What's going on everybody got Kyle here relating sports cars have been 22 23 contenders optic basketball 10 box case 28 Thank You Joel Joel am taking the Falcons and flawless down to two to go guys Down to two to go Alrighty guys this one was number 28 again. Sorry Bradley G with the Nets got Brett P with the Kings Chong T has the Pacers Chris B is gonna have the Pistons Chun Wei has the Grizzlies Got Eric S with the Mabs and the Nuggets and the Bucks Gregory M has the magic spurs wizards pelicans and jazz I'm a D has the Lakers and T Wolves John H has the bulls we got Keith B with the Blazers Ken W has the Rockets Nate S with the Cavs Nicholas O with the Thunder Orioles C has Hawks Hornets Knicks Sorry to Hawks and Hornets Paul B has the Knicks Sun's Raptors Reese a with the Clippers got Rory C with the Celtics Thomas C with the Heat Sixers and Warriors Alrighty guys, let's do it. Good luck here case number 28 What planet are you from? Might need a couple waters mixed in here Alrighty guys appreciate y'all two more spots on the night just these Just the Steelers and the Niners and flawless Steelers and Niners and flawless Got a first-class ticket of Chet. Nice one there on the hollow playing the numbers game is deer and Fox Julius Randall got a hollow Cam Johnson and bluest Miles Turner number do 99 Pacers the blue and Redemption it is Christian Brown rookie variation season ticket that want to go to the Nuggets Nuggets on the Christian Brown Variation season ticket nice one there The he's the one who won a high school championship college championship and NBA championship back to back to back. Really? Yep He is undefeated right now in championships High school college and then NBA that's crazy man. All I do is win Exactly Uniformity is Zach Levine for the Bulls and red ice optic illusions is Paolo It's when they're magic on the pow-lo. It's a Anthony Davis Got red of Deandre eight and a hollow FVV and Jeremy so haunt and 99 nice one there again for Greg on the red rookie ticket variation auto Quite a day we do goober cannot complain man. It is a good time Cannot complain box number three. Let's go Titans Let's go Titans Who's a playing the numbers game ad and red ice is gonna be Paul George sweet shots Nothing will land me on that list. I Don't know Greg. I don't know Desmond Bain got a pink nice one there is Keegan Murray on the rookie to 75 It's on their kings nice Keegan and a red season ticket LeBron Carlos boozer is the 75 all-time contenders blue for the jazz Yeah, it's not good Box for that ain't bad John that works We'll pull bartender ain't a bad one a red ice lottery ticket for OSHA a bodgy jazz and Blue ice is LeBron to 75 nice one there on the superstar die-cut This one Lakers It's LeBronnie, buddy Healds There's a hollow Rudy go bear and rookie ticket is Andrew Nimhar on the black pulsar or Pandora One of my favorite parallels in general man. The black Pandora is so clean You don't use it enough man love it and On the back is pretty no contenders max struce on the heat auto to 99 Max struce now a calf box five That's fair as well John that's fair as well. Maybe not all what you want to see Sean hangs out a little extra after Zellwood around after round of Zellwood in a Mount Dora Throwing it off the collusion's work is Jdub Sweet shots is Nicola Yokech. I've lost control guys. I've lost all control go ahead every Sweet shots Nicola Yokech for the Nuggets lost all control We got a season ticket Jeremy Grant and orange is MPJ that one is to 49 MPJ for the Nuggets and a hollow miles turn And this one is OSHA a bodgy on the silver rookie ticket On card there for the jazz It's mr. Marsh to you This is crazy a Mountain Dew dispenser and a massage chair Sean's been looking at a massage chair man We got one at our house. He uh, he got a try on dude, and it's unbelievable. They are they are worth it Oh gold rush that one is Steph Curry That's got to be super short printed there nice one Warriors. I haven't even seen one of these We'll mag that on the Warriors Curry Very nice gold rush very nice nice one Warriors A blue ice sweet shot is a Julius Randall to 75 Gold coming John Moran's got a blue Christian wood That one is to 99 and nice one there. It's Shay Gilgis Alexander on the gold One of the best offensive players in the league right there six out of ten I know the ball she'll just attend and redemption It is window more junior that I'll go to the T-wolves on the rookie ticket red Timberwolves nice one there window more junior four left See wolves see wolves can a bus the delivery service in a school bus It's a red ice lottery ticket Shaden Sharp Got a sweet shots PG-13 got a Josh Hart This one is orange BAM out of bio out of bio to 49 for the heat and a Jimmy Butler old Hemi That's tonight And redemption is chat home grand rookie season ticket boom there we go thunder That'll do nice one there the thunder rookie nice chat home grid Don't work and mag that on the thunder redemption And next time Sean's in South Florida again man Oh god Superstar Steph Curry and hoop dreams is shade on shark Season ticket is jaw Redknot number Dearon Fox and a hollow garland And this one is Bruce Brown out of 99 for a no contenders for the nuggets Bruce Brown a pacer now It's brown two lefts. It's a moment you go next A play in the numbers game Jaylin Williams lottery ticket Steph Curry There's blue Ben Matherin nice one there rookie to 99 and refractor or hollow of Devante Graham. I Don't do it. Do you not flag what? That was the latest flag I've ever seen come on Come on latest flag I've ever seen There is 299 gonna be a red rookie ticket of tarry eason for the Rockets. Oh Another shot another shot Last one here guys 10 box 28 Show us a Luca. I'm down. Had a dirk in the last one. That was nice I'm definitely down for Luca a legendary tandem's Janus and drew holiday Get a blue ice jade and hearty rookie for the Mavs the 75 Wow Wow Say Julius Randall base orange is gonna be rookie O'Shea Bajie to 49 and red is Steph On the back. We have a George McGinnis auto to 125 that'll be a all-time contenders for the Pacers Pacers on the all-time contenders All right, you guys do a quick hit recap and then we'll get moving on to Bowman you now Bowman you Just to to go on breaks tonight guys got these Steelers and the Niners in flawless to to go all nights All-time contenders 125 McGinnis had Bruce Brown It's a 99 O'Shea Bajie Max Strauss had season ticket so Han nice one there to 99 Carlos Boozer had Christian Brown this season ticket as well as Wendell Moore Had sorry eason rookie ticket red Red 299 had two redemptions one was a rookie season ticket chat home good for the Thunder and Case hit gold rush is Steph Curry Steph Curry for the Warriors. You already there guys. I'll do it for contenders optic case number 28 Get some contender or some Bowman you go next


Welcome you to the second lecture of multiphase flows okay and what we are going to do today is basically look at a very specific problem in microfluidics and that is the problem of stratified flow in microfluidics. So like I had mentioned we will have one consider a system which is has a t shape okay and we have 2 inlets through these 2 limbs okay. What I want to be clear about is that the view I am drawing is the view of the channel as we see from the top. So the t junction is placed horizontally on the board on the table and we are viewing it from the top and so the 2 fluids are flowing side by side and you would have 2 different phases an aqueous phase and an organic phase which are flowing. Now the objective today is going to be only to understand the hydrodynamics okay. What we are interested in is microfluidics which means 1 of the dimensions is less than 1 millimeter. So one of the characteristic features of any flow in a microfluidic channel is that the Reynolds number is very low because the Reynolds number as you know is going to be defined as the density multiplied by the velocity average velocity multiplied by the characteristic dimension divided by the viscosity okay. So now we are looking at channels which have a very low diameter so we are talking about very low Reynolds number flows. So what does this mean? This means the inertial forces are negligible and viscous forces are dominant okay. So we are looking at dominant viscous forces and very low inertial forces. So more specifically since we are looking at lower Reynolds numbers we are looking at the laminar regime okay and so when you talk about laminar regime flows are very well defined and so that helps us go towards getting an analytical solution. So whereas if you had a large Reynolds number you would possibly go towards the turbulent regime and then you would possibly have to go to a numerical solution. So our objective in this course is to try and get understanding of flow problems transport processes analytically and so to keep things simple we are basically going to exploit the fact that the Reynolds number is low. So we exploit the low Reynolds numbers seek to obtain analytical solution. So let us come back to this figure here. What do I expect? I have 2 liquids now which are actually immiscible okay. The aqueous phase and the organic phase they do not mix with each other and let us say they are completely immiscible. So we are going to be looking at stratified flow. The aqueous phase is going to flow through this inlet channel it is going to come and flow along this main channel here the organic phase comes and turns around. So this is going to be the path of the aqueous liquid this is the path of the organic liquid. Now if your channel is sufficiently long one of the flow regimes that is possible is what we have seen is the stratified flow which means that there is a very well defined interface between the 2 liquids and that is the aqueous phase here and you have the organic phase here. So what we want to focus on is how is the flow field in this particular portion which is far away from the inlet here okay. This particular portion close to the inlet is where you have what are called entrance effects because the fluid has to actually negotiate the bend okay and so you could have some mixing you could have some lateral interchange of mass and momentum. But we are not focusing on this because in a typical situation what happens is the entrance length is just going to be a small fraction of the entire length. So whatever you are really going to be actually visualizing which you are actually going to be seeing is going to occur over this part of the channel which is going to occupy a significant portion of the length. So as engineers you may be interested in understanding what is happening in this region which we will call the fully developed region okay. So typically the fully developed region occupies a significant portion of the channel okay. So if you are interested in how a chemical reaction is taking place between these 2 liquids or how mass transfer is taking place between these 2 liquids it is more sensible for you to focus on the fully developed region okay because that is where the actual process is going to take place. So what we are going to do today is mainly look at the flow because the flow is going to decide what the mass transfer behavior is going to be okay. So today we will just focus on how to determine the flow behavior how to determine the velocity profile when you have 2 liquids flowing in a fully developed manner in a micro channel okay. Now since we are interested in developing analytical solutions our focus is on getting not only mathematical solutions but also getting physical insight. So we want to