Alright, so what I want to do for the next 10 minutes or so of this lecture is to show you a few videos that will hopefully better illustrate some of the things we have been talking about. Alright, so you will just have to look at the screen for a while. So as the title suggests, we look at a few applications of multi-physics flows and see exactly how some of the things we have been looking at in this lecture translates in the real world. So this is an image in a microchannel of a stratified flow in an aqueous two phase system. So what you will have to do is if you look carefully at those bands that you see, each band is in fact a microchannel and the dimensions as you can see are about 150 micrometers. So that is extremely small width, maybe a few hair widths. Then if you look closely in each width, you will see that about half the channel is dark in black color and the other half is a sort of a lighter white and it is that white portion which is one fluid and the dark portion which is another fluid and you have a perfectly flat interface between the two of them. And the two different fluids are given here at 50 microliters per minute, polyethylene glycol and sodium citrate and this was used in some extraction experiments. So there is a video as well and you will not say anything much because there is no interface deflection at all. So the fluid just flows straight through and what we need to look at when we look at this video is to see whether the assumptions that we made in the in class actually hold. So for example, is the interface really steady and flat or is it fluctuating all the time. So we see in this experiment at least the interface is flat, it is steady and we can possibly be confident that at least that assumption was right. So we can look at the models that we used. This was the model that we looked at in class where we had two infinite plates in the x direction in this case, flow in the z direction and we were looking at how the velocity profile was in the y direction and we had two fluids phase one and phase two and then applying the simplifications to the Navier stokes and the boundary conditions you would have been able to derive the velocity profiles which are given here. Note that the viscosity ratio here is mu and alpha s is the hold up or the thickness ratio. So then after getting the velocity profiles we discussed about calculating the flow rates that is q1 and q2 by integration and then to find the flow rate fraction which is the ratio of the flow rate to the total flow that was sent into the channel. So here in fact we show the relationship between flow rate fraction and the hold up which or the thickness ratio and you see that the viscosity ratio plays a role in this whole relationship. Of course as we expected delta p is no longer to be found because that was a simple magnitude parameter that should have been lost when we took ratios of the flow rates and you remember I would said that it is only when the viscosity ratio is 1 and the hold up is 0.5 that I would expect the flow rate fraction to be 0.5. What happens when that does not hold is what we can look at now in this slide quickly. Before that the model that we considered one of the biggest assumptions was that it was an infinite plate or that we did not look at the third dimension which most obviously is going to be there in a micro channel and that third dimension will in many practical situations be of the same order as the height of the channel that we were looking at. So in this work some of the work we had done we looked at the 2D model as well so that we could you know relax the assumption of the infinity in one of the directions. So we got an aspect ratio naturally which was the width of the channel in this stratified direction that is in the y direction which we had which we previously had and d which was the now new added finite dimension in the problem. So that gave me an aspect ratio and you would expect that if h were much much smaller than d then I should be able to work with the assumption that I had before. In other words if d was much larger then it would tend towards the infinite problem that we had solved. So if lambda is 0 essentially it goes back to the previous problem for any other finite lambda we would have to use the rectangular channel. So you see that here we have partial differential equations and these are not reducible any further. So this is clearly why we had looked at the 1D problem in the first place because it gave you significant mathematical simplicity while retaining considerable physics but in some of the problems you might have to come to this stage where then you will have to deal with the mathematical complexity as you may and then of course but the good thing is you already have some insight from the simpler problem. In turns out that you can get analytical solutions and then once again calculate the flow rate fraction. So here you see a flow profile. This is part of your assignment to calculate these different profiles flow profiles. You can look first at the more familiar figure on figure B where you see that the maxima is in fact in fluid 2 and it turns out that