120 and epsilon should be less than 0.8, 0.84. So, if the porosity is less than 0.84 then this correlation works in the emulsion phase. So, there are different mass transport coefficients and one need to actually combine all of these mass transport coefficient in order to estimate what is the overall mass transport coefficient because mass transport occurs through both these cases both these mechanisms then let us look at the mass transport between bubble and cloud. So, suppose if the so let us first look at the transport of the reactant from the bubble to the cloud. So, the suppose if A is the reactant so the flux at which the species A is being transported from the bubble to the cloud flux at which it is transported is actually given by the mass transport coefficient KBC multiplied by CAB minus CAC where CAB is basically the concentration. So, that is the concentration of the species in the bubble phase and this is the concentration in the cloud phase. So, this expression provides the flux at which the species is being transported from the bubble phase to the cloud phase and similarly the for transport from the cloud phase to the emulsion phase the expression can be written as KCB where KCB is the corresponding mass transport coefficient and the previous case the KBC is the corresponding mass transport coefficient multiplied by CAC minus CAC where CAC is the concentration of species A. So, CAC in the cloud phase and this is the concentration of species in the emulsion phase. So, this is for the mass transport between the cloud phase and the emulsion phase. So, similarly the one can actually write a similar transport for the product species which is being transported back from the emulsion phase back into the cloud phase and back into the bubble phase. So, Kuni-Levenspiel once again they have developed a correlation in order to find out what these mass transport coefficients are. So, they have developed a correlation for estimating these mass transport coefficient and so that is given by KBC which is the mass transport coefficient for reactant species to go from for species to go from the bubble phase into the cloud phase and that is given by 4.5 multiplied by the minimum fluidization velocity UMF divided by the diameter of the bubble plus 5.85 into the diffusivity DAB to the power of 1 by 2 into gravity to the power of 1 by 4 divided by the diameter of the bubble to the power of 5 by 4. So, that is the correlation which provides an estimate of what is the mass transport coefficient between the bubble phase and the cloud phase. Now because the mass transport actually occurs by the exchange of volume between the cloud phase and the bubble phase, one could assume that the mass transport between the mass transport coefficient for transport from the bubble to the cloud phase should be approximately equal to the mass transport coefficient from the cloud phase back into the bubble phase. And typically the order of magnitude of this mass transport coefficient is of order of 2 second minus 1. Remember that KCB is a mass transport coefficient. So, now let us look at the correlations for cloud to emulsion, mass transport from cloud to the emulsion and that is typically given by KCE equal to KEC. That is the KCE is the mass transport coefficient for transport from the cloud phase to the emulsion phase and KEC is the transport of products let us say from the emulsion phase back into the cloud phase. And so that is given by the correlation 6.77 into epsilon mf which is the porosity at the minimum fluidization velocity multiplied by the diffusivity DAB into the velocity of the raising bubble divided by the diameter of the bubble to the power of 3 cube of that to the power of 1 by 2 square root of the whole expression. And this is typically of the order of 1 second minus 1. So, that is the order of magnitude of the mass transport coefficient. So, let us next look at the reaction in the fluidized bed reactor. Remember there are 3 factors which are controlling. One is the mass transport of the reactant species from the bubble phase into the cloud and into the emulsion in order for it to get in contact with the catalytic particles. And then the next step is the reaction which is actually occurring inside the catalytic sites to form the product catalytic reaction which is happening inside the catalytic site to form the products. And once the products are formed they are transported back into the bubble phase. So, let us look at the reaction in the fluidized bed reactor. Let us look at the reaction. So, suppose if it is an nth order reaction, suppose if it is an nth order reaction, then the reaction rate in the bubble phase can actually be given as kB into CAB to the power of n. So, that is in the bubble phase. And similarly for the cloud phase it can be given as kC into CAC to the power of n where kB and kC are the corresponding rate constants. And then for the emulsion phase it can be written as kE into CAE to the power of n where the CAB is the concentration of the species in the bubble phase. And CAC is the concentration of the species in the cloud phase and CAE is the concentration of species in the emulsion phase. Now it is important to write these rate expressions in all three phases. Although the emulsion phase actually contains the maximum number of particles, the bubble phase and the cloud phase also will have some particles. And therefore, it is important to write these expressions because the reaction can in principle occur in the catalyst particles in each of these phases. So, now next we can write a mole balance. Once we know the reaction rates, we can now write a mole balance in the fluidized bed reactor in order to capture the behavior of the concentration of the reactant species in the reactor. So, now let us consider a small element. Let us consider a fluidized bed reactor and if let us say that the fluid is entering at a superficial velocity of U0 and then there is a small element between z and z plus delta z. And if you assume that the upward motion or the direction of the fluid flow is the positive direction, then we can now write a mole balance for the bubble phase. We can now write a mole balance for the bubble phase which is basically rate due to flow into the bubble phase minus the rate with which the fluid stream leaves because of flow plus the rate at which the fluid species is actually leaving the bubble phase because of mass transport plus whatever is being generated that should be equal to 0 under a steady state condition. So, if you assume a steady state conditions and this is the mole balance. So, now when we plug in all the corresponding expressions, rate due to flow that is into the bubble phase is given by the velocity of the bubble UB multiplied by the corresponding cross section AC into concentration of the species in the bubble phase multiplied by delta. So, delta is basically the fraction of the bed that is actually in the bubble phase and that at that particular location z that is the rate at which the species is entering this small element in the bubble phase and then the rate at which the species is leaving in the bubble phase at z plus delta z is given by UB AC CAB into delta at z plus delta z and mass transport is given by minus KBC into CAB that is the concentration of the species in the bubble phase minus the concentration of species in the cloud phase multiplied by cross section area into delta z. So, that is the rate at which the species is actually leaving the bubble phase and going into the cloud phase minus the corresponding reaction rate. So, that is KB if that KB is the reaction rate constant into CAB to the power of n. So, that is the CAB is the concentration of species in the bubble phase multiplied by the cross section into delta z into delta. So, that should be equal to 0. So, that is the mole balance for the species in the bubble phase. So, now we can rewrite this mole balance as by taking a limit that so, by taking limit that delta z goes to 0 we can rewrite this model as UB which is the velocity with which the bubble is racing inside the fluidized bed reactor into DCAB by DZ that should be equal to minus KB CAB to the power of n minus KBC which is the mass transport coefficient between the bubble and the cloud phase multiplied by CAB minus CAC. So, that is the model the mole balance for the bubble phase. So, similarly for the cloud phase the mole balance is given by UB into delta into 3 times UMF a very similar balance can be written and taking the limits of delta z going to 0. One would get that the expression for a mole balance for the concentration of the species in the cloud phase is basically given by this expression here into DCAC by DZ that should be equal to the mass transport coefficient of the species from the bubble to the cloud phase that is basically added into the cloud phase multiplied by CAB minus CAC minus KCE that is the mass transport coefficient for transport of the species from the cloud phase into the emulsion phase that is given by CAC minus CAE minus KC which is the rate at which is the rate constant for the reaction if the catalytic reaction is happening in the catalyst particles which may be present in the cloud phase. So, that is the mole balance for the cloud phase and then the mole balance for the emulsion phase is given by for the emulsion phase that is given by UE which is the velocity with which the emulsion phase is moving into 1 minus delta minus alpha into delta divided by delta into DCAE by DZ that should be equal to the mass transport coefficient between the cloud and the emulsion phase into CAC minus CAE minus the rate at which the species is actually being consumed because of the reaction that may be happening in the emulsion phase. So, if we need to find out what is the concentration of the species in the bubble phase in the cloud phase and the emulsion phase then these three equations have to be solved simultaneously. So, these things have to be solved simultaneously. So, once we solve them simultaneously then we can find out the expression for CAB, CAC and CAE what is its relationship how the profile changes with respect to the position inside the fluid as bed reactor. As this is a non-linear equation it cannot be solved analytically and one has to resort to numerical techniques to solve these set of equations. However, if we make an assumption that the reaction is a first order reaction, suppose if we assume that it is a first order reaction, suppose if the reaction the catalytic reaction which is happening is a first order reaction then we can actually write the expression as UB into DCAB by dz that is equal to minus KB into CAB to the power of