make sure that we simplify the problem in such a way that we retain the important physics. So we want to make simplifications which will make it mathematically easy for us to solve a problem. So the solution is going to be mathematically tractable but then we do not want to lose information about what is actually happening inside the system okay. So our objective is make simplifications so to our strategy is as follows we make simplifications such that the important physics is retained okay but we can and still we can solve the problem analytically okay and so the simplifications are mainly mathematical. So now coming back to the fully developed flow now what I am going to assume is all of you have done a course in fluid mechanics okay this is a PG level course. So we will just go with that assumption later on we will actually derive some of the fundamental equations again. So let us look at just the fully developed region now which is x let us say this is the flow direction which is the x direction and this is the y direction and have the z direction which is coming out of the board okay. Now I talked about making simplifications so one of the simplifications I am going to make now is I am going to assume that instead of having a channel which has a finite cross section which is rectangular I am going to assume that these plates are actually going to extend to infinity in the z direction okay. So what that basically tells me is that things are basically not going to be changing in the z direction okay I am also going to assume that things are going to be sufficiently long in the x direction. Remember I am going to have to keep it small and finite because I am looking at a micro channel so the simplification that we are looking at is we assume the x and z directions to go to infinity to be infinitely long okay and in the y direction the width between the plates is capital H okay. In order for me to specify the problem what I also need to know is the location of this interface. So I need to know so this gap between the 2 plates is capital H the fluid is occupying a the lower fluid is occupying h small h region of the entire space between the walls okay. So this is liquid 1 this is liquid 1 which has properties rho 1 and mu 1 this is the density of the first fluid viscosity of the first fluid this is the second liquid which has properties rho 2 and mu 2 okay. Now clearly the first fluid is occupying the first fluid occupies the distance 0 less than y less than h and the second fluid occupies h less than y less than capital H. So one of the things that we are interested in is trying to understand how the velocity is going to change inside this because the velocity profile is going to decide you know for example the time spent by the fluids inside the channel and also going to decide any other transport processes which are going to possibly occur. Now my simplifying the z direction going to infinity basically make sure that I can neglect the velocity component in the z direction and I can also neglect changes in the z direction okay. So that is basically what whereas the flow direction is also going to infinity but what I am going to do now is only focus on the fully developed profile because that is what I am interested in okay. So z direction going to infinity allows me to neglect the flow in the z direction as well as changes in the z direction because the z direction I do not have any confinement or walls. So if the walls were there then the walls would actually affect the flow in the z direction okay. Now what I want to do is go back to understanding which velocity component is going to be important okay. So what we have done is we have simplified things by just saying that the z direction things do not change. So we are going to focus only on the x and y directions now. So in order to focus on the x and y directions we are going to look at first the equation of continuity which is since we are looking at liquids we are going to say that the liquids are incompressible no changes in the density and remember I am going to write this equation of continuity for each phase. So I am going to write the equation of continuity for this liquid I am going to write the equation of continuity for this liquid okay. So I am going to just say that the equation of continuity for phase 1 the divergence of rho 1 u1 equal to 0 okay density is a constant. So I can actually take out the density and it basically boils down to divergence of u1 equal to 0 since the liquid is incompressible and this essentially means if I am going to write it in the scalar form where u, v and w are the velocity components in the x, y and z directions okay, u, v, w are the velocity components in the x, y and z directions. What I want to do is I want to look at simplifying this equation okay. So the first thing we do is we observe that we have assumed things to be infinitely long in the z direction okay. So there is going to be no changes in the z direction besides the velocity is also 0 in the z direction. So I can essentially drop off this term. So this term essentially goes to 0 okay. We have also assumed that the flow is fully developed. So when I say things are fully developed what I mean is that there is no variation in the direction of the flow. The direction of the flow is x okay. So when I am saying that the flow is fully developed I basically mean du1 by dx is 0. So because of my fully developed flow assumption and that is what I am focusing on du1 by dx is 0 because it is fully developed okay. So what that leaves me with is that I have dv1 by dy is 0. So my equation of continuity for one of the liquids basically simplifying to this. I could have written the same thing for the second liquid and I would have gotten a similar expression dv2 by dy equal to 0 okay. Now from this what do I conclude? I conclude that v1 does not change with y that is what this means. Now what I have here at y equal to 0 is a solid wall okay. So the liquid cannot penetrate the solid wall. So the normal component of velocity which is the y component of velocity is going to be 0 at this wall and there is going to be 0 everywhere okay. So what we know is since at y equal to 0 we have a solid impermeable wall v1 equal to 0 okay at this boundary and we also know that v1 does not change with y. So from this I conclude that v1 is 0 everywhere inside the first fluid okay. So this implies that v1 equal to 0 everywhere inside the first fluid. I could do a similar argument for the second fluid. I would use the fact that the top wall is a flat plate impermeable the velocity here is 0. I would eventually come with dv2 by dy being 0 use the boundary condition here and come to the same conclusion that v2 is 0 everywhere inside the second fluid okay. Similarly we can conclude that v2 equal to 0 everywhere inside the second fluid. So I want to emphasize here I have not assumed that the velocity in the y direction is 0. I have only assumed that the flow is fully developed okay. I have only assumed that the flow was fully developed and that told me basically that there is no velocity in the y direction. Now the fact that there is no velocity in the y direction the velocity is 0 here of this liquid velocity is 0 here in this liquid basically tells me that the interface is going to remain flat okay. We will take a look at what the pressure is we will also find that there is no change in the pressure across this interface. So basically the interface is going to be flat. What this means is that the stratified flow is a possible solution that is we are being internally consistent. We assume that a stratified flow can possibly exist. What I am showing here is a stratified flow can exist okay under fully developed conditions. So basically what this means is we can have a stratified flow okay. Sometime later on we will show you some videos wherein we have examples of stratified flow being seen. So experimentally you can see this but that is also consistent with the mathematical theory. So in particular what I am saying is you can have fully developed stratified flow where the interface remains flat interface does not get deformed okay. So everything is coupled fully developed implies interface remains flat. Interface flat in turn implies there is no vertical component of velocity because if the interface had deflected that means there was a vertical component of velocity which actually caused the deflection okay. The fact that V1 is 0 follows from fully developed follows from the fact that the interface is flat okay. And you know I am doing this in rectangular Cartesian coordinates because that is really simple and easy for you to possibly visualize. Later on we will possibly look at curve coordinate systems. So having taken care of the equation of continuity and what that has told me is that the velocity component in the y direction is 0 and need to now understand our objective is what is to find the velocity profile. So the only component of velocity we need to worry about is the x component of velocity okay. So what you want to do is write down the Navier-Stokes equations in the x direction because that is what is going to decide what the x component of velocity is okay and simplify that with whatever we have already found out okay. So that is what we are going to do. So let us write out the Navier-Stokes equations and I am just doing it for one of the fluids I am not putting the subscript 1 it is the same thing for both the liquids. So basically what I have done is written down the Navier-Stokes equations or the equation of momentum this is the equation of momentum in the x direction okay. I am writing this equation here and I want to use the information that I already have to simplify this.  Remember that is what I have assumed fully developed okay. I am also assuming that the flow is at steady state. If I assume that the flow is at steady state this goes off because at steady state this goes to 0. What about this term? This term is going to drop off because we have already established that v is 0 okay everywhere inside the liquid. So this is 0 because v equals 0 everywhere inside the liquid and we have assumed things are not changing in z. We have assumed that things are not the velocity component in the z direction is 0. So this drops off. Let us come to the right hand side. What about dp by dx? The flow is going to be driven by a pressure gradient okay. So dp by dx has to exist without the only thing which is driving the flow is the pressure gradient. So that is something which I am going to be externally imposing on the system by means of a pump okay. So that is going to be there. There is something which I am controlling as an experimentalist. What about this term here? This term is going to be 0 because of fully developed flow okay and this term is 0 because things are not changing in the z direction because it is infinitely long in the z direction. This is u is infinitely long in the z direction. So things do not change in the z direction. I am having a flow only which is one dimensional. I have the u component of velocity the x component of velocity which is flowing in the x direction. So basically what this means is the equation of motion in the x direction simplifies to the following equation minus dp by dx plus mu d square u by dy square equals 0. I want you to pause for a minute and think about what I said earlier about flow being fully developed and low Reynolds numbers. Now if you remember these terms on the left basically represent inertial terms okay. This is your pressure forces. These are your viscous forces. Now