though not shown here that the viscosity of fluid 1 is twice fluid 2. So it makes sense that the maxima is there. On the figure A you see the cross sectional view of the velocity contours. So each coloured surface represents a velocity of a particular value and the max velocity is on the white colour and 0 is the blue colour. So you see that the maximum velocity is located somewhere within fluid 2 near the centre of the channel and it just a slice along the centre that is shown here as a velocity profile. Alright so now of course what every modelling exercise has to deal with is how well it compares with experiment and that is what we have shown here succinctly in this figure where you can see the data points from 2 experiments. These experiments have been carried out by Matsumoto and I can give you his reference later. So he did some experiments where he looked at exactly what we are plotting here essentially he pumped in different flow rate fractions of 2 fluids and then he using images tracked where the interface was located or the thickness ratio and what he found was that when the viscosity was somewhat similar about half each other the relationship moved more or less along a diagonal. But when the viscosity ratio is very different he got large deviations from a diagonal and the diagonal is important because it just means that phi s is equal to alpha s or in other words if you pump 2 fluids in a certain fraction you would expect the thicknesses to have the same fraction. But we see here that that is totally false if they have very different viscosities and that makes sense because the problem favours the fluid with lower viscosity because that will give it lower pressure drop if you want to think of it in terms of energy minimization. So this becomes very important when you are trying to estimate properties of the flow estimated pressure drop using empirical relations where you want to know what the hold up is and there is no simple way to estimate it from the flow rate fraction unless you do the kind of calculations where do. And of course what we were able to see is that our model or the simplified models we are looking at predict this experimental data really well. So you see the blue case follows its set of data and the red dash line follows its set and there is a considerable difference between the two and the fact that the model captures it tells us that the reason for this difference really is in the viscosity ratio and the physical mechanism of that viscosity ratio effect is what our model is capturing which basically involves the shear stress at the wall that is about the only thing that the viscosity is doing that makes the fluids different. So both fluids are moving along their own walls and the more viscous fluid exerts a much greater drag. So naturally it has difficulty to flow the less viscous guy gets pumped through an easier way. Finally here we can look at 1D versus 2D cases and see what the importance of the aspect ratios. So let us just look at the first figure where I have viscosity ratio 1 to equal viscosity fluids for simplicity and I have shown different figures, different relationships here for different aspect ratios. So this is a square channel and then this lambda equal to 3 is where my depth is smaller than the width between the two plates. This case is closer to my one dimensional approximation where d is larger than h and this is the 1D calculation it is a light pink line. So in the first case you hardly see a much difference between these four different results the four aspect ratios and from the 1D case. So I guess I could say that the one dimensional case serves as a good model here and I do not really need to go to the square channel because no matter what the aspect ratio is it does not have much of an effect on this relationship. But when you come once again to different viscosities you start seeing that the aspect ratio has a significant role to play. So the especially along flow rate fractions of 0.5 you have some considerable difference between the thickness ratios depending on what my aspect ratio of the channel is and importantly what we should verify is that whatever be these cases they should all tend towards the one dimensional case if my aspect ratio goes towards 0 which means as d becomes much larger than the width between the two plates h and that is what we see here that when lambda is 3 it is the furthest away from the line pink line which is the 1D case and as my aspect ratio becomes smaller I approach it asymptotically. So the same thing you can see here for mu equal to 5 is just that the relationship has sort of reversed. So what this tells us also is that if my channel is long and rectangular or all standing up I can have different thickness ratios and merely by orienting my channel or orienting the fluids in that channel in the right way I could have some control over what my hold up is for the same flow rate fraction. It also tells us when we would be able to use the one dimensional model with some with better accuracy. So we will stop here for today and we look at some of the other applications of multi phase flows in the next class.