n minus the mass transport coefficient KBC into n equal to 1 CAB minus CAC and suppose if we assume that DCAC by dz which is the rate of change of the concentration with respect to position in the cloud phase if this is very small and similarly if we assume that DCAE by dz is also very small then we can write the model equations for the these two concentrations as they basically become like this where the mass 0 equal to the mass transport coefficient KBC multiplied by CAB minus CAC minus KCE into CAC minus CAE minus KC into CAC and similarly for the emulsion phase the mole balance will become KCE into CAC minus CAE minus KE into CAE. So, that is the mole balance for the for the emulsion phase. Now, because it is a catalytic reaction, so the KB which is the corresponding rate constant suppose KB, KC and KE these are the corresponding rate constants for the reaction which is actually occurring in the bubble phase cloud phase and the emulsion phase respectively and emulsion phase respectively. So, now suppose if it is a catalytic reaction, if it is a catalytic reaction and if gamma B is basically the ratio of volume of solid catalyst in the bubble phase divided by the volume of the bubble. So, this provides an estimate of what fraction of the bubble volume is actually contained by the solid particles which are actually carried by the bubble phase. So, if we know this expression then we can actually rewrite the rate constant in terms of the intrinsic rates. So, that will be equal to KB is given by gamma B which is the fraction of the volume which inside the bubble which is basically which is occupied by the solid particles carried by the bubble into the corresponding reaction rate which is occurring in the catalyst surface of the particles and so now that can actually be rewritten as gamma B into rho C into K prime where K prime is the gram mole that is reactor per unit weight of the catalyst per unit time and rho C is the corresponding density of the catalyst. So, similarly we can actually write we can write KC is basically equal to gamma C which is the volume of solid catalyst which is present fraction of volume of the cloud phase which is occupied by the solid catalyst that multiplied by rho C into K prime. So, the and similarly K e equal to gamma e into rho C into K prime. So, notice that the K prime is basically same because it is the same catalytic reaction which is happening in the solid particles which are present in these three phases. The overall reaction rate is different in these three phases because the amount of catalyst particles which is present in each of these phases are different and therefore, the that is actually accounted for in the overall reaction rate constant. So, now we need to estimate what is this gamma B, gamma C and gamma E are. So, if we know that estimate then the mole balance can actually be solved. So, we need to find out what is gamma B, gamma C and gamma E. So, once we know this we can actually solve the model equation and so, gamma B is essentially given by 3 into U M F by epsilon M F divided by U B minus U M F by epsilon M F and similarly gamma E is given by 1 minus epsilon M F into 1 minus delta by delta minus gamma C minus gamma B. So, that is gamma E is the fractional volume in the emulsion phase which is occupied by the solid catalyst and gamma B is the corresponding fractional volume in the bubble phase and gamma C is the fractional volume in the cloud phase occupied by the solid particles which will be 1 minus epsilon M F into M F by epsilon M F divided by U B R minus U M F by epsilon M F plus alpha. So, these things can be estimated simply by estimating in terms of the properties such as the porosity and the minimum fluidization velocity etc. What is the volume of the bubble and what is the fraction of the bubble which contains the solid particles what is that volume. So, once we estimate these volume and take the ratio we can find out these expressions for the volume fractions in the in each of these respective phases that is contained by the solid particles. So, now if we know all these expressions then we can we can now solve for the solve the model equations in order to find out the design parameters of the fluidized bed reactor. So, the complete mole balance for the first order reaction is basically the set of mole balance equations are suppose if we assume that the time is equal to z by U B. So, remember that the time that is spent by the bubble inside the bed is actually an important parameter that controls the performance of the fluidized bed reactor. So, T here refers to the time that is actually spent by the bubble inside the fluidized bed reactor till this position z. So, U B where U B is basically the velocity with which the bubbles are actually rising inside the fluidized bed reactor. So, the mole balance will be dCA B by dt that is equal to minus gamma B into the specific rate constant for the catalytic reaction multiplied by C AB minus K BC into C AB minus C AC and the second equation is K BC which is the mass transport coefficient between the bubble and the cloud phase that multiplied by C AB minus C AC that should be equal to gamma C into the rate constant for the catalytic reaction into C AC plus the mass transport coefficient K CE into C AC minus CAE and then the third equation would be K CE into C AC minus CAE that should be equal to gamma E into the rate constant for the catalytic reaction into CAE. So, now if I look at the third equation from third equation I can actually rearrange third equation and find an expression for CAE and that CAE is equal to K CE divided by gamma E into K catalyst which is the reaction rate constant for the catalytic reaction plus K CE into C AC. So, further rearrangement of the expressions can actually be performed in order to estimate what is the concentration of the species in the cloud and that is from second equation we can find out. So, substituting the expression for the concentration of the species in the emulsion phase into the expression for the concentration into the mole balance expression for the concentration of the species in the cloud phase we can find out the expression for the concentration of the species in the cloud phase and that is given by K BC into CAB divided by gamma C into K catalyst plus K CE into gamma E K catalyst divided by gamma C into K catalyst plus K CE plus K BC. So, that is the corresponding mass transport coefficient now plugging in all these expressions into the into equation 1. So, plug in expression for C AC and CAE in equation 1 we will get. So, what we can find is that minus DC AB by DT that is equal to K cat into CAB into sum overall constant KR and this KR is essentially given by the overall constant KR is given by gamma B plus 1 divided by K catalyst by K BC plus 1 divided by gamma C plus 1 divided by 1 by gamma E plus K catalyst divided by K CE. So, that is the expression for the overall reaction rate and if I look at this expression gamma B gamma B is basically captures the 1 by gamma B is the resistance for resistance to reaction in the bubble and K cat by K BC is the resistance to mass transport from bubble to cloud and gamma C is resistance to 1 by gamma C is resistance to reaction in the cloud phase and this is the resistance to reaction in the emulsion phase and this is the resistance to mass transport from the cloud to the emulsion phase. So, this overall constant essentially captures the resistances that is all the resistances that are actually present in the in this system. So, now using the appropriate stoichiometry we can say that CAB is equal to CAB 0 into 1 minus x where CAB 0 is the concentration of the species at the inlet of the fluid as bed reactor and so we can now rewrite the mole balance as DX by DT equal to K cat into KR that is the overall rate constant which captures all the resistances which are involved into 1 minus x. So, now we can solve this equation and you can find that ln of 1 by 1 minus x that is equal to K cat into KR into T. So, this provides the relationship between the conversion as a function of the time that is actually spent by the raising bubble inside the fluid as bed reactor. So, from this we can find out what is the overall height that is required. So, that is equal to T into UB that is the height that is required for suppose if a specific conversion is set what should be the conversion supposing if for a desired conversion if T D is the time that is required from this expression for the desired conversion. So, this corresponds to the desired conversion if this corresponds to the time for the desired conversion then the height of the bed can actually be estimated by using this expression T D into UB and that is equal to UB divided by K cat into KR into ln of 1 by 1 minus x and from here we can find out what is the weight of the catalyst that is given by rho C AC into AH into 1 minus epsilon mf into 1 minus delta. So, that is given by rho AC UB into 1 minus epsilon mf into 1 minus delta divided by K cat into KR into ln of 1 by 1 minus x. So, that is the expression for the weight of the catalyst. So, let us quickly just rewrite the way to expression for the weight of the catalyst. So, that is given by rho AC UB into 1 minus epsilon mf into 1 minus delta divided by K cat into KR which captures the which is basically reflects the overall resistance into ln of 1 by 1 minus x and the height which is required for the bed which is an important design parameter is basically UB divided by K cat into KR into ln of 1 by 1 minus x. So, let us summarize what we have learnt in this lecture. So, what we have seen is we have actually designed a fluidized bed reactor. We started by looking at various parameters estimating the various parameters which is required to find to design a fluidized bed reactor. For example, what is the how to estimate the velocity of the racing bubble, how to estimate what is the fraction of the bed that is actually occupied by the bubbles etc. And then we found out what is the rate law that corresponds to the catalytic reaction that is happening in the particles which may be present in the bubble or cloud or the emulsion phase in any of these 3 phases. And then we looked at the mole balance for the species in each of these phases which incorporated the transport of species from the bubble phase to the cloud phase and cloud phase to the emulsion. And using this mole balance, we actually assume that it is a first order reaction and found out what are the important design parameters such as the height of the fluidized bed and weight of the catalyst which is required for a given conversion to be achieved using a fluidized bed reactor. Thank you.


