The science of a falling drop

1:37:08the falling drop. The first paper we will cover actually got him on the cover of Science. Woo. Um, still a a great white buffalo for me. Not just a cover. I mean, I just want to get into science. >> Uh, many of you may have noticed uh in between us, someone who made it to the cover of Nature. >> Yeah. >> Uh, happens to be behind us in studio, >> but that's not what we're focused on this episode, but it is there. >> But it is there. So, yeah. So, so he's been on the cover of Science, and this is what it's been about. Um, it's about what how drops disattach or deattach from a faucet. You

1:37:51know, like imagine you've got your faucet and you turn it up to just a tiny bit so that like individual drops are coming out of the faucet. >> You drip drip. You get a little drip. >> You get a little drip drip. >> What is the physics behind that? in the 1994 science paper. It's called A Cascade of Structure in Drop Falling from a Faucet. A >> great great title, by the way. >> We talk about titles a lot. >> This is a good one >> on the show. >> Yeah. So, what he ended up doing with his with his um students there is photographing drops made from mixtures of water and glycerol. Why glycerol? Because glycerol has a really high viscosity compared to water. The

1:38:33question they're asking is, does viscosity affect the dynamics of how this drop >> deattaches from the parent drop that's on the faucet? >> How drippy is my drip? >> Yeah. And this is a classic golden goose type of award because at first anyone would be like, >> really, >> really, why do we care? Well, there's a lot of really interesting physics that's happening there that I didn't quite appreciate, I have to say. So let's take a look at this particular image. Okay. This is figure one from their paper in a that's pure water. Okay. And you can see that the the drop is kind of deattaching. And these are all photos

1:39:14that are taken with a high-speed camera. There's a strobe light behind him that's illuminating the stuff and then the camera is kind of taking photo photographs that way. Um in a you're seeing a water droplet disattached. This is pure water. And you can see that the the the sort of trail the the part of the part that's hanging between the faucet and the droplet that's before it >> before it pinches off. >> Before it pinches off. >> Yeah. Before it deattaches is very short in E. That's pure glycerol. >> Look at how large the

1:39:54trail is. >> Oh yeah. the little the spittle the little >> which and again would you think who who thinks yeah and and this shows clearly that the more viscous the liquid the neck we're going to call it the neck the neck is going to be very long and thin and near the the lower end the smaller the neck appeared >> this is the key thing he showed that as the drop approaches the spot of separation the neck doesn't simply disappear there's a lot very cool dynamics that are happening right at the instant where the deattachment is happening. Okay? And it has everything to do with viscosity. The reason why we want to start introducing glycerol is

1:40:35because it increases the viscosity, but it doesn't increase the surface tension in the same way. >> Okay? So now we're sort of disentangling >> viscosity versus surface tension. And you would think that surface tension is everything when it comes to making a drop what it is. I mean, that's sort of what we learn about in high school and undergrad physics is like surface tension is what keeps a drop spherical. The fact that like um a water water wants to minimize the amount of surface area and the best way to do that is turn into a sphere. >> Is this when you've seen probably the memes of people playing the game of they try to fill the cup of water to the top and then whoever makes the first drip go over the edge and then there's a little bit and it's like everyone's always so

1:41:15shocked at how much water is still on the top before it drips over the edge. That's a classic experiment where you get like a penny and you try to jam as many drops as possible, right? And the classic the classic explanation and it's true is that it's because of the surface tension of the water that you don't want the water doesn't want to break >> the um the drop. >> This experiment is showing is surface tension is not everything. Okay, viscosity has a lot to do with it. We've talked a lot about viscosity in the previous episode, so I think you'll get a kick out of this. So, Here we're seeing a mixture of glycerol and water. And what they're doing is zooming in on that moment of separation.

1:41:57It's kind of like in the last episode when we talked about how we can rescale time as a countdown clock >> to some critical phenomenon. In this case, there's a critical phenomenon that's happening, which is the moment that the water droplet separates from its parent water droplet. as we get closer and closer to that moment, what happens to the neck? Okay, on the left hand side, we're seeing a sort of zoomed out picture. And on and the other two, B and C, we're seeing timestamps getting closer and closer to that moment of separation. And here's what I want you to notice. In the middle, you've got a single neck. >> Mhm. >> As we get closer, the single neck forms

1:42:40an even smaller neck. >> You see? >> Mhm. It's kind of like a fractally >> self similar type of behavior that's happening in in a there's a one long neck, but the one long neck >> creates a smaller neck and then that smaller neck is going to create an even smaller neck, right? There's this critical phenomenon that's happening that's it's like a fractal-like cascade. Uh I'm going to be annoying. As to approaches zero, we're going to infinity. >> Yeah. Yeah. the number yeah you could you could think about the number of uh the number of cascades is going to go to infinity in some sense now obviously this is it's not going to happen till

1:43:20infinity because just like the Navier Stokes equations at some point you're going to run into the molecular barrier and you're going to be like you can't get smaller than the molecules and things like that but it's still very cool that you know for the regimes that we care about there is this self similar >> type of response that's happening >> that's and it's so funny we just did the >> and the scale is shrinking and so in that paper he one he showed the experimental evidence of of this type of stuff happening and then he solved numerically the Navier Stokes equations and he showed that this does happen but only if there is noise in the system this is what's kind of interesting um if there's no noise then the neck becomes this self- similar sort of power law thing

1:44:00>> that doesn't have these discrete >> types of you know >> tuck tuck and then it becomes smaller and smaller >> it's not this rhythmic uh construction >> but if If you introduce noise into the system, then on the right hand side, you see the self- similar thing where you've got a big thing and then you zoom in. That's the second panel. And then the second panel has an inset that zooms in over there and you see a even more self- similar sort of tiny neck >> happening, right? >> And the details change from run to run, but you can repeatedly create these necks and that is robust. the details can change, but the fact that these necks exist and they're self similar, smaller and smaller and smaller, that is a robust phenomenon.

1:44:40>> We we love to see again it's it's these um these signals in observation of something interesting. And then a lot of times I feel like when we talk about it, it's like who zoomed in more. >> Mhm. >> To just double click to make sure that just because we see it like this on the outside, it actually looks like that on the inside. And >> I mean from a physicist perspective, this is already very cool. >> Yeah. Okay. Like this is a phenomenon that like you're seeing like a fractally nature happening in like the disentangling of droplets. That's kind of cool. Um, from practical standpoints, it's not just like inkjet printers. You

1:45:21can have sprays, micrfluidic devices, which are used a lot of times in biomedical applications when you want to like separate out cells, you want to separate out DNA, small little um micro thingies for lack of >> We got a thingy in this episode. You did four hours last time with not a single thingy and people are >> Yeah, people are Well, you know, there's tremendous applications here. So, so it is it is quite interesting that like such rich phenomenon can come from something that never really thought about. Um 1997, this is the next paper that we're going to talk about. This is the coffee ring effect. There's a whole Wikipedia article about it. >> Mhm.

1:46:01>> Um the idea is that when you have coffee