How's it going, friends, and welcome back to another video. So you might have heard of smartphone rigs before, but you're not sure if you actually need one. Well, in this video, we are going to talk about the Ulanzi URIG Pro, which will transform your smartphone into a professional setup. And if you stick till the end, I will show you how you can win this URIG Pro and much more, so keep watching. By the way, all products mentioned will be in the video description below. And if you have an iPhone and are new to iPhone filmmaking, make sure to download my free iPhone filmmaking guide that will help you find the right tools to create high quality videos. If you don't have an iPhone, well, no problem, download it anyways, you will still find a lot of valuable information that you can certainly use. All right, enough of the talking, let's get into the meat. So the Ulanzi URIG Pro is a smartphone rig that you can use in different ways. You can use it to shoot videos outside since you're able to grip the rig with both hands, which adds more stability when filming your videos. So when my girlfriend and I went out to shoot some videos, she used a different rig in the past, but this has been by far her favorite video rig. Isn't that right? Yes. See? I also personally think that the smartphone rig works great for people that are starting out and want to film themselves at home. The rig itself is pretty inexpensive and costs around $16. Since it has a one quarter screw mount on the bottom and on the side, you can mount the rig horizontally or vertically, depending on where you want to upload the video to. It has a spring clip, which makes it compatible with almost every smartphone and stays safe due to the secure screw right here. The great part about having a smartphone rig is that it allows you to add different accessories to improve the quality of your video. Now Ulanzi has sent me these two lights, including the shotgun microphone, which all are essential tools that will instantly improve your video quality. Now you're able to mount these accessories since it comes with three culture mounts on the top. Now the Ulanzi VL49 pocket LED light is great for adding more light into the scene because smartphones generally don't do well in low light situations. When filming at home, I like to combine the pocket lights with the window light since the pocket light uses 5,500 Kelvin, which produces a soft natural daylight temperature. Now using one of these pocket lights also comes in handy if you're vlogging since it's small and easy to take with you. The Ulanzi VL49 is priced at around $15, is rechargeable and the intensity of the light can also be adjusted. Now having at least two of these LED lights will help you to light the environment properly, especially for talking head videos. As for the audio, the built-in microphone on smartphones do produce decent quality, but if you want to get the best audio quality, I recommend using an external mic. The VMQ-1 shotgun mic comes at around $30 and is a great solution for getting good audio quality. So this mic is more a directional mic, which means it captures a sound in the direction you are pointing and will cancel the noise coming from the side. Now the shotgun mic also comes with a windshield that helps reduce wind noise, which is great for shooting outdoors. Now with the shotgun mic, you also get two cables, which makes it compatible to use, not only with DSLR cameras, but also with smartphones. So if you have one of the newer iPhone models, you will additionally need to get this Apple Lightning adapter, which costs around $10. Now when capturing audio, it's important that you're not too far away from your mic. This way you will get the best audio quality possible. To make this work with your smartphone, you basically just have to plug it in to your phone using the correct cable and you're ready to go. It's really that easy, no battery is required. When setting up the audio, I like to use Filmic Pro since I'm able to see the audio levels and have more control over it. You also want to consider getting a tripod so that you're able to adjust the camera position. I like using the Amazon basic tripod since it's inexpensive at around $30 and has all the necessary functions I need. So all in all, the setup would cost you around $120. So I will now switch over to my iPhone 11 Pro Max and use this rig so that you can see how it looks like. As for the settings in Filmic Pro, I'll be shooting 4K 25 frames per second for that more filmic look. For the ISO, I set it as low as possible and my shutter speed is set to one over 50. And I also make sure to lock my wide balance so that no color shifts will occur during the shoot. As for the picture profile, I use natural. Now, usually Filmic Pro will detect the external audio, but if not, make sure to select the right output. So this is what it looks like using the two LED lights and the microphone and my iPhone attached to the camera rig. You be the judge of it how it looks. I'm also using the window light. So whenever you can record close to a window just to have more light. I mean, if you record in daylight, you can definitely just go with the iPhone, but having additional two LED lights is just great if you plan on filming also at night where you have to use artificial light. As you will notice, I'm also quite close to the microphone, which also helps get cleaner audio. So let's now do a comparison without using the two lights and the microphone. Okay, so this is just using my iPhone without the lights and the microphone. You'll probably notice that the image is a bit darker. And also the audio is probably not as crisp as when using a shotgun mic. So let me know what you think in the comments section below. But overall, I think having a rig like this does improve the quality of the video. So as you can see, having a smartphone video rig in which you can add different accessories not only keeps everything in one place, but also levels of the video production quality.  Now, if you don't have the money, but really need one, there is still a chance for you to win this setup and much more. Make sure to head over to this video where I will be explaining you how you can enter the smartphone video competition for my 10K giveaway. If you have any further questions, write me a comment, subscribe if you haven't so that I can keep creating these awesome tutorials for you guys. Thank you so much for watching and I will see you in the next video. Bye.


