Saptarshi Basu - Spectacular Voyage of Droplets: A Multiscale Journey to Extreme Flow Conditions

追加: 2026-06-03

[00:01:29]Hello. Hello.

[00:10:24]Bonjourus. Hello everyone.

[00:10:29]Um so I will continue in English. It gives me great pleasure today to welcome Professor Saphashi Basu from the Indian Institute of Science in Bengaluru which some know as Benalor in France Bangalore but u Bengaluru is the the Indian uh official name of the the city which uh is well known to the French. It's a very advanced technology and also the the site of the Indian Institute of Science which is a special place for for research in India. Um he was uh hired as faculty there since 2010.

[00:11:14]uh received his PhD from the University of Connecticut in 2007 with uh professor Becky Setigan who was uh um from Caltech I think.

[00:11:27]>> Yes. And he was a student of >> Marble was one of the founders of the Jet Pro Laboratory >> at Caltech.

[00:11:37]>> But maybe the founder of the JPL was Chinese. Nobody else that's what you told me. So that was not Marvel. It was Chen. Okay, we will have to resolve this issue. Who founded the JPL? Uh, unfortunately, I went to the to the US last month and the JPL doesn't exist anymore. Now, it's the the Department of Aerospace.

[00:12:02]>> It's very weird. Okay, that's life and life continues. Uh so you you have been also at the University of Central central Florida. You are a fellow of the Indian National Academy of Engineering, the Indian Academy of Sciences and many other societies. Uh you received a JC BS grant and many other prizes and medals. You published uh many papers. But uh uh to me I'm really admiring your work on atomization which is on this slide and uh just for that work I'm very eager to uh to listen to you. So please professor Bass.

[00:12:44]>> Thank you. Thank you so much uh professor Zeleleski for the kind introduction and for the opportunity to come here and talk about some of our work that we have been doing over the past few years on you know droplets basically droplet atomization. Mainly the idea of presenting this work is how does atomization happens under extreme flow conditions what we call catastrophic breakup in the literature.

[00:13:12]We're going to look into a little bit in details into that phenomena in particular and advocate certain scaling arguments. Okay, which you may or may not agree. Uh so you can have an healthy debate also on that. But the idea is that this is one area of uh research which has been widely I would say neglected just because catastrophic for a long time was something that people said we do not know what is exactly going on. So we are trying to go into a little bit of depth into this. So uh apart from this we work on a lot of stuff in the lab. This is this this uh this collage essentially a calitocope gives an idea that we uh divide our problems into uh different velocity scales and length scales essentially. So at the very low velocity small lens scales you have this microch flows and this is for example a drying droplet of blood. Okay. And we study this for varieties of purpose for point of care diagnostic development and stuff like that. At the moderate velocity and small to moderate scales you have got a lot of problems like droplet impact. We have vortex droplet transport. This is a idea that we advocated uh for basically cleaning up fluid in the case of an oil spillage using a vortex phenomena. This is interesting because this we did during the COVID era when the doctors came to us and asked the question that when they do this gluccom testing uh this is essentially done with a vortex puff hitting your eye. They wanted to know if there is atomization that actually happens because of the tear film because the tearfilm might contain the virus. So this is an experiment that we did and uh for them for uh basically for the opthalmologists and then uh we also did some work on droplet impact on face masks. It was also done during the covid era just to see uh advocating the idea that mask normally people look at mask efficiencies but we said that if we cough when you are wearing a mask and if the mask is improper then these droplets can actually atomize further and become aerosols. So that was essentially uh what we did over there. This is a uh this is a nice little experiment that we did where we understood the flow within a soap bubble for example as the bubble is actually inflated. So and uh at the real high velocity small lens scales the work that we are going to present over here is the shock droplet interaction which professor Zeleleski was talking about and even at larger lens scales this is actually a sector combuster a gas turbine and this is the flow basically the combustion that happens within this sector combuster. So the idea is to that from very low Renault's number to very high renals number we cover a lot of regime okay and most of these works are multi-phase or at least two phases are involved in all of these work so this is the scales of the problem in the vasu lab and the work that I'm going to present over here is basically shock induced secondary atomization so this is how the atomization phenomena looks like and this is how the droplet actually breaks up it's highly catastrophic as you can Okay. But as you go down into the scale, you get to see this sub-secondary breakup structures. So what we advocated it's a multiscale cascade of deformations which ultimately truncates in what we call a ligament mediated droplet generation. So this is the end of the pathway right as we go and zoom in. So this is about say 50 microns.

[00:16:48]This is 100 microns and this droplet scale is about a couple of millimeters or maybe 1 to 2 millimeters. So we are going to explain in details that how this interfacial wave cascade actually works at very high disruption which is essentially at very high web number.