low Reynolds number flows basically correspond to very low inertial terms. So basically what I have done when I am simplifying I could have done this earlier. I could have just told you look we are looking at lower Reynolds number flows. We are just going to drop off this left hand side and then we could have just retain the right hand side and done the analysis okay. That could have been one approach which you can take because these are the inertial terms which are negligible in the regime of microfluidics okay. So basically these are inertial terms so which we have neglected. The left hand side represents inertial terms okay and these negligibly small okay and this is consistent with our assumption of low Reynolds number. So I just want to tell you that what we have done now is basically neglecting inertial terms and remember I started off with low Reynolds numbers which means low inertial forces, large viscous forces they are fine. So basically the momentum equation tells me that the viscous forces are balanced by the pressure forces okay. That is basically what it is. So I need to also look at the momentum equation in the y direction okay. In the z direction I am not particularly worried about the z direction because nothing is changing in the z direction but I want to simplify the momentum equation in the y direction okay. So let us do that. So look at the momentum equation in the y direction. What do we get? I have just written the Laplacian as it is. So now I like to know because clearly there is some information which is present in the momentum equation and I like to extract that okay. So let us see what information is present here. You know that we have already established the vertical component of velocity. The v component in this y direction that is v is 0 everywhere inside the domain. So essentially what this simplifies to is that the pressure is independent of y okay. So what this basically means is that the pressure does not change in the y direction. So that is the information which you are getting from the momentum balance in the y direction okay. And so whenever you are doing a problem you need to make sure you get a result which is actually consistent. So remember okay if the pressure does not change in the y direction there is going to be no pressure discontinuity across this interface. There is no velocity component. As a result the interface does not deform because the interface can deform also from a pressure change okay. Now we will look at what the regular boundary condition is at the interface okay the normal stress boundary condition. But I just want to tell you here that the pressure is independent of y okay. And this means the pressure can only be a function of x okay. This implies that pressure can only be a function of x. And clearly that is what we expect. We expect the pressure to decrease as you go along the flow okay. So pressure will change with x. But what you have found out is that there is going to be no change in the y direction. So the pressure is uniform in the y direction. So if you had a particular pressure at the inlet if you have a particular pressure this is going to vary along x but there is going to be no variation induced in the y direction okay. So the pressure there is going to be no pressure change across the interface. So there is no velocity component across the interface there is no pressure change in the interface remains flat. So far things are consistent okay. Now what we do is we need to find out how velocity is changing in the y direction okay and that tells me mu d square u by dy square equals dp by dx. This is my differential equation which I am going to work with okay and now I am going to go back to the fact that remember what about this, what about dp by dx? It is a function of only x okay. This is a function of x. What about d square u by dy square? It is a function only of y. It does not depend on x because it is fully developed, velocity is fully developed okay. This is a function of y. So the only way a function of x can be equal to a function of y is if both of them are equal to a constant okay and so what this means is that the dp by dx that you have is actually a constant okay. So you have a constant pressure gradient okay along the flow which is driving your flow. So this implies that mu d square u by dy square equals dp by dx which is equal to a constant okay. Now what do you want to do is we want to get the velocity profile. Now I am going to go back and put my subscripts 1 and 2 okay because I need to find out what the velocity is for liquid 1, what the velocity is for liquid 2. What I have done is gotten rid of subscripts now because I just wanted to tell you that this is generic for both the fluids. So in the domain 0 less than y less than h we have mu 1 d square u 1 by dy square equals dp by dx okay. In the domain I just got mu 2. Now see I have the same pressure gradient driving both the fluids. I have a particular pressure at the inlet okay and I have already told you that I have pressure only varying in x direction. So I do not use a different constant for this pressure gradient and a different value for this. Both of them are the same. The pressure gradient in both the liquids are the same okay and that is one of the simplifications we have because our flow is parallel okay and straight. So if the interface have been bent then there would be a pressure difference between the 2 liquids which I would have to incorporate. We will worry about that later right now we will do the simple problem.  So you can actually integrate this out and this would on integrating twice would give you u 1 okay maybe I should do this step by step. I do not want to make a mistake here. Let us just integrate the first guy du 1 by dy integrating once du 1 by dy gives me 1 by mu 1 dp by dx plus c 1 and u 1 gives me 1 by mu 1 dp by dx y square by 2 plus c 1 y plus c 2 okay. So this is how my u 1 is going to be varying with y c 1 and c 2 are arbitrary constants which I need to determine. So all I have done is integrated this differential equation. Similarly I can conclude that u 2 is going to be 1 by mu 2 dp by dx y square by 2 okay because I will have mu 2 here plus c 3 y plus c 4 okay. I need to now find out these constants and for that I need boundary conditions okay and what are the boundary conditions I am going to use? So we have 4 constants and we need 4 boundary conditions okay. So the boundary conditions are going to be clearly applied at the walls and at the interface. So at y equal to 0 what are the 4 boundary conditions? y equal to 0 this is the lower wall we have the no slip boundary condition okay. The no slip condition implies u 1 is 0 now at the upper wall and y equals capital H again the no slip boundary condition because the wall is flat stationary the wall is not moving okay the flow is being driven by pressure. This implies u 2 is 0 it is the second liquid okay because the second liquid is going from small h to capital H. So I got my 2 conditions from my no slip boundary condition and I need 2 more. Now what I am going to do is these 2 conditions are going to be at the interface. So at the interface when y is equal to small h we have the continuity of velocities I want a physically admissible profile I expect the velocity field to be continuous okay. I do not expect that to be discontinuity in the velocity field. So what this means is u 1 must be equal to u 2 okay and the other thing which I expect is that the stresses the shear stress the tangential stress exerted by the first fluid on the second must be equal to that exerted by the second fluid on the first okay. So we want this is coming from the continuity of the velocity okay and we also have continuity of the shear stress along the interface. So we will derive the formal equation of how to go about calculating the shear stress but right now what I will do is okay the this is the x direction and this is the y direction. The shear stress at this interface is going to be given by tau yx okay the first subscript tells you the direction of the normal and the second subscript tells you the direction along which you are trying to find the stress okay. So I am interested in finding the stress on a surface which is perpendicular to the y direction and along the x direction because that is where the flow is okay. I am interested in finding so I want continuity of shear stress. So I want tau yx in the first fluid must be equal to tau yx of the second fluid and if you are going to assume your liquid is going to be Newtonian the two liquids are Newtonian. So the shear stress tau yx in the first fluid is given by mu 1 du1 by dx sorry du1 by dy plus dv1 by dx. This is the shear stress at the interface. The shear stress at the interface given by the second fluid is mu 2 times du2 by dy plus dv2 by dx. Remember these are evaluated at the interface y equals small h. Now since the interface is not deflecting v1 is 0 everywhere at the interface as a result of which dv1 by dx is 0 and we have similarly dv2 by dx is also 0 because of the fact that the interface is not deflecting and the vertical component of velocity is 0 for all x. What this means is the equality of the shear stresses gives me for a Newtonian fluid remember this has been written for a Newtonian fluid mu1 du1 by dy equals mu2 times du2 by dy at y equals small h the interface. So these are the four boundary conditions. This is the fourth one where we have equality of the shear stresses at the interface then we have the continuity of the velocity at the interface and we have the no slip boundary conditions at the two walls. These four boundary conditions are used to find out the four constants of integration which arise when you integrate the second order differential equation of the velocity in each phase and that gives you the velocity profile okay. So these are the four conditions which I have to use to get my velocity field that is to determine my constant c1 c2 okay and they are just algebraic equations which you will use and you will find out what the constants are c1 and c2 and then for particular values once you have found out c1 and c2 you can actually plot these velocity fields okay. So what I am going to do is I am going to ask you a couple of questions for you to think about and then we will stop. So now the two velocity profiles have a parabolic dependency on y in the y direction because it is quadratic in y okay. So I am going to ask you a question which of these flow fields can be seen? One this is my interface. So what I want to emphasize is I have drawn these three flow fields keeping in mind two things. The velocity is continuous remember what I have is that the derivatives do not have to be continuous. The derivatives do not have to be equal okay. There can be a difference in the slopes at the interface that is how this tells you the slope in the one liquid is going to be the ratio of the viscosity is multiplied by the slope in the other liquid okay. So that is a discontinuity in the slopes that you are going to observe. So this is a possible flow field that is the one maxima in this liquid and there is no maxima here. There could be a maxima in this liquid that is no maxima here or there could be a maxima in both the liquids okay. So what I want you to do is think about whether these are possible. If they are possible under what conditions will you actually see this kind of a behavior or this kind of a behavior or that kind of a behavior or if you are not going to be able to see any of them you have to know we will discuss this the next time. Thanks.