So Barry Weiss, like all conservatives, is currently trying to cash in on anti-trans hate and she shared an article published on her platform, The Free Press, about a mother who claims she was bullied or felt bullied into giving her child puberty blockers in an effort to alleviate the psychological distress that they were feeling. But the mother claims in this article that the puberty blockers didn't help and actually made their child much worse psychologically speaking. Now, Barry Weiss did not write the article. This was written by Emily Yoff, but it was published on her platform and she shared it on Twitter saying, Caroline was told that a puberty blocker would relieve her child's psychological distress, but that's not what happened. Now, we're not going to dive too deep into the story here, but I did read it, and it's exactly what it sounds like. A parent claims that they felt pressured by Washington University Transgender Hospital at the St. Louis Children's Hospital to put their child on sepulon, which is a puberty blocker. Now, the mother claims that once she approved this treatment for her child with gender dysphoria, it led to a lot of issues.  So the overall takeaway after you read this article is that gender-firming care for trans youth is bad, and this is a scary phenomenon and parents who seek out gender-firming care for their children either don't really know what they're getting themselves into or they're being manipulated by politically motivated woke doctors.  This isn't a story about one child's bad experience with gender-firming care.  And we know that this is the case because the child in this story spoke out and said that this is indeed the case. The child in question is Alex, and this is their story. Quote, I have reinstalled Twitter to respond to this story and make sure my voice is fully heard. I am Casey. My real name is Alex, but my mom decided it would be best to hide it for anonymity. But this is my story, not hers. This is not the Free Press' story. About a week ago, my mom contacted Emily Yoff without my knowledge and told her what was supposed to be our story. She expressed her frustration with the transgender clinic at Washington University, many of which are false perceptions that my mom has about doctors and the clinic. I learned of this article through my mom over the phone when she asked if it was okay that the Free Press published the article. I said that I wanted to read it first. When I read the draft, I was disgusted with what the reporter and my mom had made my experience out to be. Upon interviewing Emily Yoff myself, I was told that I had no say in whether or not the article was published. I asked if my consent was required to publish the article and the reporter told me, quote, that's not how these things work. After she had edited the article and published it, I had not found this out until 20 hours later. I was extremely frustrated. The article makes it out that my mother had no say in the implant of sepulon. This is completely false. My mother claims that she was pressured into saying yes by the doctors. A big issue they point out is that the doctors quoted suicide statistics in transgender adolescents. I do not deny that these statistics were quoted, but I also maintain that the doctors didn't say that I was at substantial risk of this. The article mentions that my grades dropped from A's and B's to D's and F's in a semester. This is a completely exaggerated statement. My grades were on a steady decline since 2020 due to unrelated mental health concerns. Speaking of mental health, the article claims that my mental health issues can be attributed to the sepulon implants. However, my personal experience shows that this is not the case. Since COVID-19, my mental health has been declining and it was already an issue. I was in counseling with the Washington University Transgender Care Center in which I was treated amazingly by my counselor. She was a friend to me and offered a great amount of support. This was taken away when my mom revoked consent for the sepulon. After she revoked consent, my father and I, along with the university, attempted to set up a meeting with my mom. She did not attend this meeting, claiming that she was not contacted. Later, she admitted that she was. So in other words, the mom, who was already seemingly reluctant to approve of gender affirming care in the first place, but the child, the father, and the clinic recommended it, tried to blame puberty blockers for her child's mental health decline and tried to stop the treatment, even though the child wanted it and it was recommended by the other parent and the doctors. And the mom actually responded to this thread, which was not a good idea because immediately she contradicted herself, saying, my child was in the middle of a mental health crisis and they chose to drop the counseling but keep the implant. Medical negligence. Now, the problem with this statement here is that in the article, she is the one who stopped the counseling. She was quoted saying, I also do not want Casey to receive any more counseling at the transgender center. He's not transgender. He's a 15-year-old child. The only further treatment I authorized as joint legal guardian is the removal of the puberty blocker and the subsequent aftercare. Please call me with any questions. So she's the one who stopped the counseling, not the clinic. And you can see a total change in her demeanor here. No longer is she this mom who's a little bit reluctant about gender affirming care but trying to do what's best for her child. In that quote right there, she's outright denying that her child is trans and purposefully misgendering her child who goes by they she pronouns. So this seems like a classic case of a hateful parent who refuses to accept their LGBT child. And furthermore, she explained why she didn't attend the meeting referenced in Alex's thread. Actually, babe, she writes patronizingly, they gave me two days notice and sent an email confirmation that only found last week. They were supposed to call me on speaker and never did. Also, I was not going to that meeting without an attorney. Let's get it all out there. So she's really showing her true colors here. And it's worth pointing out a couple of interactions that she had on Twitter that gives us a little bit more context that I think is really lacking in the article, obviously.  But she responded saying, this is actually my story about how I was treated as a parent at this center. Alex has a story too, but this article wasn't it. Don't confuse the two. And one more interaction that she had on Twitter where it's clear that her brain succumbed to right wing propaganda on this issue. So someone told her that she seems like an awful human being and an even worse mother, which I agree with. But she responded to that saying, only time will tell, I guess. Awful because I don't want my child experimented on. Okay then, I'll wear that label. Yeah, so that kind of tells you everything you need to know about her. Rather than trying to educate herself and understand her child's concerns, she seemingly got radicalized by anti-trans propaganda, blamed all of her child's problems on the doctors and gender-affirming care, and then tried to make an example out of her own kid for propaganda purposes. I mean, I guess as she put it, only time will tell if she's an awful parent. But unfortunately for her, it's already pretty obvious that she is indeed an awful parent and a pretty shady person. She's showing her true colors online and she responds to people. But I can blame her, but I also have to blame the opportunists in this story too, like Barry Weiss, who is choosing to keep the article up while knowing that it is a misrepresentation of the actual story. And I also have to blame the author, Emily Yoff, who hasn't responded to Alex's claims yet, and that's probably because she knew exactly that she was only telling one side of the story, because that was the goal. Her ultimate goal was not objective journalism. It was to fuel right-wing hysteria over gender-affirming care. She knew what she was doing, and we know that this was her goal because she retweeted a bunch of shocked reactions to her story. For example, this person shared it saying, Read this, my God! Another person said, Emily Yoff with a blockbuster on gender-affirming child abusers. So she got the exact response that she wanted. And there's more responses that she retweeted, but what I found really despicable and just sad overall is that Alex was sharing their Twitter thread to each of these retweets in a desperate attempt to get their story out and not allow their treatment to be used for anti-trans propaganda purposes. I mean, a 16-year-old child shouldn't be forced to correct the record when there are journalists who should be responsible enough to either delete the article or at a minimum include an update with Alex's side of the story now that they spoke up. But Weiss and Yoff aren't doing this. And it's because, again, objective journalism isn't the goal here. Anti-trans hysteria is the goal, and they got exactly what they wanted. So this is one of the grossest examples of unethical journalism that I've seen. And really, it's not surprising considering that the Free Press has also promoted the witch trials of JK Rowling in an effort to, I guess, sanitize the Harry Potter author's transphobia.  We can disagree on the facts and the substance, and we'll debate that. But when you publish blatant propaganda under the pretense of journalism in order to dupe unsuspecting people into believing this nonsense, that is where we just get into territory that I think is so evil. This is medically necessary life-saving care, and you're trying to pretend as if it's going to make children worse, not better. And that is just despicable. I would say that Emily Yoff and Barry Wife should be ashamed of themselves, but unfortunately, these immoral bigots lack the capacity for shame. And as a result, a 16-year-old trans teenager is forced to clean up the mess that they made. It's truly despicable, but totally predictable for the modern fascistic bigoted right.