[00:17:04]Okay. So this is the entire area and this ranges a wide range of what we call the spatiotemporal scales. Okay. So droplets under extreme conditions for this audience we don't need to give a whole lot of justification why this is important. So primary atomization many people have worked and this is also from our work where we show actually how a sheet actually flaps and breaks up. This is primary atomization and then you get the secondary atomization downstream of the primary atomization with a little bit of an overlap. So all of them are very important if you go if you want to deise new fuel injectors. We did some work on metal powder production for example. So you need atomizers for liquid metal atomization as well as anything from agriculture to hypersonics. You need primary and secondary atomizations and this has of course got a whole gamut of benefits that you can see over here right from combustion efficiency to improved drying. So I think the application is already there and some more that you know a liquid jet in a supersonic flow or a drop impact on a mark II projectile. This is the metal powder production that we did with professor Cameron Tropia. So this is what we call a closed coupled atomizer where you actually atomize a liquid metal and this is a sheet atomization coming from our work. Uh this is in swirling flow. So this is actually an example of primary atomization. Okay. So I think the application context is quite clear. Now if we look at the classification of breakup historically what was done and again for this audience this is a slight amount of redundancy but as you can see that initially when the webber number is low you get the vibrational mode of breakup as you go on increasing the webber number you get the bag type then you get the multimodal type then you get thinning and ultimately somewhere around here you get catastrophic breakup. So this means that as you increase the aerodynamic loading or in other words the Weber number is increasing you migrate from a simple uh or a very controlled type of a breakup to all the way where hell literally breaks loose and uh you can read some part of this in the recent annual review paper that we wrote over there. So this part is not uh something that is unknown. So we look at a few examples.

[00:19:21]This is a bag breakup web number of around 12 and that is how it happens.

[00:19:26]This is a multimodal breakup where you can see a bag and a stamman essentially.

[00:19:32]All right. This is where Weber number is a little bit high. So this is a sheet thinning phenomena that actually happens around Weber number of 200 and this is 14,000 remember. So this is where you can see basically you see a mist all over and this is atomization occurs across the droplet surface. So this is how progressively uh you go up in the Weber number ladder quite a bit to get all these wide gamuts of breakup. Okay.

[00:20:00]So we are going to focus on this particular part. So this was a famous map by Jerry Faith done in 1995.

[00:20:08]If you look at this particular map, it is basically a geometrydriven or a topological kind of a map where he bucketed essentially in a Weber number on number space. He bucketed what are the kinds of breakup that you can get as you move up in the Weber number and as you move up in the onsa number. So essentially what you see is that up to a certain ons number nothing really happens. It's all a function of web number primarily once the ons number crosses a certain threshold the curve starts to curve upwards essentially. So the viscous effect starts becoming more and more important in this particular region. This is totally governed by what we call thus the aerodynamic loading over here. So this was a famous map and it is independent of onsort number for quite a bit. But the old regime map I'll tell you what happens. It suffers. It is only a geometric indicator or it's basically a topology indicator. You say it's a bag or you say it's a it's a bag with a stammon and stuff like that.

[00:21:10]Okay. It lacks what we call the physics-based intuition about it. And it only spans a very small range of Weberon number. Above that you call everything catastrophic. So you bucket everything above say 300 and say these are all catastrophic. Okay. So you don't need any separate demarcator. Okay. Above this number. So it has got a vague interpretation. But we will show in the later part of the talk that this is basically a cascade of alternating Kelvin Helm and RT instabilities happening at very rapid scales which is what we call as catastrophic breakup uh in the literature. All right. So we did a reclassification of the breakup based on the instability mechanism. Okay. So this is the first thing that we did. So the problem is broken into several pieces. First and foremost there are two instability mechanisms. One is the relay tailor piercing and the other one is a shear induced entrainment. This is basically the relay tailor instability and this is basically the Kelvin Helmold's instability. How it happens?

[00:22:09]You have an air flow around the droplet.

[00:22:11]Okay. So what happens is that the droplet initially deforms in both the cases. Now in the case of relat piercing you have an accelerating uh you know lighter fluid versus heavier fluid. So you basically develop the wavelength or the instability on the droplet surface.

[00:22:28]This leads to the formation of this bag and this central statement. This is what happens in the case of a relay tailor uh in instability. In the case of Kelvin Hellbs these there are waves which are generated okay at the forward point.

[00:22:42]These waves basically migrate to the equator. They forms this sheet. This sheet subsequently strips and breaks up.

[00:22:49]Okay. So this is the conventional view if you look at it from an instability point of view that what leads to the breakup that you see uh overall and this is an example of shear induced entrainment. This is an example of a back and statement breakup. So how it happens if you look at it carefully from vibrational to multimodal or part of multimodal it is dominated by the rel piercing. Okay beyond that from multimodal all the way up to catastrophic this is basically shear induced entrainment. Okay, this is the classification but this is incomplete in the sense that when you look at these are very high fidelity image of the droplet as it atomizes. So you you see you create the Kelvin Helmold's waves you forms these sheets these sheets form ligaments and the ligaments breaks up into drops. Now when the topology is changed when you actually have these pro protrusions appearing on the droplet surface what happens is that these protrusions are actually accelerated.

[00:23:46]Okay, as a result of that you have what we call an azimuthal relayer instability that develops at the top of the relay tailor of of of the Kelvin Helmold's uh topography. Okay. So the primary driving mechanism is still Kelvin helm molds and even on the top of this you have an imposed relay tailor instability that actually happens and ultimately you can have asimutal as you can have longitudinal and ultimately this ligament breaks up by the capillary mode which is basically the relay plateau instability. So you see one is a driver and the other ones basically build up on the top of that just because you have changed the topography accordingly. So but the dominant makeup breakup mode is still this. Okay. So this leads to a restructuring of the jerry faith's map where we now have the sheer induced entrainment and the rel plateto all these things mapped. So now it is no longer a geometric based phenomena. It is basically an instability based uh map and on the top of that we added a secondary axis which takes into account the mark number the compressibility effect essentially which uh now you get a three-dimensional map mark number on number and the webber number okay so this is the map that you get is a 3D map okay but this map also is better because now you have an instabilitydriven map but it is still static in nature it is unable to capture these kind of events or the progression of events that how it actually goes to that particular breakup mode because it is not just the static shape the static shape the shape actually evolves before it finally atomizes. Correct? So this is an unsteady topology evolution is it is unable to capture it totally and the breakup temp spatiotemporal scales are not captured at all. This is just a map which you can kind of use as a first order or maybe a zero order estimate. Oh okay this is sheer induced entrainment.