So, there are plenty of couples that have separate residencies while they're raising their children. However, if you are talking marriage, then it's time to integrate your children into each other's lives on some level. You know, Bennett and Stephanie did that. You know, early on, this is a dear friends of ours who when they met, their children were just about not quite teenagers yet, like nine or 10 or 11. And they integrated to, they met on the soccer field. You know, Bennett and Stephanie met on the soccer field where their children played. So, their children knew each other. They were able, they were friends with one another. So, they were able to integrate their lives.


hoping on Friday night. Well, it's Friday night by RSVP'd. We're gonna go see The Whale, and Brandon Frazier will be there for Q&A after. Heard a lot of Oscar buzz about him and that. That's my prediction. You think he'll win? One, yeah, I haven't seen it, obviously, but I think from what I've heard, it's a good enough performance and he's gonna get the sympathy vote. Very, very possible. I think that's my, I haven't seen any probably ones that are going to be nominated yet. Have you seen Elvis yet? No, okay. So I'm just going off of instinct and my instincts are always right. So that would be my prediction right now, which would be crazy, because I've always thought he was one of the worst actors ever. Really? Oh, yeah, he's terrible. Did you see any of the series, The Affair? No. He's very good. But also, he just announced, obviously, if he was ever nominated for the Golden Globes, he wouldn't attend. He wouldn't attend? He's not going, because the person he was sexually assaulted by was one of the high-ranking people of the press. That's still there? I don't know if they're still there, but that's the person who's sexually assaulted them. Got it. So, obviously, he said my mother, you can say a lot about me, but my mother didn't raise a hypocrite, so he said. Got it. I don't know, I haven't seen it. Once I see that, I will root or not root for Brendan Fraser, depending on what happens. See Elvis too. He seems like a good guy. Yep. Juice! Hey, welcome back to our show, but right now it's your turn, Corbin. I'm Brendan Fraser. And you're also on Instagram, Twitter, for more juicy content. Thanks for your Patreon followers, for your Patreon. Button. Although my favorite movie of his is still George's Jungle. Do you love me some George's Jungle? I never saw it.  Yeah, I know. And so, that's why I never saw it. It fits him well. Yeah. But he's, I'm excited because of the buzz I've heard about this. In fact, my expectations are really, really high, so we'll see. I hear some good stuff. Yeah. I'm still, my heart's pulling for Austin for a lot of reasons. Austin, the butler? Yeah, for a ton of reasons. Today, we got a cricket video. This is called Zero IQ Moments in Cricket. Excellent. I think we've had like 100 IQ moments or whatever the, I forget what the title was, but high IQ moments, I think it was. Right. Okay, so these are, I think it's the opposite. The IQ moments.  Where are you evidence? Zero understanding of the game. Like us. Yeah. We could probably be in this. Zero IQ Moments for cricket. Yeah. You want a good highlight reel? Just add us to the Indian team. Probably. It's not gonna be good highlights. No, no, it didn't say good highlights. Yeah, here we go. Just highlight reel. Wow. That's funny. Couldn't she have just... Yeah. Well, he missed it. Yeah. And then he just gives up. Yeah. And then he throws it and he doesn't even. Yep. Don't give up while the place is still going on. What? I have no idea. I see it. He, what? He, why didn't he do anything? Where? What? What's going on? Everybody thinks the game's over? He did. Like, can I just pick up here, Matt? I don't know. That's so hard. I think he's... Oh! Because he was just lackadaisically going over there. He comes to make it. He put it on the line. He comes over there. Wow. He's out. He's out. Take another look. Is that what he thought? Did he think it was a four? He could have taken his... He could walk faster normally.  