Hi my name is Katie Purfit. Have you ever been to the Museum of History across the river from Parliament Hill? I've been going there every summer since I was a little kid. I remember learning about the Arctic for the first time there, being awe of the beautiful totem poles in the First People's Hall and each time leaving with a deeper appreciation for the planet we live on. Little did I know that Big Oil had plans to use the museum to provide cover to some of the world's most destructive companies. Today, I work with an organization called 350.org. We work around the world to build a people-powered movement, standing up to the people most responsible for the climate crisis, Big Oil. Massive oil companies like Shell, Exxon and TransCanada are wrecking our water, land and climate. To get away with it, they pay lobby groups big bucks to sell their dirty works to politicians and the public. The biggest oil lobby in Canada is called the Canadian Association of Petroleum Producers, or CAP. CAP worked closely with Stephen Harper to dismantle environmental protections for Canada's rivers, lakes, coastlines, parks, endangered and protected species and protections for our climate. Even today, CAP meets regularly with government to push tar sands expansion. They're even lobbying to make it so that a federal carbon tax would give money back to Big Oil. The same people that the tax is supposed to stop from polluting. Here in Canada, standing up to Big Oil means standing up to CAP, and that's where the Museum of History comes in. CAP sponsors a number of exhibits in the museum, including a three-story exhibit celebrating Canada's 150th anniversary. In exchange, they receive brand promotion in the museum and exclusive access to events with our political leaders. Not only that, CAP has a history of meddling with museum content. CAP might just be Canada's most dangerous lobbyist, with anti-climate action and anti-environmental protection agenda that ignores indigenous rights. They threatened the very landscapes and cultures I first learned about and fell in love with at the Museum of History.  If one of the most iconic museums in the country was to cut ties with Big Oil, it would send a powerful message to people and decision-makers across the country that the age of Big Oil lying to public for their own gain is over. That's why I am speaking up and calling on the Museum of History to cut its ties with CAP. Will you speak up with me? Sign the petition today and ask your family and friends to sign on too. CAP has already secured its place on the wrong side of history. If thousands of us, all across Canada, speak up together, we can make sure that the Museum of History stands on the right side.


Hi everyone, Joe for jasmizcasebreaks.com coming at you with 2021 tri-star best of all time, boat, multi-sport break, random hit number two. So there's only four items in this big case right here. We're gonna open up, there's Ruben. We're gonna open up the case, Ruben. We're gonna, I'm gonna show, I'm just gonna randomly pull all the hits. All right, there's PJ. I'm sure Nancy's listening as well. Thanks to these three for getting in on the action. So I'm gonna pull out the hits, just kind of randomly, and then type in the hits, randomize your names, randomize the hits, and see what you end up with. Good luck, this is a fun breaker. So, I know it's gonna be kind of hard to see, but the sticker on here, it's box 65 out of 80. You can see on the top camera right there. Very limited release, they only made 80 cases of this. Nothing inside that packaging. First thing I see is a boxing glove. This is gonna be pretty easy. Who am I? Part of the International Boxing Hall of Fame on June 12th, 2011, so almost that anniversary. The undisputed heavyweight champion, WBCWBA, an IBF heavyweight champion, youngest heavyweight champion, two-time ring magazine, Fighter of the Year, WWE Hall of Fame in 2012, and I have my pro boxing record, 56, and oh, it's gonna be pretty easy. On Holyfield, not Roy Jones here, and there you go, Will, Will's got it. Yeah, it's a cell sheet hit, Mike Tyson. So there's the Everlast glove tag right here, retail tag, and there's Mike Tyson's autograph. That's pretty nice. There's a tri-star sticker right there. We actually saw Mike Tyson at the Nationals. I think it was the Panini party, maybe. All right, so nice. Mike Tyson autographed boxing glove. Let's flip back here, we can type these in as we go. It's a nice boxing glove, too. Our next thing I see is a jersey. Ooh, we got some pinstripes on here. Who do we have? Looks like Cubs pinstripes, looks blue. Looks like a nice Mitchell and Ness jersey as well. Let's get the little, Mike, our tri-star gives you little game show cards. All right. I was a one-time, I'm a retired baseball player. I'm a one-time NL MVP and 10-time All-Star, sporting news player of the year, nine-time NL gold-glover, seven-time silver slugger, three-time league leader in runs scored, a 1990 home run leader, and held the career home run record for second baseman at the time of my retirement. That should give it away. Hall of Fame in 2005, no, not Kyle Schorber. Cubs wish Kyle Schorber turned out to be this guy. Nope, not the hawk, Andre Dawson. Not Mark Grace. Yes, PJ's got it, Rhino, Ryan Sandberg. Nice, so, ooh, this is nice. Look at all the, there's Sandberg's autograph.  Ooh, that's a sick Cubs patch right on the shoulder and right on the front too. You got the Mitchell and Ness tags right here on the bottom. You even got a little 87 Ryan Sandberg patch down here.  The big Cubs logo is pretty awesome. I do like these Mitchell and Ness jerseys. That's a $300 jersey right there too. So three for the jersey, plus the autograph. All right, autographed M&N, Mitchell and Ness authentic jersey. All right, here's another jersey. That number might give it away. I don't wanna reveal it too early. All right, who am I? Three-time Pro Bowler, four-time Super Bowl champion, two-time Super Bowl MVP, 1978, AP NFL MVP, 1970s all decade team and played college football. There you go, Mike Bobby. Yep, the original TB12, Terry Bradshaw. This looks like a custom jersey. I wanna leave this folded in here. I don't wanna unnecessarily, yeah, there's no retail tags on this. This is a custom jersey, but still pretty cool. There's the Bradshaw, nice big bold autograph right here, Terry, I like that. Right across the one, big bold auto. Nice, and the TriStar authentication card and sticker is all on the bottom. You know your baller when you have your own authentication sticker as well. All right, and the fourth and final hit and then we'll do the randomizing. Anything else in there? This should be good. It's a special redemption card. That means it's too big to put into the box. It could be a basketball, it could be a baseball bat, a massive framed poster, who knows? All right, who am I? Hall of Famer, a rookie, it's a baseball bat, by the way. Hall of Famer, 1991 NL rookie of the year, 1994 NL MVP, 1994 Gold Glover, four-time All-Star, three-time Silver Slugger, my number retired by my team, and played my entire 15-year career as a first baseman for this team. Who am I? It's a Louisville Slugger game model autographed, inscribed HOF 2017, think about your 2017 Hall of Fame class. Not Ted Williams or Ozzie Smith, first baseman, not Will Clark, not Kent Herbeck, not Frank Thomas, played my entire 15-year career as a first baseman for the Astros, not David Ortiz, not Maddingling. I ended up my career with 2,314 hits, 449 home runs, 297 batting average, there you go. Hollywood PJ, Will Rex, the Astros gave it away. It is Jeff Bagwell, nice bat. So they should be able to redeem that pretty quickly. Pretty great player, Jeff Bagwell, let's flip back here. That's a redemption right there. All right, good luck to these three right here. Let's roll it, let's randomize it. Six and a one, lucky seven times for both lists. One, two, three, four, five, six, and a one, seven and final time, after seven we got PJ, Nancy Rubin PJ, six and a one, seven times for the hits. Good luck, one, two, three, four, five, six, and seventh and final time. After seven, we got Jeff down to Ryan. All right, congrats everybody, some nice hits here PJ with the Jeff Bagwell autograph bat redemption. Nancy, you got the Mike Tyson autograph boxing glove, silver ink on that nice boxing glove, Rubin with the Terry Bradshaw autograph jersey and PJ with the Ryan Sandberg autograph, Mitchell and Ness jersey right here. So there is the bat, that's pretty cool. There's the, I'll show you the hits again. There's the Terry Bradshaw, really bold autograph there, nice Terry. Here's the Ryan Sandberg, got all sorts of inscriptions on here to great authentic jersey. It's pretty sweet and nice iron Mike boxing glove autograph. That looks really sharp. There you have it folks, another great break in the books, that's all the tri-star boat that we had but maybe we'll try to get some more and next time you see it, get in on the action. Jaspeyscasebrakes.com, I'm Joe, I'll see you next time for the next break, bye bye.