[00:25:41]This is relay plateau etc. Okay. And it ignores completely the cascade behavior of the deformation concerned. And on the top of that you have a viscous dominated region. Nobody knows how it actually came. Why the curve actually curves up exactly the way that it does. Okay. I mean what's so special about this? Okay.

[00:26:02]What is this uh what is so special about the onsen number limit that you have? So this we are also going to deduce and show that why uh this line comes into the picture. Okay. So this is the regime map. It's a new regime map but still incomplete, very static and still incomplete. So if you now want to probe this regime map and watch the dynamic evolution of the droplets, you can do it in varieties of ways. One is basically a drop tower. Basically you drop and the velocity increases. This webber number goes up to about um order 10 or maybe maybe 10 around 10ish. So you cannot do a whole lot. Okay, this is very suitable for raindrop type of experiments as this paper by Emanuel Viller will actually show. You can also do it in a continuous jet. That means you have a jet and you in inject the droplet. It's like a droplet in a cross flow, right? So it penetrates the shear layer. Okay, this comes from the work of Naven and you get uh the atomization of the drop.

[00:27:03]Okay. So here the weather number you can you can slope up to about 100. Still not high enough for all practical purposes.

[00:27:16]So it is not high enough for all practical purposes to go into that you know the catastrophic mode. The way that we did it is use a shock tube. Okay. So a shock tube we hit the droplet with a shock. it you can go up to a Weber number of approximately 10 ^ of five and there you can probe what happens to the droplet but you do it in a special kind of a way so that you get the high fidelity measurements as well it's not just you know blast it with a shock okay so that brings to the shock droplet interaction and this is the shock facility that uh me and Alok we together made okay out of an Indo-German uh science and technology project so what happens is that you basically levited the droplet using an acoustic levitator because you basically fix the droplet in space and this shock tube works in any direction. So that means it can operate vertically, horizontally in whatever way you want. You can use different contraptions and you can direct the shock. You can also condition the shock front. Okay, so as a result of that, this is how the shock front actually looks like. This is where the droplet is stationed and you basically hit the droplet and then you image it. So this gives you very high fidelity measurements. Okay. And the interesting part is that you can also attach a inert chamber around this shock tube and you can actually probe oxidizing type of fluids as well. The for example metal droplets which can oxidize if you do it in air you can do it in a nitrogen environment so that you can uh you know probe the atomization behavior. So this shock tube facility we have used it for polymers, for Newtonian fluids, for liquid metal, for clay and basically everything under the sun and it all works beautifully. Okay, so this is the and the size is approximately half my footprint. So it's half of my size and exactly my footprint. So it's very compact and uh we actually have a patent also on this. This allows us to go up to a mark number of around four and a Weber number of around 10 ^ of five. So that makes you know we can do very sophisticated experiments at very high web number limit. All right. So the global overview is that this is the shock front. It interacts with the droplet. You can see the reflected shock. Nothing happens to the droplet.

[00:29:39]Okay. When the shock actually passes through it. Okay. But what happens is that after the shock has passed the entrain flow which is called the CVR or the compressible vortex ring that is entrained behind the shock that actually interacts with the drop and it leads to atomization. Two examples are shown over here just to illustrate that this is a relat piercing bond. This is a shear induced breakup board. All right. So this is the two pictures and you have stage one which is this particular stage. This lasts for microsconds. This one lasts for milliseconds. Okay. So together the entire phenomenon is over by around say 30 40 50 millisecond stops. Okay. Everything is over. So you see whatever phenomena is happening uh within this this uh this time period.

[00:30:28]All right. So this is a global overview and to illustrate the point as you can see this is web number of about 1300 all the way up to 8,000. Okay. You can see as you go on increasing the weberon number you form the Kelvin Helmhold's waves as you can see over there and uh you have first you have the droplet deformation in all cases then the Kelvin Helmhold's waves these waves actually goes towards the equator and this leads to the droplet stripping essentially the same thing that I showed just broken up into several pieces of images all right so you have the global instability so if you look at the Kelvin Helmo's instability these are perturbations that are created on the front you can clearly measure them with quite a bit of accuracy. So what happens is that uh if you now do a simple linear stability analysis, okay, we will show why that is insufficient in a minute. But just as a primary first order estimate, if you just do the linear stability analysis of the wavelength, the first set of wavelengths that are produced on the droplet surface and if you introduce the finite vorticity thickness method, there are varieties of other ways in which you can do it. Essentially it takes into account the boundary layer in both the liquid phase as well as in the gas phase. Okay. So that you don't have a velocity jump. You get a fairly you know uh good match with the experimental data in terms of the primary wavelengths that are created. Okay. And you can do the same thing with your azimuthal relatability.