so it's a little bit quieter in the dorms right now, so I feel like I can do this. In this video, I'm basically just gonna be talking about like a very productive 24 hours in like my typical life here at the University of Edinburgh. For this past week, this has been like my second week back, or this is now starting with my third week. And yeah, it's been good. It's been very crazy, just like meeting a lot of new people, being myself out there again. And it's been very busy. I went out for Burns Night, which was kind of fun. Went to a Kayleigh and I went to one last semester, but I didn't really talk about it, but that's, it's always a fun experience. On Saturday, I was just sort of catching up on work, and then Sunday, I just getting my actual life together again. I basically did like a deep clean of my room, and it looks so nice now because there was just like weird stuff that was accumulated from last semester. I like redid my little bookshelf over there, and it looks really cute. Yeah, so basically that afternoon, after I tidied, I just like, I went to Tesco to pick up a couple of things and specifically to get more hand soap because I was out of like antibacterial soap, which you can't be out of that in these corona times. It did get rained on a little bit, but I was trying to go to the store before I got dark because right now it gets dark at 4.30 p.m., which isn't that bad. It's not 3.30, but it's definitely something that I haven't totally gotten used to because probably the darkest it ever gets in D.C. in the winter, and like the peak of winter in December is like 5 p.m. So then after I got home, was responding to messages from you guys, and I think it did like a little bit of work for one of my tutorials that was, I guess it was on when it's this coming, it's tomorrow, but I did some work for that anyway. I have just started hearing about this in like the last month so much because they made the bus free for, if you have your young Scott Card for anybody under 22, which I wasn't gonna get mine because I am 22, so I can't get the free bus. But I also, I found out last week that you get like a discount at like historic sites or like tourism places, so I applied for my card. Yeah, then after that, it was cold and dark and rainy, which is like a very Scottish day. And so I sat by my chair in the window, which is like my favorite place because the radiator is right there. And so I just like read there and like the rain was going. It was very, very nice. The day is Sunday and tomorrow I don't have a ton of stuff going on, but I am gonna have a gym class schedule that I'm going to. But so to keep some updates, so in case you watched my last vlog, I was reading Catcher in the Rye. Actually, I ended up finishing it on the day of the plane and I love this book so much. So I have this app that I, I kept getting recommended called Likewise. It was really good. So I, it gave me like a list of like other books related to like the Catcher in the Rye that I could possibly read. So I went to like a bunch of different vintage bookstores and I found this one, which is HD Walls, The Time Machine. And I read this last week. It was very interesting. I'm glad to have read it. I didn't really love it as much as I loved this book, but it's been nice sort of like expanding my horizons. I have found that the vintage bookstores like Tills and then Armchair books can be a little more expensive. So I went into like another like actual vintage store and I found this ton of friendship book, which I've read her before, but I got this one for two pounds, which is really excellent. I'm liking it so far, but I'm only like, you know, this much further into it. Yeah, that's what I had going on. I went out for a burn tonight on Friday. That was pretty fun. I tried Haggis, took one bite of Haggis, maybe two. And that was it. It was weirdly buttery. I don't, I don't know how I felt about it. Oh, also I posted about this on my Instagram, but like a month ago, my mom gave me blue light glasses. Like she just ordered a bunch of them for my family, which they actually like have lowered the amount of headaches that I get. So I've been wearing them a lot. She got a pink pair. So I immediately took them and I put them on and I swear to God, like the spirit of a woman named Karla just like entered me. And I just like, I am Karla when I put them on and I don't know how to explain it. But yeah, so basically I just had an early night on Sunday because I was looking for a gym class that I had signed up for it. The one that I really like going to. So yeah, I got up early for that set my alarm and just like, I always make time, make sure I have time to have coffee in there too beforehand because I can't do anything without at least a cup of coffee. But then so after that, I just, I went for a walk. I went for like a hike up. Not even like a hike, there's like a path but up Arthur's seat, which was, which is always nice.  Last semester that is like fully in person. That's live lectures. I have to go to a building three times a week. And then I have one class that's completely asynchronous. It's all I can just like watch lectures anytime I want. Finally have one that is like a live lecture. So I have to be online like at a certain point in the day. And all my tutorials are in person, which is really nice. And yeah, I just got back from my first marketing tutorial which is very interesting. I really liked my marketing class. But yeah, I'm so used to doing things online that it's been really nice to have, to really have somewhere to go almost every single day of the week, which yeah, I mean, last year I had internship where I went down to an office three days a week. But then the rest of the time was just at home because it was the pandemic. But so I really haven't had this experience since my last year of college in 2019 which just like seems absolutely crazy. Yeah, that's really it. Okay, thanks for watching.


That's a great way to start today. This is Mission Control Houston spacecraft communicator, Ken Cameron, waking the crew on board Endeavour to the tune of Start Me Up by the Rolling Stones. Today's greeting for Mission Specialist number four, Mark Garneau, on board Endeavour. This is Houston, please call Endeavour for a voice check. Endeavour, this is Adelaide. How do you hear me? Adelaide, this is Endeavour. This is Ron Cole. How many? Andrew, it's Dean Brown speaking to you again from Adelaide, and at this very moment I think you're about to pass over Adelaide itself, and certainly warm greetings to you and the rest of the crew from all of the people in South Australia. It's a pleasure to have this chance to talk with you, and so near to the end of your mission. And I ask you, how do you feel at present? I feel fine and good evening to you, Mr. Brown and people of South Australia. Yes, we are about to fly over Adelaide. It'll be night time for you, but we'll still be sunlit, and I believe if the clouds are clear enough, which I'm not sure they are today, you may be able to see us. Right now I think we're south of Perth, crossing across the Great Australian Bight towards Adelaide. I'm feeling good. We've had a wonderful mission. We've done some outstanding experiments, both in some technology and in some science, and I'm sure you've probably seen some of the pictures that we've sent down of the satellites that we've deployed and the instructor that we inflated on orbit, and they've really been breathtaking to watch all of this unfold. It's been a wonderful mission. I'm fairly enjoying it. I'm sorry it's coming to an end. Andrew, what do you see as the next major challenges in space for mankind? Obviously you've had this challenge, but over the next 20 years do you see us then moving out away from Earth and to what planets, and what do you see as some of those challenges that mankind will achieve over the next 20 year period? I think the biggest immediate challenge facing us is to learn to live and function on a day-to-day long-term basis in space, and that of course is what we will achieve with the International Space Station, and that will provide a platform from which to do that, a platform from which to perform life sciences experiments for human habitation in space, and a platform from which to do Earth observations and resource monitoring and ecological studies of the Earth, something which I think will be profoundly important. And after we've operated that facility, then I think we'll be in a position to start further colonization of the solar system. We'll begin, I think, with a return to the moon and colonization of the moon, followed some years later by a colonization trip to Mars. It's still a long way off. I certainly don't think it'll happen in my professional lifetime, although I hope to live to see it. But I think that's the direction that we're going to be going. And you're conducting all sort of experience that will be useful to Canadian. Can you give us a little bit of insight about the success of what you've done? Yes, sir, I can. One of the experiments that I spent a lot of time on during this mission has been the commercial float zone furnace, and that's a furnace that melt materials and then re-solidifies them, and these materials are semiconductor materials. And semiconductor materials are the materials that we use to make integrated circuits and chips that we use in our computers and in a lot of our electronic equipment. And we're trying to make a better quality of crystal. And there are two Canadian scientific organizations that are flying crystals on our mission. One is called CANMET from Ottawa, and the other is the University of Dalhousie in Halifax. And we've had some very good results with the float zone furnace. Another experiment that is Canadian on board is the Aquatic Research Facility. And this is an experiment to study the effect of weightlessness on sea light forms. We're carrying sea urchins, starfish, and blue clams. And we're looking at their embryonic development up here in space. And those are experiments with scientists coming from the University of British Columbia and also once again from Dalhousie University. We also have two other experiments in the cargo bay, which are thin, organic films and another one, semiconductor materials, the vapor diffusion experiment. And they come from the University of Toronto and the University of Moncton. So Canada is well represented up here in space research. Mark, the Houston Chronicle. Dr. Lucid, can you characterize your spirits at this point? How are you doing near the midway point? And could you also touch on your working and personal relations with your Russian hosts? How is that going? Questions at the same time, because from my viewpoint, I think everything is going along just really great. I mean, I couldn't ask for anything more out of a flight than what I've gotten out of this flight so far. And if the second half is as good as the first half, then all I can say is you just