Hello Hello Writers, I'm Christine Kiefer, author of fantasy fiction and creative writing resources and you are listening to the well-sturried podcast where I share insights, encouragement and actionable advice designed to help you craft sensational novels and build your best writing life, always in 30 minutes or less so you can get back to writing of course. Ready for the show? Let's get talking. Hello Writers and welcome or welcome back to the well-sturried podcast. I'm your host, Christine Kiefer and today is Monday, November 16th, 2020. Today's episode is titled How to Write with Focus and Efficiency. If you'd like to read along as you listen in, head on over to well-sturried.com slash efficiency. Now let's dive in. Wish you could crank out your stories more quickly? You aren't alone. Run a quick Google search for how to write faster and you'll find hundreds of blog posts detailing writing productivity hacks ranging from disabling your internet connection to dictating your first draft, practicing your typing speed and writing while groggy to smother your inner critic. These tips may prove helpful for some or even many writers but the hack-centered conversation around writing productivity often fails to account for the full complexity of this topic and in doing so fosters an unhealthy approach to getting words on the page more quickly. The simple fact of the matter is that more isn't always better. There's nothing wrong with seeking to improve your efficiency as a writer but storytelling is not a mechanical act. Any number of factors can impact how much creative work you are able to complete in any given period, the emotional intensity of your latest scene, the level of skill you've developed, the amount of energy you're able to commit to your work. Quantity can easily belie both quality and progress yet high work counts are often lauded as a sign of writing success. Don't wonder so many writers struggle to maintain faith in their skills and stories. Let's talk about a healthier approach to increasing productivity. Earlier this week I watched a YouTube video from Joey Schweitzer of Better Ideas called Why You're Tired All the Time. In the video, Joey explains how many people seek magic bullet solutions to their low energy levels, such as going on a gluten-free diet or taking pills for iron deficiency. These solutions may work well for those with genuine medical needs, but for most, the answer to their lack of energy is much simpler. Eat right, exercise, get a good night's sleep. A failure to address foundational needs is where many writers go wrong when chasing increased productivity. A quick fix solution such as completing writing sprints may work well for some, but achieving true creative focus and efficiency often requires a more foundational approach. By my account, seven key aspects feed into writer's ability to get good words on the page, so let's take a look at each of these items together. First up, time. You can't increase your productivity without first making time to write, but not all writing sessions are created equal. Where one writer excels with short daily sprints, another needs larger blocks of time to find their creative flow. Where one can hammer out hundreds of words before dawn, another finds inspiration in the bright embrace of midday. Figure out what works best for you and strive to create that time whenever possible. Two, energy. The amount of mental and emotional energy you bring to your manuscript can radically impact both the quality and quantity of the work you produce. Honor this energy accordingly. If you only have enough gas in the tank for 10 minutes, then give that 10 minutes you're all. Try researching or brainstorming when you can't seem to write, or consider taking a break to refill your creative well. A mindful writing practice is a sustainable writing practice, and as we'll discuss in a moment, sustainability is key to ongoing efficiency in your writing life. Three, clarity. Writing is more than putting words on the page. It's more than even polishing those words to high shine. Writing is thinking, researching, developing, and brainstorming, and it's in these aspects of writing that we find the clarity we need to produce our best work. So before putting pen to paper, consider what you're going to write. You don't have to know exactly what's going to happen, but get clear about what your characters want and why they want it. Give yourself a compass for the journey ahead, and you'll direct yourself towards progress and momentum. Up next, enthusiasm. There is incredible power in passion. When you're excited for the work you're going to complete, or perhaps more accurately for the results of the work you're going to complete, you naturally write with greater focus and efficiency. Each time you sit down to write, consider why you're excited to complete the work to come. Will your characters finally confess their love in today's scene? Or will their argument lend lots of juicy tension to your story?  Or are you simply excited to fix that passage that's been bugging you for weeks? If your search for enthusiasm comes up empty, consider why that might be. Is the scene at hand not working? Do you not know enough about the story you're trying to tell? Or do you simply need to take a break to refill your creative well? Writing is difficult work. Despite the passion we hold for our stories, many writers struggle to simply sit down and write thanks to resistance, that strange internal force that pressures us to do anything but put pen to paper. Learning to write despite the call of resistance is a skill we all must cultivate if we're to finish our stories. I like to call this skill grit, the determination to push through internal difficulty to achieve a goal worth fighting for. Developing grit requires passion and motivation, but more than anything, it requires the willingness to look within, to interrogate and resolve the limiting beliefs that hinder us from completing our best work. Number six, consistency. Momentum is the key to sustained efficiency in our creative work. The more consistently you write, the easier it will be to overcome resistance, maintain clarity and develop the confidence you need to keep moving forward. Finally, seven, strategy. Cultivating each of the aforementioned elements can help you repeatedly log into your work's fantastic and fulfilling writing sessions. But to truly make the most of each moment you write, developing a strategic approach to the craft is key. This strategic approach is otherwise known as your personal writing process. The tools and techniques that best enable you to bring your stories to life. Discovering your writing process can take time. Tips and techniques may seem an obvious fit for your natural tendencies, but you'll likely need to trial other options to determine whether they're right for you. It's at this point that many writing productivity hacks come into play. Dictating your first draft, completing writing sprints and other common techniques may help or hinder your writing process. There's only one way to find out. Not sure which techniques to try? Consider reading through my articles or checking out the podcast episodes on pre-writing, drafting and editing to gain a better understanding of common approaches to the craft. Then test the techniques that appeal to you and see what sticks. The more you explore, the quicker you'll discover your personal writing process. As you cultivate these foundational keys to writing efficiency, you might just find that what you're actually developing is a creative practice. To hone your ability to write with focus and efficiency is, after all, to deepen your commitment to the craft. To become the writer you want to be. As you develop your practice, bear in mind that efficiency isn't always pretty. There will be many days when the result of your best efforts isn't much to write home about, and that's okay. More than okay. Because efficiency doesn't demand a staggering outcome. It simply asks that you produce your best work with the limited resources available to you. Time, energy, clarity, enthusiasm, grit, consistency, and strategy. Rarely will each of these items align in perfect harmony. Sometimes you won't have much time or energy to write. Other days you'll struggle with tough story issues or seemingly insurmountable resistance. Your writing process will fail you and your enthusiasm will flag. On those days, lofty word counts may fly out the window, but your writing efficiency need not. As bestselling author V.E. Schwab often says, show up, put in the work, let go of the outcome. Rinse and repeat, and you'll soon finish that story that's been idling at your fingertips. Thank you for listening to today's episode of The Podcast Writer. I hope you found it helpful to your writing journey. If so, make sure to subscribe to the podcast so you never miss a new episode, and to give the podcast a quick rating or review. Doing so goes a long way toward helping the podcast reach new writers and lets me know that you're enjoying what I'm creating. You can also give me a shout out directly on Instagram at christen underscore keeper. For additional guidance as you work to craft sensational novels and build your best writing life, be sure to head on over to www.well-storied.com where I share blog posts, workbooks, e-courses, and other helpful resources for writers. Again, that's w-e-l-l-s-t-o-r-i-e-d.com. Thank you again for tuning into today's episode, my friend. Until next time, happy writing!