[00:31:59]Okay. Again you can calculate the ligament spacing and it also shows a reasonable patch up to the order that you can see over here. Remember these are experimental data. Things will get multimodel very soon. This is the first order estimate that we have. Okay. And these were all done by imaging at you know side view and the top views and you know careful imaging. Okay. It's a good match considering it's a very simplistic model to begin with. All right. Now there is one other thing that we need to to tell that there is always a spatiotemporal race between the relability and the SIE waves. This is always the case. the SIE waves always wins because it has got a faster growth rate. Okay, so the idea is that why does the relay tailor instability appear at all? Okay, so this comes from uh from another play that if you divide the droplet diameter with the primary Kelvin Helmold's waves. Okay, if the droplet size is such that the Kelvin Helmold's waves cannot fully develop. Okay, you do have the formation of the rel waves in those cases. So that you can see over here across a large Weber number limit so long as the droplet size is small you have a you know emergence of the relay plateau of the rele tailor instability.

[00:33:22]This is what we call the compatibility criteria. So it is not just a growth rate. It also has to be spatially compatible. You have to create the waves okay in the available space that you have got. Okay. So uh that is what we see and you know this is also uh we put a lot of data in this particular thing.

[00:33:42]So you you can see if you normalize the droplet diameter with a Kelvin Helmo's wavelength and plot it with webber number. Okay, these are the regions when the droplet diameter is small. You have a clear emergence of RTP before SIE actually takes over. This is not just our data. This is multiple data from different papers. We have all normalized it and packed it together just to prove the point. So the compatibility criteria is rather important. Okay, when you do the breakup, it's not just the growth rate, it's also the available space.

[00:34:13]Okay, that is also important. Okay, what about other droplets? Okay. So we have just shown Newtonian. So non-newtonian and complex fluids molten liquid metals we have done all of them. Okay. And uh complex fluid was done in association with a look over here. So the idea is do they exhibit very similarity in the mechanisms. I'm just talking about the mechanisms that the emergence of this SIE and the relay taylor and then the relay plateau etc. Okay. Indeed it is.

[00:34:43]So this is water this is polymer. This is gene. forget about the last stage of the breakup. But if I just remove the labels and show you up to this just this particular block, okay, you won't be able to make much of a difference that which one is which. Okay, so the essential idea over here is that they visually up to a certain point they all look very similar. Okay, so and we have shown that if you probe it, you will see the emergence of the same thing. It is the once again the SIE and the relay tailor instabilities and how the switching actually happens that leads to the deformation and the you know the eruption of the instabilities that ultimately leads to breakup the the effects like for example in the case of polymer the elasticity that comes into effect only at the last stage okay when this is actually getting stretched okay and it is going to break up okay so this is basically a two-dimensional map.

[00:35:42]Right? Now, this is addresses a part of the static thing that we talked about.

[00:35:46]Okay. Now, it just puts them in a stage-wise fashion which has got the time information inbuilt into it. So, you have a droplet, there is a deformation phase and then there is this Kelvin, hell moles or relat waves up to stage two. They are universal across all liquids. Okay, across all liquids so long as a Weber number is maintained.

[00:36:07]Okay, it is only at this particular stage, the last stage where things like viscosity, elasticity and the complex composition comes into the picture.

[00:36:16]Okay, so up to this, this is a map which is different from what I showed earlier because that was just a static map. Here we at least put in some of the time information that how things should proceed up to a certain point and how things are universal up to a certain point. Okay, so that is good. So we decided okay this is something that one should look at in the in the future. But then comes the real interesting part that we still did not address how the spatiotemporal scales actually evolve.

[00:36:48]Okay. So the evolution mechanism is vitally important and that is the main crux of this particular presentation. So if you look at a droplet over here okay as I already I told you so there are azimuthal instabilities. Okay, there are sheets, there are hole formation, it looks pretty messy though we say that it is Kelvin Helm moles and it is really tailor. Okay, but still it is messy. How do you analyze this particular problem?

[00:37:14]Right, you have to show some light into it. Right, it's not sufficient just by saying okay this is happening primarily due to this or primarily due to that or it's a combination of the two, right?

[00:37:25]That is not not what we what we aim for.

[00:37:28]Okay, so we decided to take a closer look at the stripping process itself.

[00:37:33]How does it happen? So you see this is a disintegrating droplet. This basically is a pancake shaped droplet with the first uh you know the Kelvin Helmold's waves that are already created on the surface. You can see that right? What it does is that now you have an incoming flow. Now this incoming flow can have a disturbance or it can be a uniform flow depending on what type of flow you have.

[00:37:55]What happens is that this deforming droplet now starts to modulate the airflow locally. Okay. So locally you get all this vortex shedding at these topological points. All right. And the same thing happens across each of these topology. So the flow is getting deformed. Right? It's essentially what we call a two-way coupling. Now if you look at a small section right over here.

[00:38:20]Okay. This one has got a local Weber number. It has got a local undulation feature. Right. This has also got a local Weber number and a local undulation feature. Now this particular undulation features now strips and it exposes a new surface. Okay. So what I'm trying to say over here is that the local deformations and the local velocity profile here matters a lot when you ultimately are treating this kind of a problem. And as you can see that this is also a cascade in a way that this process actually repeats and it happens.

[00:38:54]over multiple length scales and time scales. Okay. So that is the that is the that is the whole idea in a nutshell that these waves undergo a stripping process. It's a cascade process to begin with. Okay. Now if you now look you take a droplet this is the deformed droplet and this you take a small very small section out of that droplet.

