 Does this work? Yeah. Does this work? Okay. It works finally. No? Oops. Maybe that was okay. Okay. Well, thanks to the organizers for having me here. And thanks for accommodating this last talk of the day, because I couldn't make it on Monday. And this reminded me of a joke about Indian railways. So in India, we have these very, very long trains. And usually, by the time you get to the last compartment, it's exhausting. And one of the feedback that came in the form was, please don't have a last compartment in your train. If you do, please have it in the middle of the train. So, well, something like that about these talks. Also, Hugh told me that maybe I should change the title of my talk and see if anyone notices. And clearly, so I'm going to talk about collective behavior at the end of the day in synthetic active matter. This is going to be very, very different from the talks that we have heard in this conference so far. So I thought I should start with a flock of birds, because we've been seeing movies of flocks of birds through the conference, and it seemed like a little tradition that I needed to follow. So inspiration from flocks of birds. Also inspiration from various other things that we've seen. Collective behavior in ants, in bacteria, in fish. So this is a movie of bacteria that are moving on a substrate and thousands of them are being tracked in this frame. Each individual color you see is a different bacterium. So, I mean, really I don't need to say much about why collective behavior is interesting and so on and so forth. And also the fact that there have been ideas looking at these aggregates as some kind of a very interesting material and thinking about them as fluids comprised of individual units which are active, active meaning that they're consuming energy and dissipating energy and using that to propel themselves, so to speak. We've also seen efforts towards building intelligent mimics of these kinds of things using robots, et cetera, and trying to get various interesting behaviors. So what I'm going to tell you in the next half an hour or so is can we do something similar with something completely mindless like plastic beads or oil droplets or things like this, right? What kind of collective behavior can we start to get in systems like these without brains, without having to design many things about the way they interact with each other and so on. So what I'm going to tell you about these kinds of experiments, what you're seeing here are two different movies comprised of the same system. You're looking at many small circular things. Each of them is a little droplet of oil and there are thousands of these droplets of oil in these movies that you're seeing. So each droplet of oil, I'll come to this in a moment, is self-propelled, it's moving and they interact with each other simply via the fluid mediated interactions and you see very different and striking collective behavior. In one instance, all of these guys are forming these aggregate which seems to somehow stay together and you change something very, very simple. Just take the lid off the experiment, suddenly all these things start demonstrating such collective behavior, right? So this is the system I'm going to tell you about. I'm going to tell you about why these kinds of things form, why those kinds of things form and so on. And when you look closely at each individual droplet, this is what they look like, right? So there's some structure inside each one of them and I will also tell you why they look like this and what it might mean for them to have this, what might look like a head and a tail and so on and so forth. So much for the pretty movies, I hope I have your attention and I'll delve into the science. And luckily for me, this work, a bulk of the work that I'm going to tell you about has just come out in P&A as of yesterday. And so you can go and if there's one thing you want to note down, maybe it's this and you can go back and read the paper and you'll get everything that I talk about. And this work was done mostly at Princeton and some of it is being continued in my lab now in Bangalore. Okay, so the initial motivation to create these objects which do these very interesting things was to mimic propulsion or motion at the micro scale. Okay, unlike trying to build these robots which can walk like, let's say, wildebeest or so on, what we were trying to do was mimic the swimming of algae or bacteria and so on. So inspired by how they move, people have over the years thought about very simple models about how to describe motion of these microorganisms without having to deal with all the complexity involved. Like they don't want to take care, describe the motion of a beating flagellum and so on and so forth. So there are very simple models. I will tell you about this model very briefly to describe these small scale motions. What we have attempted to do is to create a synthetic mimic of this simple model rather than create a simple mimic of this object. And our aim is to use the system not only to learn about potentially new physics that comes up as I will show you in some of these systems, but also that might lead to new insights into biology itself. And since we have created an object inspired by a very simple model in mind, maybe that also leads to some potentially new technology. So the model for micro-scale swimming that I have in mind is a so-called squirmer model. This is inspired by the motion of, let's say, a paramecium. This is a micro-scale organism which has many, many thousands of cilia or hairs on its outer surface. So how this organism swims is that each of these cilia beat and the beating of the cilium causes perturbation in the fluid outside and it's like tiny little ores around the body and this is what propels this object. So a sort of continuum description of this kind of motion is to take simply a sphere and say on the surface of this sphere I will prescribe a tangential slip velocity. And you can write various forms of the slip velocity and so you immerse this object with