Hey, we're Prima Queen and this is our song Dylan for Black Star Sessions live from Austin, Texas.


here to talk about is to what extent does, is the town of Rochester wanting to take possession of the Dan Lyme daycare building, which, whether that is sold or kept for town purposes is another decision. But the, my feeling is, I hope to start into that, that it would be hula. So here comes Tom. I'll just preamble a little bit more then. I got almost to the point here and then I took that. Sorry about that. What's that white stuff? It was snowing in my house, man. My car says it's 37 degrees. It should not be happening at all. Oh, you want to come? No, I don't need to come. Shall we come? No, we can't. We can't. But it's snowing. You like writing? I know. I got to come. I would call. Okay. This is going to be a pretty nice change. I heard that. But I just wanted to double check on one of her editing buildings. It's really interesting. We can be addressed in here. Okay. We're going to leave this there. Thank you. That's not where I'm going to go. We still have stuff. I want to go. So we opened the meeting and I was introduced to the fact that we're talking about the extent that it was Julie Warnsch and the posted and the website. Can I mention this? Well, Mason has a question. Excuse me. I'm going to counteract you. Matt's Valley Market took down there. I saw that. I have called down. They have not responded. But I'm going to continue posting things there until they tell me I can't. So otherwise, I have to come up with another place. I'm not sure the market's going to qualify the hardware. It needs to be a place where people go regularly. So I need to post. I spoke to one of the cashier today because I was concerned about the community board as well. Yeah. They said that the owner or the regional manager from Rutland came around to all the stores and made them take down community boards. Yes, they did because they were community. But she said to call the Rutland office and express your... I did not call that. I'm going to do that myself tomorrow. Yeah. One of the cashiers told me the same thing. And so did Dick and Larry. They said it was too messy and they didn't like it. It didn't look good. Well, they didn't like the fact that people put out tires for sale. Or here's my services. I do the carpentry. What else is a community board for? Don't get me going. Not now. Okay. Thank you. Mason, you had a question? Well, kind of. Doug failed this. So Monday was the meeting, the 26th. And the 27th of the morning, everybody kind of went into action to make this meeting happen. And from that evening meeting, I was under the impression that our official news outlet would do something on it. And there was absolutely nothing. You're talking about? The Herald. This meeting. This meeting. I knew nothing about that meeting. I understand.  And I guess that didn't happen. But Dune was going to call the Herald on the morning to make sure that everybody was... Well, all I'm trying to say is there is a transparency issue that many voters in this town, even though there's a sign at the store, they have no idea that this is happening. I'm hoping in the future that there's more ways of communicating to all the voters because in the room right now, there's more school board members than public with the select board. So I'm feeling like a lot of people don't know about this. I just want to leave that alone. Okay? Luckily, we'll be on more media so people can still find out what happened that they cared to. And I will explain that since we've gone past deadline for this week's Herald, this will be in next week's paper. Nancy? Except I just asked Mason why the Orca Media recording of last Thursday's school board meeting was not posted on Orca Media yet. Yep. So he's got to find out. All right. So this was a warned special selection to address the topic of the schools, the town's interest in the Dan Lyne daycare building. And I was just about to say, and if we made a new appearance, that I'd start with my opinion is that it behooves the town to take the building and the town can then decide to sell it. I think that there is a big enough of an imbalance between what Rochester is bringing to the union versus Stockbridge in terms of real estate that's my point. Now I understand you have, and with your donated realtor hat, you've found someone who's interested in the property and this would not preclude that from happening, but I think the question is whether it's bought from the school or the town, which in a way they're the same, but legally it would be a different thing. So what do you guys think about that? I've been to a lot of the school board meetings throughout the last year, year and a half, whatever, how long it's been, it's been forever. But I do remember when the merger was drafted and discussed and pulled together that one of the points that Stockbridge made quite clear was that they did not want to carry the Dan Lyne building and that if it were to be sold, proceeds from that could go to paying down the debt that they will be assuming on July 1st and since Stockbridge doesn't seem to have as much debt as Rochester does on their school buildings, it seemed fair that we were keeping the high school building in the equation, the elementary school in the equation and sacrificing the Dan Lyne in order to make the merger go through. So I think that for the people that were at those meetings and the people that voted for the merger, that was made quite clear. It may not be specific in the actual merger language, but that was definitely the tone of Stockbridge agreeing to merge with Rochester. I could speak on that, that in the actual merger document it does state that the Rochester school board will seek to sell Dan Lyne daycare prior to the July 1 merger. It does not state though how those funds, where those proceeds would go. I know it was indeed discussed, but in the document it does say that the board will seek to sell the daycare. I think Stockbridge is more interested in getting it off the books so they don't have to maintain it. Yes. We really didn't talk about the proceeds of the sale. Harlan? Just a dog at it. I mean, why let it go? I mean, you have to try and run it as a daycare center, seeing as though that was what it was purpose for and remodeled for and brought up to date for it. But if that, if there's no way that could happen, at least the town could sell it and get something out of it. I mean, we've been dumping money into the supervisory union out of the town funds, you know, for the school thing. For a long, you know, I mean... No, I'm dead at your point. What do you think about that? Well, I mean, a daycare center is a great idea, but unfortunately you have to find somebody to actually want to control the business there. Exactly. And there's so many state statutes going through it. Like seven days or something, you know, looking for a professional daycare operator. There's something that's got the kids out there. Yeah. Yes, if we own the building as a town, we don't have to rush into selling it. We can first explore what Harlan's speaking about is as a town, we can subsidize getting an entrepreneur started. And this will help maybe sell real estate and have people move to our town if we have some good childcare facility. So before you rush into selling the property, once we acquire it, we should have some serious town discussion with the community. I agree that this community needs daycare. The school board did advertise in a number of locations, not just the Herald, but Valley News. I don't have the list of those number online places that we were looking for somebody to run the facility. We contacted Vermont First with Kids or Let's Grow Kids, Vermont Let's Grow Kids, and they thought it was wonderful, but they didn't have any more resources or anybody interested in doing a daycare in our area. Orange County was involved. Orange County's parent-child organization really took a serious look at it and just found that it wasn't going to be profitable for them. They're in their bylaws or in their policies. They have to have two people on staff at all times, and they found that they just were not going to be able to pay the two people on staff with the amount of kids that would be able to be in the daycare. I also think that the last time that it was run as a daycare, one of the reasons that it closed and helped me if I'm a little wrong was because they were no longer able to take children under the age of three because of mandates and certain stipulations, so they closed basically because they could only take three-year-olds and up, which now a three-year-old can go to pre-K. So the daycare may be something that phased out now that we've opened up pre-K and kids can go there at the age of three. It could complement because it's only a two-and-a-half-hour program at three-year-olds. It could complement that, and that was the original idea behind opening it back up, but it can't take... It wasn't able to take babies. The last time it was opened, that's why they closed. The actual discussion, you know, if it can or can't, isn't as critical at this time. The issue is the town acquiring the building. It's nice to have a background. Why