[00:39:18]Interestingly the if you look at the droplet the global weber number is about 2,000 right you are looking at a very small section which is about say 100 micron what you see over here and you have to just do a lot of imaging to see these features okay you see the formation of this bag you also see the formation of this ligaments okay now this was surprising because bag is something that we we done and dusted it long time back it happens at lowber number. What has to do with catastrophic breakup? This is the general consensus, right? Where is the bag coming from? But at a very small scale, you do see the occurrence of these bags, you see the occurrence of these ligaments and all this kind of stuff. Okay. So, we are going to advocate that okay, ultimately all the droplets, every type of stripping process actually ends with something what we call a ligament mediated droplet generation. We'll come to this in a little bit. Whatever is the topology at the end of the day, you will get this ligaments highly corrugated ligaments and this will ultimately atomize. But what is the general feature? Why does these bags actually happen? So here we propose something which is called the self similar breakup topology. How is this how is how does this thing work? So you say you take a droplet and you have a low enough weapon number say around 12 or 15 or 20 you do get this bag and you get this nice you know break up this everybody knows you take the same droplet now at a very large webber number say 2,000 okay instead of 20 now have 2,000 like two orders higher now if you look at a very small section the local velocity scale and the local protrusion that is created It produces a local Weber number the value of which is around 20. Moment that value is 20. Okay, it forms locally a bag out of that small protrusion. This is not the whole droplet. This is the whole droplet. This is not the whole droplet. This is just a protrusion of the droplet and it forms a bag. The bag breaks up and ligaments comes out of this ring. So what we are proposing is that these are topologically similar but they occur at different scales. And what actually connects them is the Weber number. At the droplet level, this is the Weber number. At the undulation level, this is the undulation velocity and this is the undulation length scale.

[00:41:47]If these two are the same, then whatever features you are seeing here, those features will be replicated here alit in a small segment. So as if these protrusions are like independent blobs like independent drop-like features which basically follows the same physics that you would normally get if this was a low enough weber number. So you see the cascade that at the end of the day no matter what is your Weber number right and the smallest scales when the Weber number sufficiently declines just because of the length scale and the and the velocity scale at that particular point it actually can actually mimic features which you get at the you know at a small web number but for a large droplet or a global scale. Okay. So this is the topological similarity. This can further be now explained that you first look the deformation cascade. So you have a flow velocity, you have the first generation deformation which is basically the wake feature and this kind of a a you know the droplet deformation that you get. Once you look at this you get this topology. Okay, this topology if you just kind of invert and look at it like this. This will form these are finite Kelvin Helmold's crests. So you get this flow features that are produced around this now get stretched this flow feature. This forms like a liquid sheet over here and this liquid sheet if you look at it from the top view it's like a tank that is actually protruding into the flow. If you look at it from the top view that means from the top here. Okay.

[00:43:25]because it moves like this. This actually creates locally the the rel instability front. This instability front now gives rise to this bag like feature. Exactly why how the relatability normally would work and then you get the fourth generation where you get these ligaments the ligament breaks up due to the rel instability.

[00:43:47]This is the full cascade of events that happens ends with the fourth generation deformation and breakup and it exposes now the fresh surface. The process repeats if your flow has a continuous you know if you have a continuous perturbation of the flow field in this case we don't because it's a shock it goes it is a finite time scale disturbance. If you continuously produce it it will continuously go on into this tripping mode. All right. So this cascade actually terminates. Therefore we say with a ligament mediated mechanism which generates the relay plateau. Okay. So this is what we call the subsecondary breakup process which has got topologically a self- similar behavior. All right. This was good. And you know this is again to reiterate whatever I said over here. The growth rate the cycle time is at approximately given by 2 pi divided by omega i. Now this is a very fast cycle. So this happens so fast. Okay, so it is very hard to basically diagnose the entire front, okay, in a normal practical flow situation unless you anchor the droplet and do all these fancy things that we kind of did. Okay.

[00:44:58]All right. So, uh this is the entire cycle process. But this is not the end of the story. This shows this beautiful breakup. We have established that there may be some self similarity over here.

[00:45:10]Our job is still not done because ideally as a practical guy you also want to predict what will be the droplet size coming out of this right you know things like gamma distribution the rosen rumbler distribution works quite well in practical devices because you can kind of they are all curve fitted uh to the droplet so you measure the droplet size and you somehow uh you know do this but uh of course this is a process which is very fast so Therefore, uh using any traditional tools to measure the droplet size is a problem. But we are not just interested in measuring the droplet size. We are also trying to predict that why the droplet sizes should be like that. So the droplet size measurement was done by my student Jatin. So he used and with with Camtropia. So this was done from a technique called depth from defocus technique. So the main problem with this kind of shattering events is that 50 milliseconds 30 milliseconds is the total time as a result of that stuff like shadowgraphy normal shadowgraphy is not going to work because you have lot of droplets which are not in focus and stuff like PDPA which is like the interferometry based techniques they are too uh you know they require a lot of samples basically the acquisition time has to be high enough to get a meaningful sample not really valid over here. So we intentionally used the depth from defocus that means from the blurry kernel you can reconstruct both the droplet size as well as the velocity.

[00:46:42]Okay. So this is also a new technique.