can't beat it. Right now, I'm feeling really good and I'm busy. As you might know, we've activated Prota and I've gotten busy doing a lot of the non-state experiments in that. And of course, there's a lot of activity on board right now because Yuri and Yuri have been doing several EVAs and they're going to be doing another EVA this weekend, and so that keeps us all busy involved in that. And it's just been a lot of fun working with Yuri and Yuri. And I think that they have helped me out tremendously, and I hope that maybe I'll help them out a little bit. And all along, I've always said that it doesn't make any difference what kind of complicated science experiments or complicated satellites or what have you that you might do on your flight. What makes a flight memorable, what makes it something that you'll always remember is the people that you work with. And if you have really good people that you're working with, then it's a great flight. It doesn't make any difference what the actual work is that you're doing. And I just have absolutely wonderful people and Yuri and Yuri to work with, and it's just been going really fine. And I have a final question. What have you found so far that you would consider most insightful about life aboard a space station, the sort of thing that you might like to pass along to future colleagues who'll be involved in the assembly and operation of the space station? Just from an operator's point of view, from a person that's actually working here on the space station, the thing that has sort of taken up more time than I think is really warranted is trying to find things. You know, you put things somewhere and then forget where they are or things have been put somewhere and you don't know where they are. And it just takes a lot of time just to get everything together that you need to do whatever activity you're going to do. And I think that some way of keeping track of just where things are, I think is a very, very important activity. Hey, Shannon, this is Phil Chen, Earth News. I heard you talking to your family and friends a couple of days ago, telling them how exciting the EVA looked from your point of view. How different is it aboard me or where EVAs are just a regular normal, not day-to-day, but week-to-week occurrence as opposed to on a shuttle flight where they're pretty rare? It was a normal, everyday thing for Yuri and Yuri to go out and do an EVA. I mean, it was pretty exciting. I've never had the privilege of watching an EVA from the shuttle viewpoint. Now, I saw Linda and Rich do their EVA on 76, but I was on the mirror side. I was on the mirror side of the hatch and I saw that.  You know, they're out a long way. And I'll admit that the first time that I saw Yuri out on that long pole that the Russians used to take equipment and people from one module over to the other, the first time I saw Yuri way out on that pole and going out just to cause nothing to get to the other module, my heart went up in my throat just a minute. My heart, I sure hope the other Yuri knows what he's doing as he's rotating the pole around. This is Irene Brown with UPI for Dr. Lucid. After two months in space, what issues do you feel need to be addressed for longer duration flights such as those lasting six months or longer? I had a whole lot of time to think about that. The things that have made this flight very enjoyable for me have been the fact that I've had some regular contact with my family and that's, for me, that's very, very important. I've been able to talk to them on the radio, I've been able to talk to them by TV, to two-way video contact, and also I've been able to get letters or messages from them by an email connection. And that to me is extremely, extremely important. Come on, we'll be here. Here's one person. Okay, come on in. Okay, well now you can see us, but we can't see you. We say that there's a lot of equipment there and from various countries, could you describe some of it for us? Well, Yuri Vladimirovich will do the honors here, and I'll be showing. Okay, over here. This is the glove box, which is being used by Shannon mostly, because we're preparing for EVAs. This is a very interesting chamber with these black gloves in which one can work, little shades, so you can see what's going on in the chamber. What do we do inside? We perform experiments here for microgravity isolating platform for various weightless experiments, and over here we have a very interesting furnace. It's a four hour timer. We have an experiment for processing of some specimens, honestly speaking, I don't know which ones. We have very good visibility when the results are in. Then Shannon performed an experiment, which is a little bit further down, unfortunately. We have specifically gotten rid of a lot of equipment here so that we could pass through here, so it's a little bit further down there in a box. Maybe Shannon will explain a little bit more detail about the experiment. Very good results. You just have to believe us on that. I'm talking in general. Shannon doesn't want to be talking anything specific so as not to tire you. We just wanted to talk with you. That was the picture from here. Great.


I will talk. I am mentally exhausted, emotionally drained, physically sick. I just want to go home, hug my mother, sleep. I really miss my family. An incident of the intervening night of August 10 and 11, 2017, at BID Hospital in Gorakhpur, the entire city, in fact, the entire country. A doctor who is a perdition was first lauded for saving so many children who were dying allegedly because of lack of oxygen, but after that he was jailed. And we are talking about none other than Dr. Kapil Ahmad, who worked out of jail this evening and we are joined by him. Dr. Kapil, thanks very much for the time for talking to us. My first question to you, sir, is please share your experience in jail. Jail is jail and Gorakhpur is the barrack we were residing. It is really pathetic. The capacity is 60% used to have and we used to have 150 people in the same barrack with one toilet and we used to have to sleep on the floor. And you know, in Gorakhpur, the total capacity is 800 and right now there are 2,000, more than 2,000 prisoners are there. Most of them are on trial and actually 90% on trial, very old. I don't know why government are not giving bail to them or they are just shooting number. I have already written in a letter that we have to sleep with millions of mosquitoes and thousands of flies, bath in front of us. I have never done that. People do that, but I have never done that, bathing naked in the field. But I go, every day was like decades and I used to just wait for the Sunday, Tuesdays and Thursdays to meet my family.  You know, jail is jail. When Yogi Ji has said that jail is jail, so jail is jail. Can you describe what actually happened that fateful night of 2017? There are so many things have already you know. I don't have to go into the detail. It was on 9th, Yogi Ji came. So we were just preparing for 9th of August when he was supposed to inaugurate that high dependency unit on 9th of August 2017. So we worked for 7 days continuously and you know, to start that high dependency unit. And then when he left on 9th, we were very tired. So I just asked my HOD for leave and she said, okay, for one day I can give you. I said, okay ma'am, I just want one day rest. So I left. 10th I was at home all the day and then suddenly, you know, around 12, 12, 26, I think that was the time I actually remember. One of my senior residents, he messaged, we have an AIS core group. He messaged that there is no liquid oxygen and this is a crisis. So I just ran and we did everything, what humanly possible, okay. We arranged cylinders from nearby hospitals. We asked everyone, all the gas agencies, fellow. Actually, by 130, 50 cylinder arrived from Faizabad, IGL, Imperial Gas Limited, Faizabad, who was, supposedly he has to deliver around 250 cylinders but he's delivered only 50. But by the time like 1.32 o'clock they reached and that was sufficient till morning. Then morning again the same problem occurred. So we have to run and we have to search for the cylinders. But it was not enough. I ran to the IGL SSB, asked them for their help. We went to each and every corner of BRD to get an empty cylinder and we gathered so many people to carry it and put it on a truck and then we went to all the gas, Modi gas agency actually, he helped. And he, we got around 120 cylinder in one truck. So around 250 cylinder per day we used. So see, whatever I did, it was not a something heroic thing. I always said, I'm not a hero. Whatever it is, because anybody would have done the same thing, you know. Because kids were dying, you know. I am also a father. I have a, my daughter was that time 11 month. And whenever, I remember one girl, three year old, that was around morning 9, 9.30. And the oxygen was not there and we put her on an Ambu bag. And she started, you know, when we did Ambu, she started bleeding. She started bleeding from nose, the whole ET tube, what we put on the throat. She started bleeding with that and we tried hard to resuscitate her, but she died. And the parents, they started screaming and crying and we also cried. Sir, what actually went wrong? You were not either, though you were associated with the Pediatrics department of the hospital because you are a pediatrician. Secondly, you were not in charge of the AES ward, acute encephalitis syndrome ward, 100-bit ward. You were not, you were just posted as nodal officer of national health mission. Then you went extra mile as you are saying. You are in cylinders. Then suddenly what went wrong? Why were you sent to jail? Why? First question you ask, why this happened? So it happened because the system is like that. You have to improve the system, you know. Pushpa Shale Limited, he has written numerous letters, at least 14 I remember. He has written to HOD Pediatrics. He has written to principal. He has written to DM Gorakhpur. He has written to principal secretary. He has written to DGME Health and Education. He has written to health minister. But what all they did? They did just forward to like DM when he got that letter. He said forward to CMO Gorakhpur. CMO when he got the letter forwarded to principal BRD. You know, that was the thing they were doing. They just forwarding. You know, even in our charge sheet when I read that in the investigation officer when asked the DGME Health and Education about his responsibility and what he did when he got those reminders. He said I forwarded to FC. So that's the way this system works. What is this? FC? Financial commissioner or something. So he should have acted. He should have called. He should have said that no, send the money. They are saying I have sent the money on 5th. I am asking why he didn't send in April? Why he didn't send in June? Why he didn't send in July? You're getting my point. So that's the way they were working. And then, you know, that