this very special velocity at its interface and immerse it in a fluid because it pulls also the fluid ambient to it, this object itself starts moving. So that's the mechanism for the propulsion of this so-called squirmer. So what we sought to do was to create a physical mimic of this squirmer model. So we said let's take emulsion droplets, oil droplets and put them in a bath of aqueous solution which contains a lot of lipid. A lipid or a soap molecule is a molecule which comprises of a hydrophilic part and a hydrophobic part such that all these molecules spontaneously assemble at the interface of oil and water. It's literally soap that one uses at home. So one gets a nice monolayer of this surfactant and if you create situations where the concentration of the surfactant is not uniform around the droplet but rather there's a gradient of this concentration one can generate spontaneously flows associated with this gradient which corresponds exactly to that situation and then this droplet itself will swim. So how do we actually create such a gradient? That becomes the question and we take advantage of again a very well-known phenomenon to all of us that soap in water will dissolve oil. So what we put is oil droplets in water and these soap molecules are in the form of these so-called micelles and they come and dissolve this oil away and become these swollen micelles. And in the process of this dissolution what happens is that you leave behind patches of the interface which are devoid of this surfactant and the result of having such a situation where you have some region which is covered by surfactant is that the interfacial tension is different over here compared to here and this causes a spontaneous fluid flow and this is something that we all know which we all will probably observe in an hour or so from now is this so-called Marangoni effect which you've probably seen as tears of wine in the wine glass. It's exactly this effect of having a gradient of interfacial tension which gives rise to these wine legs over here and in this case what it does is it gives rise to spontaneous fluid flows. So the system that we use to generate all of this motion is a special kind of oil. It's called 5Cb, its name is 5Cb and at room temperature it's a pneumatic liquid crystal. It's comprised of rod-like molecules and these rod-like molecules give an internal structure to the droplet and this 5Cb emulsion droplet that we have immersed in a bath of surfactant is gradually dissolved away and what eventually happens is if you remember the previous picture I showed you these swollen micelles keep forming and eventually if you take a droplet let's say that's of 250 microns in size it gradually decreases in size so that it completely disappears, it's dissolved away and in this whole dissolution process I told you that you're generating gradients of this interfacial tension which causes flows. The rate at which this dissolution itself occurs can be tuned by the amount of surfactant that one adds. So you can change how these objects shrink away and thus move. Alright, so if you put one of these droplets into a bath of this surfactant and water you observe a large scale flow inside the droplet like so. So this is a droplet which is 1mm in diameter and you're able to view all these textures inside the droplet because of the factor it's a pneumatic liquid crystal. And what you're visualizing is the flow that's generated because of these interfacial tension gradients that I just told you about. So what we then do to create the kinds of droplets that you saw in the first movie that I showed you is to use a technology called microfluidics. So we break off the oil or the pneumatic liquid crystal into uniform droplets. Each droplet is about 50 microns in size and now we can create literally millions of these droplets in the matter of an hour. And the uniform and nice and well controlled. And if you put these droplets now into this bath of surfactant and water you see that instead of seeing those large scale motions that you saw you get these gentle motions of the individual droplets themselves. The droplets are indeed swimming in this media. And as I also told you the amount of surfactant that you add changes the rate at which you dissolve things and in this case when you have these swimming droplets of this liquid crystal the amount of surfactant you add changes the speed at which they move. So you have a regime in which you can nicely control the speed with which these droplets swim around. You need to do something. It's ironic that the slide actually said control. I think it's okay we just keep going. I think we just keep going. Okay, I'm going to skip that slide in the interest of time. Okay, so the fact that it's liquid crystalline this droplet and it's not a simple oil droplet also allows us to visualize this in interesting ways. So if you have a droplet which is comprised of this liquid crystal I told you that there's a monolayer of surfactant at the interface. What this causes is the rod-like molecules of this liquid crystal sort of orient perpendicularly to the interface. And as a result you get all these rods oriented in such a way that you get a net orientation where you have a defect right in the middle of the droplet. And if you look at this droplet using polarized light let's say polarized in this direction through an analyzer you see a texture inside the droplet that looks like so. And so one of these little droplets which has this symmetric director configuration inside once it starts to swim there's a breaking of symmetry both inside so you see that this defect that was right at the middle sort of escapes to the end and it's in that same direction as in which the droplet is moving. So now you know that in the previous movie that you saw there's a head and a tail of the swimmer which comes from this director orientation inside the droplet okay. And if you look if you put tiny little tracer beads and follow them so you see that this defect has moved to the edge you're following the droplet as it's