[00:46:44]So this is one way of saying is that for finding out the physics you develop new techniques very similar like when people develop new algorithms to probe into a problem. Okay just because you need to know what is going on and this was exactly what was done. So we could develop the droplet sizes as well as the droplet velocities in different windows.

[00:47:03]So that means at least we divided the measurement uh you know total time into three windows. So you can imagine these are like 10 to 15 milliseconds each in which you could construct the PDF construct that what is the size distribution that you are having and what is the velocity distributions that you are. So that was great. Okay, using this now how you use this but before doing that we did one more stuff and this we did it in two ways. I am going to show the first way first and then uh you know uh propose the second way okay and you can debate me as far as you want. So what happens is that we decided that there is a total aerodynamic energy right this aerodynamic energy is fed to the droplet. This this deformation actually percolates at the smallest scales without say any viscous dissipation happening in the picture.

[00:47:59]And where does this deformation actually go? It creates new surfaces at the smallest scales. Okay, smallest scale.

[00:48:06]These are the daughter droplet sizes that finally you get. So this is fed at the top scale. This is what comes out at the bottommost scale by creating new surfaces. Where will this energy go?

[00:48:18]There's no viscous dissipation. So this energy has to go somewhere. If we just do this and like two pages of math after this, what you can predict is that the average droplet size provided that the aerodynamic forcing is sufficiently random or sufficiently high, you are going to get a scale where the average droplet size scales as Weber number to the power of minus one/3. So that means as the Weber number increases, let's do the sanity check. As the Weber number increases the droplet size is supposed to come down.

[00:48:54]>> Yes. Yes.

[00:48:56]>> So, so, so there are factors. Okay. I'm just talking about the front part of the scaling. Okay. So, this is not you can normalize it by the initial diameter of the of whatever that you are trying to do. So, this scales as Weber number 1/3 and this is exactly what we are talking about. This is D / DN essentially. So you get a scaling and this is not just our data. This is all data from whatever sources we could get. All have been pumped in together. Okay. And you get a Weber number minus 1/3 scaling that starts to happen.

[00:49:32]Okay. So, so this was I thought was a was a great finding because we could finally say that what will be the average droplet size distributions that you are going to get out of this uh particular scenario. All right. Now, oops.

[00:49:55]What happened to this now?

[00:50:00]Okay. So now what we did was that after that we constructed the PDF okay of the droplet size distribution which is normalized now by the average droplet diameter okay and you plot it for all the cases and this is basically a compound gamma distribution you we found out that this PDF was a self similar PDF and it is invariant with respect to weberon number so what we are saying the average diameter scales as we number to the power of minus 1/3 n the droplet number density therefore scales as weber number and the pdf or the normalized pdf of the droplet diameter distribution is invariant of weber number okay so what you need as a practitioner that if I give you a priaryy that your average droplet diameter has got a weberon number minus one/3 dependence and your pdf the normalized pdf is independent of weberon number you can basically calculate whatever droplet sizes you want. All right. So this was what was done and this actually assumes two other factors. The principal factor is this N that you see sitting over here. This N is basically a corrugation signature that mean how much corrugated the ligament can be and one can show that this maximum corrugation of the ligament is about four for highly catastrophic event. Now if the Weber number is small and small this leads to actually isotropy directionality and this particular distribution is not going to happen. Okay, we did a couple of other things also over here that we also did an integrated approach that means we tried to calculate the cumulative distribution of the droplets. Okay, because this is a blast wave front so it had a inherent DK profile. So if you do that you are also able to match the tail of the distribution. Okay. And we are also able to show that the corrugation PDF or the PDF of N basically it peaks around that four with very little at the sidebands. Okay. Of course it has a little bit of a spread but the predominant feature is arrested within that four. So that is what the main thing was. Okay. So uh so this was good.

[00:52:18]So you could predict the droplet size average size. you could predict the PDF and you could show that the PDF is independent of the normalized PDF is independent of Weber number. So all these things were good. Now we decided that can we extend this ideas further.

[00:52:36]This was done on droplets. How about if you have a sheet or a you know uh a jet okay or any other types of surfaces okay does this phenomena can we extend this and this deformation cascade and stuff like that can we extend this further all right so a general assessment therefore just to look back so this is the fragment length scale after atomization and this is the lens scale before atomization okay and these are all the terrest ustrial events that you can think of. So this for example are the sprays man-made. Why it is so vertical?

[00:53:15]That is because sprays has got a finite initial length scale and the atomized fragmentation length scale that is produced after that can be whatever depending on what is the aerodynamic loading. You have volcanoes, you have oceans, you have meteors, all these things are packed over here. Okay. So what this actually shows is that for the catastrophic event if you look at it very closely. So this is uh this is a large length scale. This is a very small length scale. So as you go on increasing the degree of catastrophe this PDF actually starts shifting more downwards.

[00:53:52]Right? And if the lens scale if if it is a normal vibrational type of a mode of breakup this lens scale is more pushed towards the top. So this is where the catastrophic breakup is most likely restricted in this particular domain. It pushes the PDF of the droplet distribution more towards the you know uh towards the smaller and smaller droplet sizes. So this is the landscape of atomization and I call it a multiscale mess because it is a mess.

[00:54:20]Okay. And you have oceans, you have volcanoes, you have lots of things and these are all active areas of research.