thing happened. Lower level also that the central pipeline operators, they did something. I don't know. Maybe it's some bigger conspiracy. They informed on 3rd of August that the oxygen is less and then they forgot. They should have informed when the oxygen, liquid oxygen goes down to below 14,000 units. They informed when it was 900 and they informed only on 10th. You got. So they should have informed on 7th or 8th. Actually, Yogi Ji was coming. Maybe we would have informed Yogi Ji that there is a problem with this. Maybe the principal would have informed Yogi Ji that there is a problem with finance. And he would have arranged it himself. The problem would have not occurred. You're getting my point. So this is the way the system works and I think the system has to improve. The higher 30, the way they shed their responsibility is not that. You know, I remember principal was saying, I didn't know that but in the jail he was telling me. On 3rd of August when he got the legal notice from Pushpa cell that he is going to stop liquid oxygen within 15 days, they had a video conferencing where principal secretary Dr. Anitha Jain Vettnagar was sitting that side and this side DM and principal were sitting. And they talked about how he is threatening, Manish Bhandari is threatening to stop the oxygen. Liquid oxygen fund is not there. So I don't know what happened between them after that but everybody knows. They said that we didn't know. They just said, they were like, I don't know. Even the common people know that doctors don't buy oxygen. I was not involved with payment. I was not involved with tender. I was not involved with order. I was not involved with supply of oxygen. I did because kids were dying. Because I am a father. Because anybody would have done. One reality in this case, so many innocent lives were lost because of someone's negligence. Be it the doctors, the management of the hospital or the government of the day. Who should be held responsible for that? There was sudden increase in the number of deaths on 10th night, 11th and 12th. This is the bigger truth. Who is responsible? I have already written you. Later I have written from jail. Who is responsible? I am not an inquiry head that I should go and blame anyone. But I have already said that these people, the higher authorities, those who are sitting in Lucknow, they should think and I think if any proper investigation would go, they have not done the investigation properly. I am not going to blame anyone because I am already in so much mess. You are free now. You are in depression. I am scared that maybe some more charges will be put and I will be behind the bar again. Who knows if the honorable high court judge has categorically stated that the government has not produced enough evidence. He has written no evidence against those baseless charges they have put on me. They have slapped it and they have just put it behind the bar and they forgot for 8 months. And we were like, okay, after Diwali we will get, after Holy we will get, okay, after Chunao we will get. We were just waiting. Then that one day that was enough. Then we thought that no, we have to hit the street, we have to come forward. And then the break, you know, they will say, when that fear is gone, when Manish Bhandari got that fear, when he got bail. The one who closed the auction and got bail, then why me? What did I do wrong? In few months I was feeling guilty that maybe I have done something.  I said, no, I will write there later then. That was the one crucial point. That was Dr. Kapil Ahmad who said accountability should be fixed for those who are really responsible for it. There was a very important point he made, was the later forwarded not only to the college management but higher ups, which were ignored just paperwork were done. And innocent children were, innocent children lost their lives. It is up to you to think about it, to question the system who are really responsible behind this mess.


We'll go in three, two, we're going to start on John. What, oh. Straight up. Are we just going to do? We're just going to start on the white shot. Oh, okay. I thought we were just going to stay on the white shot, right? Yeah, just stay on the white shot, okay. Okay, stay on the white shot. Yeah, white shot. Okay, and we'll go in three, two. Okay, we're here to announce the Cube Madness winners. I'm John. With the Cube. And we're Palo Alto, Ariana and myself. We're going to announce the Cube winners. 64 to 32 to 16 to eight to four to two. And we have a winner, Ariana. Please announce the Cube Madness winner. All right, that's right, John. 64 entered 1-1. And the winner today is Jesse Proudman. Woo! Jesse, congratulations. Congratulations. So it came down between Pam Murphy from N4 and Jesse Proudman from Blue Box Cloud. And we are so excited to announce that Jesse was the winner. Thank you all for participating. And those who voted as well. It was a very exciting few weeks. And we're looking forward to, you know, continuing with the Cube and more interviews. So, John, where's the Cube going to be next? The Cube is kicking off the spring tour. We're going to be here in San Francisco on April 9th for AWS Summit. That's all about the cloud. MIT IDE in London on that next day, the 10th. Of course, I'm not flying to London. Dave Vellante will be there. Mark Logic World on April 14th. And then Service Now in Las Vegas. And then after that, it's going to be we're going to see IBM Edge, Informatica World, EMC World. You name it. All the shows again, we're going to hit again. All the tech coverage here in the Cube. So we're super excited. Congratulations to Jesse and everyone who played. And a lot of fun. We had a lot of fun this year. I got to say this was a great year. Thanks for participating and thanks to the team for putting together. Yeah, so check out more interviews at siliconangle.tv. And you're here watching the Cube. Thanks for watching. All right. See you next year, Cube Madness. Perfect. Done. Right. All right. How about a look at the other news?


Okay. Hi, everybody. Hi. Nice to see you. Well, yeah, welcome. I'm, I'm Peter for those who are joining you. And yeah, we've got another wonderful movie workshop day. This terrific series, really mind opening series. So, yeah, I'll just let you know how the day is going to flow. We start with David and this episode for today. And afterwards, we're going to have a 10 minute break, and we have breakout rooms where you can share any emotions or anything that came up during the episode. And then we'll have a 45 minute break, and then a Q&A session with me. So I see David there. I'll pass it over to you now. Thank you, Pete. Hi everyone, welcome. Welcome to our beautiful movie session workshop all day workshop today. And wow, these episodes that we're seeing from Netflix on psychedelic drugs and spiritual awakening and healing just generally the category of healing are all so very, very helpful. It really kind of puts everything in a, in a perspective because in this world of projected opposites there's all these conflicts and, and it's conflict between self concepts is really what it is. Some people who have been very open to drug use have been told their whole life that it's an opposition to spiritual practice. And then those that have other spiritual practices can sometimes point the finger but all conflict in this world is just, it's a conflict of self concepts that the ego made up. Christ has no conflict. Heaven has no conflict. Nirvana has no conflict. But when the mind is wanting to hold on to a belief system of the fear, which is the ego, then that projects out a world that reflects conflict and we're really praying for harmony, we're praying for unity oneness. We're praying for happiness and joy and peace and love. So, sometimes, if you've followed along with me over the years, you know that I say basically that the sleeping mind or the human condition is, is both psychotic and schizophrenic psychotic in the sense that the sleeping mind involves a break from reality because heaven is reality. Nirvana is reality, love and light, eternity is reality. So, by definition, perception is a, a break from reality. So, even though you may not have been diagnosed. Jesus is giving us a diagnosis. And he's saying yes, psychotic break from reality. He's not necessarily saying that, that it's real because reality is real. Truth is real. Eternal love is real. Light is real. But to believe in time and space and bodies, that is a psychotic episode. Well, it can be a brief episode or a long one depending on what you want. If you want it to be over, then it's over. If you don't want it to be over, then it seems to drag out a bit. And also schizophrenic. I mean, most people think of schizophrenia as, as a condition of a split mind in which you hear multiple voices. Again, the human condition sits very well into that definition. The mind that believes in the ego belief system is has a split. Because the right mind where the Holy Spirit resides is, is there always to be remembered but as long as the mind is holding on to the belief in the ego then there's a split mind. And that split is so intolerable because of thought system of love and a thought system of fear. They really don't have meeting place. They don't meet. There's been a lot of philosophies over the years, including the yin and the yang and many kind of philosophies that say you have to come to a reconciliation in the mind. Jesus is saying, it's all done. It's your state of mind, your right mind is the is a perfect reconciliation because the right mind is a reflection of truth and the wrong mind doesn't exist. So, the reflection of truth is, is really the only same choice. And that's what this mind training is all about is coming to that. You voted for different themes this week, and I'm going to run down some of the themes because it's always interesting to see which themes are are on top. What you're really calling for we try to keep these sessions as relevant as possible. And the first one is giving lifelong dedication to the calling to the calling of your heart to remember God to the calling of your heart to remember home, heaven. And lifelong dedication means that that basically you have to give time over to the Holy Spirit to use for the purpose of awakening to the extent that you don't give time over to the Holy Spirit for awakening, you give it to the ego. The ego is an ingenious master at wasting time. It's a it's a master of delay, it's a master of disguise, it's a master of deception, and to the extent that you're not giving everything of time and space to be used by the Holy Spirit. You're giving it to the ego, to the extent that it's not given over as a, as just to use as a, as a use of symbols to let go of all the symbols, then that is what we would call delay. And anybody who goes into spirituality or religion starts to realize that what Jesus is teaching us is he's saying this course will be believed entirely or not at all. This is not a video game where you can keep trying to score higher and higher and try to, to get a higher score higher scores and lower scores don't matter to the Holy Spirit. This course will be believed entirely or not at all very uncompromising salvation is not partial. You can't, you can't have a partial salvation, you can't have a partial healing, you can't have a partial awakening, you cannot believe in the ego, even in the least bit and, and feel a sustained consistent happiness because the belief in the ego is saying I choose to remain with a split mind. I choose to remain afraid of God's love, and, and even the slightest, slightest lean towards the ego, the slightest bit of protection you give to it the slightest bit of investment that you have for the ego will simply maintain the sense of a split mind. And of course that's intolerable. It's like the story of the princess and the P you know even though princess was sleeping on all the mattresses. You could still feel the P at the bottom.   