don't you know we did our homework on this? Right, right. And we have the ability... But the issue is not, is the town going to open the daycare? The issue is, is would the town like to, you know, purchase that, the billing from the school board or the nominal fee of a dollar? Yeah, yeah. And one day, would they under stipulation that you guys would subdivide it? We'd subdivide it, what you mean, in terms of the separation from the school board? We can't really sell it to you until it's... Well, of course, that would be part of the deal. I think that we could, you know, between the school board and the town, I mean, we're washing each other's hands. They would have to be... They would have to be surveyed. Oh, we're good at regular fees. I have a question about the preschool playground equipment that's presently on the property. And if we could move it to a different part of the school to have the preschoolers still have their ability to have, you know, a playground. It's a piece of side building, too, that should be moved out. Yeah, okay. A sand thing, a table. There's a number of stuff. The preschool relies on, you know, that little, the little play set for the little kids, because the other one's a little too big for the smaller kids. Absolutely. Okay. So I would move that the town enter into the... Are we purchasing it from the current Rochester School Board or are we purchasing it from... Oh, stop the unified board. It's not being the unified board. And it would definitely be... I think we're here asking if there is any interest from the town, we would need to discuss it as a board to see if we have an interested party that would purchase it from the school board, and therefore we could take that money and put it back into... We could establish, you know, anything that scholarship funds or, you know, support for outdoor education or, you know, it could go back into the educating of the kids, whether or not... We just need to have that discussion, I would say. I think that would also... The discussion of what's going to happen to the school buildings is important, because, I mean, if... We could be having this conversation about one of those buildings after the unified board evaluates what they want. Another point of view you can see, you know, if we take the session of the... of the Tainterland Daycare Building and then sell that building, those funds could be used to potentially improve the due repairs on the school, which we may move other services into. So it gets kind of complicated, and I think there's a lot to think about. I don't think we want to brush it in. We need to look at it. We have a deadline to sell. I think we should retain the building first. After that, they don't own it anymore. After that, the unified school district owns it. But I think that... If the building were to be sold, could the funds from that be applied to the bond to reduce the bond expense? Do you mean right now? Yep. I would say yes, but I would need to make sure on that. The lawyer that... No, it wasn't the lawyer I was talking to. This is our financial manager I was talking to, and he stated that we could basically earmark that money. We could place a reserve on that money so that it wouldn't go into the new district. But it would never... Can you prepay bonds? I don't know. I would need to... The bond for the school... There's bonds for them, yes. Right. My understanding is those are part of what is unified. Yes, exactly. And I know that was another little thing of contention was the stock bridge is that we had debt and they don't. Right. I would say it's a big point of contention. It sounds like it's a big point. And I think we should probably try to work off, or find a way to reduce our bonds. We are walking in there with $390,000 in bonds and they have no debt. It's affecting our ability to be able to work together. I think moving forward, I think we need to figure out a way to get our debts down and our buildings under control. We have bonds, but we also have several million dollars with the assets in the buildings, too. So it's just complicated. It's very complicated. Martha... I just wanted to point out that this is not actually something to do with dandelion, but when you were saying assets, that the high school building has got things that the stock bridge doesn't have. We have a really nice auditorium that the players work hard to help repair after Irene. Yeah, there's definitely assets. The value is more than the debt. And also it sounded like you were starting to maybe make a motion or something? Well, I was going to move to have the select board express its desire to pick that building. And that still is... I don't think we can control the school board's decision or I don't know how exactly legally it's picked, but I think that you at least need to... The question for this meeting was, would the town be interested? And I would move that and say yes. I would say based on the public opinion that we do have here, I would also move yes. All in favor? All right. You still would be here. You would do the subdividing. Yes. And there's a guy that helped us do it, right there, walking in the door. I just had a quick question. So, should I say, and this won't be until next week, but should I say that you're looking into purchasing it from the current public board for a nominal fee? Is that correct? Yeah. Because... Details would be worked out. Okay. Yeah. You don't even have to... Don't put the nominal fee. Yeah. Okay. Because that's not, you know, definite, but I just wanted... Harlan and Mason. I was just wondering about the bingo property. I mean, it was talked about, but... The principles of the students, that has nothing to do with the town. Okay. So, we're going with the deed set. As it is at this point anyway. With what the deed set. I think that's another way. So, well, is the town going to, like, be a trustee for the high school student? We'll have to see that, but stay the way it is. Yeah. I mean, we need to have that discussion. Okay. I hear you. We need to have that discussion, but it's not going to be today. Not on this meeting. We'll put it on the agenda for the next meeting or something. Or, you know, this is all time related. Does that need to have a resolution by July 1st? I don't think that was even included in any of the work. It is. It is actually... It is. I have some information about it, but, again, it's... I think we need to warn it to talk about it, right? Frank Russell said that it wasn't private. Well, at the last meeting... You can tell me how much I can say about it. Right. So, that's a different topic than we're going to. But it's an important... It's going to come up, and so stay tuned. Mason, you have a question on this topic. Yeah, unfortunately, I wish Nancy was able to see that footage on Thursday, that Amy was spoke about the new merger board having a lawyer looking to probate court to secure the bingo property for the new merger situation. So, there is activity going on with the new merger board in relation to legal issues. I'd like me to speak to it. I can. I just don't want to step out of line. Please make it understandable. Okay. Good. I'm sorry. Well, through discussion with our lawyer, I found out that the Rochester School of Property is actually a trust. The principal and the high school students are acting as trustees. The school probably means the school of property. Yes, the bingo forest property. Yes, the bingo forest property that is in discussion. That the principal and the high school students are actually acting as trustees. It's a trust. Like the library. Okay. So, the purpose of the trust becomes frustrated or failing when it gets brought into the new district. So, if the new district feels that the property is of value and would like it to come into the new district because we did put it on the table and in our agreement that this was... We did offer it. We didn't realize it really was an ours to offer, but we did offer it as part of the deal. So, if the district feels that there is value to keeping at them, we would need to look into going to probate court to change the terms of the trust. Interesting. Yes. And if, you know, depending... to modify the terms of the chair of the trust, which may largely depend upon whether the town is going to oppose the petition to modify the trust and to allow the new district to hold the property for the benefit of school-age children in Rochester. Amy, another question. Wasn't that the principal and the high school students? That's correct. High school students. That's correct. Okay. So, we were actually... Tonight, we have a meeting after this. We were going to have a conference call with the lawyer to get a little more in-depth as to what it would take and if it is something that the new district is interested in going through this whole process if they find that it has that value. But we are really swamped with our budget and building usage discussion tonight that I would have put that off for another week. Why go home at all tonight? How does that work when there's no high school? Then we still have high school students. The trust becomes... Oh, right now... We still have high school students going to high school. So, the town should be a trustee for the property, for the future students, high school students of the town of Rochester. So, if you're tuition doubted. So, right now, we still have high school students.  