Just take a look at that. Look at what he bought there. Great throw by him. Great throw. Wow, he went to sleep. Sounds good, right? He saw somebody very pretty. Yeah. By getting out of the way of the ball and not focusing on crossing the line, he let the ball pass. Got to focus. That is the look of disappointment. Why didn't... Instead of throwing it, he ran it in. You can throw it faster than you can run. This is all your fault. The ball always played well. I'm just going to let this go. Yeah. Just a straight, straight ball. I'm not going to watch it go by. I think he thought he was playing baseball. I think he just got really... That happens in baseball where they get frozen because they're expecting one pitch and they get another pitch and so they freeze. He was probably expecting a totally different kind of ball coming in. I shouldn't get out of the way. Do you need to hit it with the ball, right? Right. And he just picked it up. Did he just hit it again? You can't do that. He's going to have blocked the ball from hitting the wickets. Yeah, he's out. This is interesting. According to the law, he's out of his growth. No, can't hit it. That's one way to do it. Why didn't I think of that? It's good defense. A lot of cricketers think of it. I didn't realize we could do that. It's good defense, really. Just everybody round up around the crickets and put the bats down. Barraza wearing a glove and actually caught the ball and then that was deemed illegal fielding. Five penalty runs, you can see at the bottom of the screen. Right, first in every, there's five penalty runs and that's because of illegal fielding. Yeah, those were some questionable at best decisions. I gotta say, I'm feeling very good about ourselves. Knowing what happened. Stupid babies feel like we are at a place where we can comprehend where we're not just gonna sit there and go. The first year we probably definitely wouldn't have. No, we would have seen this and gone. I don't know what's going on, guys. I think when we reacted to the cricket explained, we were still confused. It was very, it's a yes. Well, it's confusing if you don't know. I mean, any sport that most sport games are. Any sport that you're like explaining in detail, the scoring systems and what you can, can't do and that you've never experienced in your life is gonna be confusing. I'm sure if I explained football, American football to a lot of you.  Without, of all the sports I've ever been exposed to in my life, nothing even is a close second to NFL football or college football. American football as we know it. It's a complicated game, really complicated. I mean, you'd think that take this ball, you try to get into this end zone. There's a lot more variables there. So much is going on. Stuff you can do, stuff you can't do. Just, it's amazing to me the number of plays. Scoring system, you get six points and then you kick it and you get an extra. The number of plays that both an offense and a defense have to learn, but especially an offense and the variations on those plays, there's literally, there's books. Like the playbook is a binder that's like that thick for an NFL team. And the quarterback needs to know it all. All of it. Yeah, hopefully all of them do, but the quarterback has to know everything. Yes. It's probably the most complicated. I think it's been voted like the hardest position to play in any sport. Yeah, the most complicated in any sport to do at a high level. Because there's just, there's so much you have to know. And obviously you have to also have the skill.  So it's crazy. I get it.  I didn't create the name. No, we didn't. Sorry, but it's... I love, I love me some American football. Yeah. But yeah, that's cool. It was fun. That was good. It probably wouldn't be fun if it was my team making these mistakes. No, could you? So embarrassing. Oh man. Yeah. Especially the guy that just gave up. Yeah. I missed it twice. See, that's bad. It's one thing to do a bonehead play where maybe you didn't realize, okay, I stuck my hand out and I didn't have the ball in that hand. But just to be lazy, that's not good. Not a good look. Let us know what other cricket videos we can react to down below.


So relationships are kind of like playing Jenga, but like with your heart. You stack your hopes and dreams on top of each other, hoping that everything will stay in place. But one wrong move and the whole thing comes crashing down. One moment you can be flying high, and the next you're plummeting towards the ground. So if you're struggling to make a relationship work, don't worry, you're not alone. Sometimes it's like trying to solve a Rubik's cube with one hand tied behind your back. It's tricky, but not impossible. Just remember to keep your sense of humor handy, and who knows? Maybe you'll end up building a sandcastle that can withstand the tsunami after all.