I like this something is not right. So, the very first theme that you all voted on on the English polls, the Spanish polls and tribe movie polls combined was giving lifelong dedication to the calling. And if you look at it just in terms of things of the world, anything in this world that you just give partial attention to partial effort to partial devotion. It's going to be kind of sloppy. If you're not attentive with your driving skills. Notice that it gets kind of sloppy. If you're not attentive cleaning your house. Notice that the house gets kind of dirty and and disorganized. You're trying to learn something from a school, and you don't give full effort to studying or to really trying to learn it, then the chances are, when you get to test time, you're not going to do. You're not going to ace the test, unless you give your whole heart to succeeding at the test with spiritual awakening is quite simple. You have to be attentive to the Holy Spirit, in order to transcend the ego, you can't hope that you can give a 30% effort and transcend the ego because the ego will be laughing at that 10% that it gets and going, Oh, I can make this 10% into madness. Thank you for the 10% I'm a death wish the ego says so I'll just make, I'll just wreak havoc with that 10% of your mind that you're going to give me. Of course, Jesus saying there's it's not a matter of percentage, you know, you believe this course entirely or not at all. The second theme is accept the means that are given me for my awakening. A lot of times people think of means as things in form. They think of well if I had the means that would make my spiritual journey a lot easier, the means being things like money or clothing or possessions or houses or cars. If I had some of the goodies of this world that would make my spiritual journey a lot easier. If I had those as a means that would really help me in my accelerate my spiritual journey. Actually, it's not the case at all the means for awakening that Jesus is offering is the miracle and the miracle comes in your mind. The miracle comes from prayer. Prayer is the medium of miracles so if you pray sincerely and honestly to the Holy Spirit into Jesus, and you say, bring on the means show me the means. You can say, I want to be lit up and aligned in the means, and that is the prayer of your heart, then then you've done your job, everything else that you perceive in the world there are no means in the world. Because we're accustomed to seeing a world where money is a means and you can do things with it or physical strength is a means you can do things with it or intelligence is a means you can do things with it. Even in time is a means, and you can do things with the time that you have actually Jesus is saying no miracles are the means and miracles collapse time. And eventually miracles collapse time it miracles clap money miracles clap the body miracles collapse interpersonal relationships miracles collapse a linear perspective that is a total distortion it's a total projection of the ego. So, it's important that we accept the means that are given me from my awakening and, and in our case we'll call that miracles. Even with the use of will say psychedelic drugs, it would only be helpful if you prayed for the miracle. First, the miracle is brings you back to the mind and it shows you how powerful the mind is and it shows you that nothing of this world has any power at all because the world and the symbols of the world are just unreal effects from an unreal cause and the unreal causes the ego belief system. Third, open mindedness love what is. Ah, how sweet to be in the present moment and simply love what is Jesus says in the workbook of a course and miracles he says God, we say God is and then we cease to speak.  God is love. What is God is and, and this world was made as an attack on God a place where God could enter not. But more importantly than that, you start to realize that that the world is not outside of your mind. The only recognition necessary for healing is a recognition that the world is not outside your mind that the world has not left the mind that thought it. Therefore, all attempts to blame all attempts to project all attempts to look for external positive value or external negative value are the same that there is no external world. As Jesus says in the course there is nothing outside you that is what you must ultimately learn. There's really only one of us. And that one is the Christ. And even if we take that toward the split mind we can see that that says there's only one mind. There must be only one right mind and one wrong mind there. And the good news with that is there's only one ego. So whatever is perceived to be an external source of conflict, an external source of difficulty, an external challenge is simply the ego projecting itself out into a world of form and generating a hologram of conflict. Again, the spiritual journey is about ending the attention given to the hologram and giving full attention to your right mind, full attention to the Holy Spirit, and just merging back into the light and letting go of all attempts to make something of the world. It's only the attempt to make something positive or negative about this world that makes the world seem external. But if you realize it's not there, God didn't create it. If my goal is God, then I don't have to keep trying to change and fix the world. I just have to go inside and listen be very internal with my inner listening. Go into the silence within. Next one, realizing it's a perceptual problem, exclamation point. Wow, they put an exclamation point at the end of that that's, that's again, just realizing that the problem is always in the mind the solution is always in the mind and when you bring the problem and the solution together the problem disappears. If you bring darkness and light together, the darkness disappears. If you bring the error to the solution. The error disappears. Or as it says in the Bible, perfect love, cast out fear. So basically, the main thing to remember the one thing to admit is that it's a perceptual problem. And finally, extend the blessing I have received. You feel these miraculous experiences happening in your life and we're going to see lots of examples of that and lots of demonstrations today in the episode we're going to watch. But when you feel it, you want to extend the blessing. That's what I love about these. I call them psychedelic therapist or psychedelic researchers. They're just people that will say back in the various years but a lot of times back and we'll say in the 1950s 1960s that they started to have some really amazing, expansive experiences with these psychedelic drugs, and then they became very happy and they wanted to share the happiness. Just like St. Francis said I wish this piece on everyone. These psychedelic researchers and therapist had such amazing miraculous experiences that there's something in their heart was just so loving it says I wish this for everyone. I wish everyone could be happy. I wish everyone had the same freeing expansive experience that I just had. I wish everyone is free from suffering free from struggle and challenge and free from nightmares. A lot of people who have gone through experiences will calm spiritual awakening experiences. They start to feel that they're being freed up from slavery, they're being freed from the captor, and they don't even know what the captor was. Some, maybe some religions call it the devil. Some psychologists call it the ego. Some people just call it the air. But even if you just call it the air wouldn't you want to be free from the air. Especially if the air is bringing you heaviness if it's bringing you fear and doubt. So what I love about what we're going to watch today is we get to see the extension. As soon as people find something that works for them. They want to share it. They don't want to bottle it up and keep it to themselves. They don't want to make money off of it. They want everyone to have the same experience. They want peace and happiness and joy for everyone. And you can see it on their faces. These are not closet psychotherapists or closet psychedelic researchers. These are ones that are opening up and being transparent. And if you if you didn't want to be transparent, then you would try to hide it. But this is a, this is a beautiful episode that we're watching today called how to heal the mind and it's on Netflix. If you want to hide yourself, don't put yourself on Netflix. If you go on Netflix, you are suddenly out in the open. The Beatles was all, hey, you've got to hide your love away. No, this is like the opposite. Hey, you've got to give your love away. And these people have opened the cameras, open the, their, their lives up to to be filmed so that everybody can can see the joy of this. Now, before we start to go into the actual episode, and, and I might just say that that what we're going to do today is after I give this setup will will have a beautiful musical interlude. Don't you like it when we have musical interlude, we're going to have a musical interlude of a song called miracle of the mind. I've shown this, I've shared that before so I think you all might remember that. So we'll have a song miracle of the mind, then we'll have a little two minute.   So I'm going to give you a little musical interlude, and then a little to recap, and then we'll launch in to this episode that I'm going to show today, which is episode number three. The, the psychedelic we're going to use today.  