Just the fact that they're not knowing that they didn't have the authority offered something, they never had the authority to offer it. It's got to come back off the table. I mean, my truck's in the trust. If they offered up my truck, they don't get taken. It's a mistake. People make mistakes. You got to back up and say it didn't belong there, which it doesn't. Oh, well. Correct your mistake. And the point is, does it have value to educating our kids? That's the biggest question. Does that have value in the education of our kids? Because that's what it's all about. And it's a discussion that, like I said, the new board needs to have. And it just got brought up at the last meeting. And, you know, because we do have a lot of national force around us, that's not posted that we kind of want Heisen. Do we need our own property? But on the other hand, we have this resource that maybe we could do, you know, some other activities there. When was the last time it was used? Right. And currently there's no good access to it. Most importantly, we have the intent of the person that donated it to the town. The principal and the high school kids could get it back into the town's hands. And again, I think that's a discussion for another day, but there was some concern that maybe the town would want to trade it for other property, and then it would not be. What other property? It's a property around subject, something from the national forest. Somebody had mentioned about that the town might be interested in trading that property with the national forest because of some national forest property that's in town near our septic. Oh, yeah. You're the Wells. You're the Wells. You're talking about the Wells. You're talking about the Wells. Yeah, right. So, I think that what needs to be done is to legally explore what the intent of the trust was and what the parameters in which that can be modified into the best purpose. We have to keep this pretty short because the next meeting starts in a minute. Quickly. So, how does that work with a new merger board lawyer where is our town lawyer in that process? Just, you know, in the whole process. School schools. It's us losing our independence to have town governance. This is not happening next week. This is we have a little bit of time, a few months to deal with it. And that's why these guys are headed to another meeting to deal with that. And is someone going to stay here to talk with the planning board about what we take for a subdivision process? Yeah. 630 or are we doing the walk around first? I'm not sure. Exactly the walk around plan. It's 630. Yes. I'll stay until 650. So, I think we've covered the topic of this special meeting now. The planning board convenes here now in 30 seconds. And while they're getting set up, I'd like to request a small executive session with the select board to do it with a separate legal matter. Yeah. Okay. So, when we can go in, we can go in the other one. Just get a quick session. Yeah. All right.


Abstract liquid foams undergo a transition from a dry state to a wet state when they are exposed to moisture. This transition is characterized by a dramatic increase in the number of collective rearrangement events, which can be observed through the simultaneous occurrence of multiple T1 events. The probability of these events occurring follows a Poisson distribution, indicating that there is no correlation between them. These findings provide insight into the dynamic behavior of soft jam systems, which have applications in biology, materials science, and food science. This article was authored by Naya Inabisawa and Ray Curita.


Sean, do you have any thoughts on that game? Well, firstly, I think you can't guarantee it, but I think it's befitting to win after the week we've had and the sad loss of the chairman. So that one certainly goes out to him and his family. Behind that, I think very pleasing, very tough place to come. They've proved that over the last couple of seasons and certainly over the last calendar year. And I think it was a very good performance for lots of reasons. I think we're trying to work in different ways with the team when you're with the ball, but also when you're without the ball. Can you defend? Can you see a game through? And I thought we did that very well today. And then two people were going to talk about the regular movements. What is so much quality out there, Tim? I think a lot of that will show you the goal. Yeah, I mean, look, Don's a very good player. He's had a really tough couple of years. I think, collectively, we found a way of managing that sort of come back to true fitness. He's very close now. You can tell it in the way he's performing, his body language, his desire to do what he does. And I think it's a fine finish. I think he is the bar as well. The Q of a makes a great save and do because, well, you know, there's some big moments that didn't quite go for us, but we saw it through. And I think it would be remiss of me to not mention Jordan, who played very well second half. I thought first half we kept him very well protected. And the two centre offs, I think were immense. I think they have been all season. I think they're very good. Jared continues to learn. He continues to find that Premier League sort of way. We're not overcoaching him. We're letting him go a little bit, but he's done a very good job. The team in front of that, you know, the belief in what we're trying to achieve, the belief in change, as I've said endlessly, you know, I have about we've got to change the story, don't wait for everyone else to change it. We've got to, there's signs that we're beginning to try and do that, I think. And it's, I think we're improving from last season. That was my first marker when I asked about it. I said, what do you expect from us? We want to improve. We want to be better than we were last season. I think there's clear signs of that. Yeah, absolutely. And he's looked like, say, since he's come back to fitness, he looks stronger, he looks sharper. We hope he continues to pay him back. But no, a real good marker for him, you know, to get to that number is very pleasing for him, man, for us. Good job, thank you for the question. I was playing in the second part. But it's a really safe to make until the 90th minute. And that kind of shows incredible concentration. Yeah, well, I thought the defensive side of the game was really intact against Liverpool last week. You know, we did very well with that. And I think, you know, the thing that I've been trying to impress upon the players is how important that is. Because I believe we've got quality here. And I think we've shown that, I mean, you know, I find it a little frustrating this season when I've got more points on the table due to our performances, particularly at home in the first three home games. But the resoluteness of the mentality to keep going, keep playing well, keep finding the ways. And I think I've been pleased with that. I think we're changing it. I think we're beginning to change the group. I think there's a firmer edge to us when the game's not as perfect as we'd like it to be. And I think that's important over a Premier League season. I've been in it a long time. And I know that these tight games coming out on top of them, you know, the ones when you're not playing as well, how can you find a way to get points to win games? Because the ones when you play well, they usually look after themselves. And I think that underbelly of the mentality of a team is very important. I think it was there today. Well, I mean, that's our frequent club. What takes you a bit to start with? Yeah, not really over, I've spoke about it because we had plenty of time here, you know, even though as sad as it is, we spent a bit of time with the players earlier in the week. I cancelled training. And then when we regrouped, we just had a little moment for ourselves, you know. So I didn't want to make it too emotional for the players, but they know, you know, they know. A lot of them had deeper relationships with the chairman because obviously they'd had longer, many, sorry, more years at the club. So we've only just joined.  They know what, you know, the depth of the chairman's love for the club was. So they're well aware of that. Well, you don't want to be too greedy, but I think a couple of moments, getting key moments first half there, Keven makes a fantastic save, second half from Duke. We hit the bar, but like I say, I'm not going to, I certainly don't think we made as many as early season. I mean, our three first home games of the season, it's unfathomable how we didn't at least draw them games if not win. Today's a different kind of performance, you know, finding key moments and defending very well and playing a mixed way of playing, which I really like. I want us to mix up, and I talked to them endlessly about it. You know, there's different ways of winning games. So I said, can we work on finding different ways of winning games? And we've done that today. Any further questions? Thanks, everyone.