[00:54:27]For example, ocean, how does it atomize and how you integrate wave turbulence with oceanic atomization? These are still unanswered questions. There are lots of groups which are working on that. So, we started with this catastrophic mode of breakup. But we can actually show that you can also take the same thing for a jet and again you have a coaxial flow now. Okay, this is a head-on flow and you can show very similar features that starts to arise and one of the simulation that you showed was actually the mushroom formation but this is actually a coaxial shearing uh of the jet and this actually creates the same type of Kelvin helmolds instabilities and stuff like that that you see over here okay so this is my proposition once again okay once again you know this is supposed to come out in the physical review fluids invited paper in a couple of months time uh this was based on that APS talk that I gave. So what I am suggesting is that say you have a liquid you have a inner liquid region okay and then you have a inner mixing region then you have an outer mixing region then is a inner gas region and an outer gas region you can segment this whole thing okay into many parts okay and systematically people have done a lot of work on this particular region the outer mixing region in fact people who work with dispersed flows actually do exactly that that How these flows actually are carried by the fluid and how they are entrained and how they are transported. Everything is done in this part. This particular part which sits right around here is the part which comes into atomization and how it affects the turbulence and how the turbulence is imposed back on this liquid layer. It's a hot topic of research and hitherto it is kind of still unsolved to the best of my knowledge. Okay. So the idea is that to take a look at these two fragments. So here you have in the breakup region you have this maximumly corrugated ligament theory that I just now said. Okay. There is something called curvature statistics and multihase transport turbulent transport and fractal dimensions. And then you have the droplet size distributions. And everybody knows about the kvogor of hints scale hypothesis which basically tells you that the ad size has to match the the droplet size for it to actually break up. So can we actually bridge these two because after this whatever happens the heat and mass transfer the transport many people have done it okay it is a area of research and many people like Balachandra and others they have been doing it for ages.

[00:57:08]Okay. So this is the part which is still an active area of research because it's complicated to begin with. Okay. Because this is interfacial. Uh so people have done a lot of work on the material derivatives in the case of turbulence that how the material lines deform and all those things. This is also a material line. So how does this deform and how does this scale? These are things that are for the for the so uh as I said that you know uh again revisiting the same thing uh we we stated two things earlier that as you feed energy the energy cascades and it is ultimately goes at this at the at the smallest scale. This is the smallest scale of the droplet and the count is skewed towards the smallest scale and the deformation rate is basically constant in this and that is how you derive this particular relationship. You can also come through it through a time scale argument. This is the matching argument of the time scale. So you have an inertial time scale and you have the capillary time scale. If you take the ratio of the two they scale as Weber number to the power of minus half. So obviously this is not a good parameter to use but however if you do this capillary time scale at the smallest scale instead of ln not you use ls okay and if you match the two then you get recover this webber number minus 1/3 scaling once again so what comes from a deformation casket the same thing comes from a time scale compatibility criteria as well okay so these things uh so this also indicates that there is a generalized scale separation like in turbulence you have a general Generaliz scale separation okay which scales as Renault's number to the power of minus 5x4 I think okay here you have a scale separation which is webber number to the power of minus 1/3 okay largest versus the smallest scale the scale separation that actually happens higher is a webber number more is a scale separation you are stretching the scale further all right now if you also now take the inertial time scale now you calculate the viscous time scale at a length scale say LV okay and you have a concurrence of inertia and viscous dominated events.

[00:59:17]If you compare these two time scales, you can recover that there will be in the Weber number on number map the boundary which uh decides the transition to viscous dominated region is scales as Weber as ons number to the power of minus6 and if you plot this minus 6 you recover uh that Jerry faith map okay where you say that when these curves actually start to climb upwards you can put your own scaling argument and you and say that when it actually starts to starts to move upward. Okay. And this is first principle approach. We didn't do anything funny over here. And you can recover this from this map. Okay. So that is not arbitrary. It comes from a generalized physical principle. And I will also propose two other things over here. Okay. And uh this is once again food for thought that uh how I want to do this is that if you calculate the curvatures of this interface this corugation okay the curvature statistics of this interface what will happen to this curvature statistics this will evolve over time okay as it evolves over time it will ultimately go to a drop which will be given as 1 / d ultimately the curvature right But intermediately when it's a flat curvature this curvature is zero. Okay. And ultimately the final form is 1 / d. Okay. So it will pass through an intermediate set of values this probability curve of the curvature. Okay. And ultimately it will go to this particular value which is nothing but the probability distribution of the droplet sizes. Right? Ultimately that's the end goal. This is how curvature should actually evolve. Okay.

[01:01:05]So this curvature statistics is something that is worth looking at.

[01:01:10]Okay, because in the case of simulations or experiments you have all these statistics. Okay, you can actually try to evolve something good coming out of it. And how to do that is that if you have a segment of the blob like this, like all these strange shapes that you see, when you actually have a negative curvature like this, this implies that the ligament is going to neck and you know pinch. Okay. If you have a positive curvature over here, this basically designates that you are going to form a blob. Okay. This is like the undulations within this blob. Now you can calculate the all the statistics coming out of this curvature. And if you plot the probability distribution of this curvature with the curvature element, you will find that the total curvature is always biased towards the positive side because ultimately it it will lead to the detachment of the drop and the formation of the drop. So that is what signifies by the positive value of this curvature.