We were on magic mushrooms last week and we were on LSD together, as we were going through this, this event. Because I talked to some friends and my friend, Lisa I talked to her on the phone today. I think it was the day after and she said it was like I was stoned. When you feel stoned from a session that is on a zoom room, then you know something's gone on. But I got a lot of reflections and people felt so transported by the session last week so so this week we'll ease our way into it with a beautiful song miracle of the mind and then we'll have a two minute trailer as a recap then we'll dive right in. And this week, we are are going to look at MDMA we're going to look at ecstasy. The, that's extra street ecstasy is the street name MDMA. But before we do, I thought we would all come into a beautiful focus on on the purpose for our lives on the purpose for our mind training and the purpose on everything. And I'm just going to dip into chapter 12 from a course in miracles. So here's what the master Jesus has to say to identify with the ego is to attack yourself and make yourself poor. That is why everyone who identifies with the ego feels deprived. What he experiences then is depression or anger, because what he did was to exchange capital self love for small self hate, making him afraid of himself. He does not realize this, even if he is fully aware of anxiety, he does not perceive it source as his own ego identification, and he always tries to handle it by making some sort of insane arrangement with the world. He always perceives this world as outside himself, or this is crucial to his adjustment. He does not realize that he makes this world, or there is no world outside of him. If only the loving thoughts of God's son or the world's reality. The real world must be in his mind. His insane thoughts to must be in his mind, but an internal conflict of this magnitude he cannot tolerate a split mind is endangered, and the recognition that it encompasses. A split mind must be endangered, and the recognition that it encompasses completely opposed thoughts within itself is intolerable. Therefore the mind projects the split, not the reality. Everything you perceive as outs as the outside world is merely your attempt to maintain your ego identification. So that's a great starting point for us because oftentimes when, when people take a mind expanding drug, they're called or psychedelic drug, the experience that they have is so expansive that they're having an expanded experience of consciousness that doesn't sit with their previous self concept. It's kind of got like getting a glimpse of the forgiven world or the happy dream getting an expansive glimpse of this. And in this state, they feel the freedom, the peace, the bliss of, of no ego identification. And from what we've just read from Jesus, the entire world, we can see the projected world was made to keep the mind from knowing itself as a divine mind. The entire world was made to be a distraction by placing the cause of upset as as external as in the world. The entire projected world is a trick to keep the mind from accepting the correction in the mind. And Jesus tells us God placed the answer where the problem was. So the answer was placed right next to the problem. The Holy Spirit was placed right next to the ego and the ego was solved forever. In fact, it was, it just was showing that it didn't have any reality, any existence. But the projected world is always the attempt to see the conflict where it's not. And then the ego will counsel now you have to solve the conflict where it's not meaning solve it in the puzzle of of time and space in the situations of the world. So, in the end, we're here to give a lifelong devotion to inner guidance, which is really just calling us to come back with the Holy Spirit and to watch and see the world. As an external reality but as as just a simultaneous group of thoughts that really have no validity, no reality. The ego thought system doesn't have any seriousness because it wasn't created by God. It doesn't have any eternal nature to it. It's just a, it's a temporary fling into madness and the Holy Spirit and Jesus are saying, let go of that fling and come in here, come inside, watch it from the perspective of the light and you'll see that you are free of it and it never had you. So, the episode we will watch today is episode three of the series how to change your mind. Our guide through this episode is Michael Poland, who's an author researcher, and he's just a sweet guy he's he's like our guide through the whole thing where he's, he's interviewing researchers he's doing his own research, he's basically an author who's curious about psychedelics. We'll also find out today that in terms of, of psychedelics. The MDMA is, is a little bit seems a little bit different than our first two of LSD and the magic mushrooms, psilocybin. Basically, it just seems to, in terms of the world and the brain it seems to release the floods of serotonin so there's a lot of these gushy loving feelings in this whole report. They want to be in love puddles, they want to feel that expansive connection they want to just just give themselves over to this love. And of course scientists try to put it down into the brain, you know, as, as the serotonin flood but actually, we have to remember that that the brain and the body and the psychedelic drugs and the world are all connections. And as I just read from Jesus, there is no external world. That's right. psilocybin is in your mind right now. That's right. LSD is in your mind right now. Maybe don't tell your parents, but where did you get it. It's been it's in my mind it's been in my mind all along. LSD the psilocybin and now the MDMA the ecstasy, because, of course, this is the main teaching there is nothing external to your mind that everything without an exception is a thought in the mind. And the thoughts of God differ from the thoughts of the ego in the sense that the thoughts of the ego are temporary. And the thoughts of God, they last forever. That's just one little distinction. So, when you realize, and you don't identify with these thoughts of time anymore, what's left in your mind was what's always been there which there's your, your eternal thoughts. I am as God created me as an eternal thought I am spirit is an eternal thought.  So let's use like the war in Ukraine as an example, you know, many people would say, I have nothing whatsoever to do with that war. But some people would even say I have no opinion about that war. I have no opinion whatsoever about the war. But if you perceive that there is an actual war in an external world. That is an example of believing something that God didn't create. God doesn't know of war. God only knows of love. And so, if there's a belief that they're not just an external war going on in Ukraine but if you believe there is a Ukraine. And that's part of the separation you see just the belief in countries, just the belief in in continents, just the belief in stars and planets and the belief in time and space that the belief that that is external to the mind is what the separation is. See, it's not about which side should I take in an illusory world is more like, am I wanting to hold on to the thoughts that made this world and make it seem to be external.  You can see people that go from huge traumas PTSD from nightmares from experiencing huge levels of pain every single day of their life, and then suddenly they have an experience as you'll hear the witness today of something that's so radically different from the painful perception that they were having that they know there has to be a God, there's going to be a man on here that that's going to be a soldier who goes to Iraq. He comes back with PTSD, the neighbors fire off the fireworks on the fourth of July and he feels like he's going crazy. Basically, he will take. He will take three, three different doses of MMM, MDMA and of ecstasy and he will have such a different perspective on the whole world that after eight years of suicidal thoughts, he will have a day where he doesn't have any suicidal thoughts. It's a pretty radical shift. When you go from eight years of suicidal thoughts, every single day of eight years, and then suddenly you wake up one day and you go through the whole day and you don't have a suicidal thought. This is an amazing miracle and it has to be that the prayer of the heart is being answered that it's not, it's not the ecstasy. Otherwise, we could just, we would just turn the world into an ecstasy factory. What's your gross national product of your, what's your industry of your nation. Well of course it's ecstasy. Do you have any other industries know, nobody grows food or builds buildings anymore. Oh no we just we manufacture ecstasy. If it was in the if it was in the drug you know people would have done a lot more just to find the drug or to maintain it but but the, the world is just a reflection of what's going on in the mind. And we're going to indeed see witnesses to the miracle of the mind today. And I think, as we move along, you're going to find out this. This is our last Saturday, we're looking at psychedelics, but what's kind of exciting is there's, there's a man in here today and and basically he is so devoted to making these psychedelic therapies available to people who need them the most there's a lot of people that are involved in it. But he spent his, he went to Harvard, he got his doctorate. He's now involved in politics, and now he's got to the point where this past summer in July, July 26 that there were two senators in the United States. Dr, a Democrat, and Rand Paul, a Republican who's also a doctor Dr Rand Paul, they sponsored a bill this past summer that allows people with like cancer and a lot of terminal illnesses to try experimental drugs that have been shown a positive result in the test in the early test. Up until their bill, they were still preventing people, even with like cancer and terminal illnesses from even trying some of these drugs. And this shows you what we've been dealing with starting back and we'll say the 70s the war on drugs, and all the war on the counterculture and and trying to eliminate these psychedelics from being used even calling him schedule one elicit illegal drugs. And so this episode we're watching today is going to give a full context, so much so that they will come to the conclusion that they're hoping in 2022, which is this year that they will get approval from the Food and Drug Administration. And it hasn't gone quite, quite that fast for them but what they are finding is the Biden administration has said that they are going for FDA approval within two years. Wow, even reflected in our politics. Now, the Biden administration is on on board to get bring back these. These two of them at least I think MDMA and psilocybin I think is what what they're hoping to bring back out of the. I think LSD has such a name, such a negative connotation in the in the collective or the overall mind that that they're not they're not going for LSD they're going to go for the other two. Everybody remembers Timothy Larry and and and from DOS and all the different things they went through and this is just where we're at right now. So, sit back and joy. First of all, the beautiful song and then the recap trailer and then we'll jump right into this amazing episode together. Thank you.