[01:02:12]And surprisingly this bias is also observed if you do wave turbulence. The wave turbulence literature is full of events like this. Okay. Though the wave turbulence typically has been weakly nonlinear and stuff like that. This is highly nonlinear. Okay. And the last slide and I promise you I won't show anything else is that like in the case of wave turbulence people have devised this energy cascades which is basically uh in their case it scales as k raised to the power of minus5 or minus4 depending on what you are trying to do.

[01:02:46]If you calculate now this energy of this wave wave number and the energy of these different wave numbers, you will find that regardless if you just have multiple you know cuts across this across this uh you know this this solid jet and if you plot the energy versus the the frequency or energy versus the wave number you are going to get this minus2 scaling uh universal. Okay. No matter what you do, uh this is different from what we actually get in the case of ocean waves and stuff like that because ocean waves are typically triangular.

[01:03:25]Okay. So this is a very distinct characteristics. Okay. Uh but it is different from the classical wave turbulence. But this is something that we are currently working on because this feature is rather universal and it is similar in nature to the wave overturning and steepening kind of a profile but still it is unique in its own way. It has got certain amount of shock-like dependence. So it's like a sawtooth type of a profile. it goes up and then chash it just comes down and it shows that universal characteristics okay across you know different Weber numbers different time scales also okay and this is all done in the fyear space therefore so this area of interfacial turbulence okay that how this actually interacts with the flow and how this is actually imposed this has got a lot of similarities with oceans okay distinct but yet similar in in many ways this is something that one needs to decipher as we want to go forward okay because I think there are certain inherent similarities of course there are certain distinct features as well okay so uh so I I think since many of you actually you know it's a computational group also so you know simulation wise one can create different types of perturbations in a 2D or in a 3D type of face and watch how these perturbations actually interact. This comes from your work actually. Okay. So I mean this is something that can work in conjunction with experiments. That's what we think it can be. Okay. Uh giving you examples that you can also create different types of local perturbations with local you know length features and one can derive statistics from experiments as well as from simulations. This is this is something to something to look at. Okay.

[01:05:24]And you know one can also do full 3D sim this is once again comes from professor Zeleleski and then of course uh greater travas and zeleleski's work where you actually show the full-fledged simulation but can you incorporate the interfacial turbulence okay into the into the into the into the turbulent flow physics something that experimentally we can also achieve. So there are lots of things to do. is just the small bit of the story that I showed. Okay, albeit in a hurried fashion. So, uh there are a lot of future directions like for example the turbulent nature and you know the role of singularities. Okay, in this kind of context and uh the determination of the balance between the local and the non-local cascade features and predicting the fragment sizes using statistical principles. This is a long way ahead but I have given you some glimpses that how experimentally at least you could make a lot of inroads into these kind of physics. Thank you so much.

[01:06:36]Thank you very many questions.

[01:07:00]>> Yeah. Yeah, sure. Sure.

[01:07:14]>> Uh I have a question uh regarding uh that blurriness of the the droplet. So how how do you process when there's a like lot of droplets like >> Yeah. So you have to do the measurements a little downstream so that you don't have this overlapping cars. Okay. So blurriness is okay but if you have overlapping levels of blurriness for example it's like say three or four droplets kind of overlapping with each other that is something also that we are doing currently by assuming different curvatures and recovering the whole thing. still a work in progress. It's not yet finalized. But uh the idea of doing this is that in this particular way you are basically kind of circumventing uh the the difference in the depth of focus that you'll have in this events like this because these are very catastrophic. So things will not be in the same plane. So that is what uh the main target was okay to but this was a need-based discovery rather than we didn't want to really develop a way of measuring droplet sizes it was needed here to develop the statistics there was no other way of doing the statistics and we needed the statistics to provide the scaling Okay.

[01:08:50]This is one of the cases where I have so many questions and so many comments that I don't know what to ask.

[01:09:01]>> We just make one comment. Uh For the record there is no justification neither experimental nor mathematical for the gamma distribution.

[01:09:15]>> Yeah.

[01:09:16]>> The theory that deres the gamma distribution is wrong and the experiments that of course are correct.

[01:09:28]Um when you look in detail about how the occurs, you will see a lot of different things and recently this was refined by other experimentalists and we are deeply engaged to analy theories.

[01:09:52]I think that's the >> Yeah. Yeah.

[01:09:55]>> They pushed very very strongly. It used to be in 100 years ago in the 1930s again spread of disease theory.

[01:10:05]>> Right. Right.

[01:10:08]>> Was now fashion but I like what like you show you the t I like that very it's not a question it's a comment >> right >> yeah I think we fitted it's not like the the probability curves actually merge now you basically use a gamma distribution to show the functional form because but the data overlap is real that means you still get a probability distribution kind of merges.

[01:10:55]>> Yes.

[01:11:05]>> Thank you for your nice and really clear.

[01:11:08]Um I have I'm doing numerical simulation. So my question is are you investigating comparison numerical simulation? Yeah, that was a that was the whole idea of presenting the last three slides that we want. I am not a computational person. So I but this requires uh with experiments you can do so much uh with computation if one can look into this fine features deliberately uh then there is a lot of potential to make more breakthroughs because I think this is just the tip of the iceberg.

[01:11:41]There are a lot of things that needs to be done. Okay. Any other questions? It's quite late so maybe I will relieve everyone.

[01:11:53]>> Yeah. Yeah.

[01:11:55]>> Thank you again.

[01:11:57]>> Thank you. Thank you so much.