moving and you see these flows that are associated with the gradient of interfacial tension that I told you about before right. Associated also with the flows inside is a flow outside of these droplets which we can follow by putting tracer beads on the outside so this is the swimming droplet which is held in place we have many, many fluorescent tracer particles on the outside and you see that they're also dragged along by the flow right. So what the swimmer does is that it generates a flow field around itself through which neighboring swimmers can interact with each other right. So the interactions in the system are purely physical and I will show you how those are what give rise to all the interesting phenomena that we just saw. So for the next few experiments that I'm going to show you the configuration is like this we have two glass slides or cover slips and sandwich between these two is a layer of these swimmers. The direction of each of these swimmers is randomly picked because the symmetry is broken randomly and all of these swimmers move isotropically in this sort of quasi two-dimensional arena with the same, roughly the same speed and if you follow the trajectory of one of these droplets it does something like a persistent random walk okay. But I also told you now that there are interactions because of this hydrodynamic flow fields and what I will show you is that these flow fields can be affected by the presence of boundaries which is these walls that I just described to you as the configuration of the experiment and how they are placed will affect what collective dynamics that we see. So I will quickly run you through a series of movies just observations that we see and then I will rationalize what's going on. So if you have a case like so where the gap between the two cover slips is more or less the size of the swimmer itself, one notices that there's a tendency of these swimmers to form these lines or bands which travel together which are unstable and then to something which looks like a splay mode you know. So once one of them starts deviating in its direction the entire band itself breaks off. However when we increase this gap slightly something dramatic occurs those bands no longer unstable but become suddenly extremely stable right. So you see large scale bands of these swimmers which seem to even be able to pass completely through each other and reform right and it's just this simple effect of pulling the plates slightly further apart which has taken the situation from those unstable bands to this one. Now what we will do is take away one of the walls completely okay. So I will present to you a situation where there's only one wall the other wall is really far away whether it's a solid wall a cover slip or a liquid air interface okay. So this is water and air. So it's a different kind of wall this is a different flow boundary condition. In both of these situations the isotropic or uniform distribution of these swimmers is unstable and you spontaneously get aggregation of these swimmers into these tiny little regions okay. But then there's a very interesting difference in the nature of these aggregates depending on if the wall is solid or if it's liquid air. If the wall is solid the aggregate looks like so where you have a sheet of these swimmers so if you look very closely you will see that there's something which looks like a crystalline arrangement of these swimmers in the plane and there are swimmers which are coming out of plane and being dragged back into this aggregate. So it sort of looks like a crystalline sheet where you have this vortex of swimmers which are leaving the floor and coming right back. But once you have a liquid air interface you do form these crystalline arrangements but then you don't do these excursions out of plane. The crystallites simply just walk around in they're confined to this sort of 2D plane and they're moving around and you will see that they're very dynamic right. So they rearrange, break off, come back in, join together and so on and so forth. So what's going on here? Okay so that's the snapshot of everything that I told you. In these configurations so-called Healy-Short geometries depending on the size of the gap you either form very stable bands or unstable bands and then when you have just these walls you form aggregates either which excurs or go away into the third dimension or not. Okay and now I will take you back to this squirmer model and what we've been able to do is to write a generic version or a general version of the squirmer model where we don't assume that this form of velocity that's prescribed on this sphere is symmetric in any way. It can be asymmetric, it can have chiral components and so on and so forth. But what is important is that given a slip velocity that we prescribe we can actually calculate the forces and the torques that act on these objects due to these hydrodynamic interactions. Okay I showed you that this kind of a thing will set up a flow field through which they interact. What we are able to do is calculate what kind of a force and a torque this object will exert on another squirmer nearby. Okay so where do we get this slip velocity we just measure it from experiment. So we have a measurement of the flow field in this configuration of the Healy Shaw that I showed you. So we fit this slip velocity so that the flow fields in our simulation slash theory match and from that point on we can use this slip velocity that we have fit to the measurement and change this is a detail of how we actually calculate the forces and torques the so called greens function. So this greens function is specific to the boundary conditions that we use. So for a given boundary condition let's say this Healy Shaw geometry we are able to take that and calculate the forces and torques that result on every squirmer. And using the same parameters we can predict what will happen when we have this no slip wall or this air boundary liquid boundary. To cut a long story short our simulations so this is the situation that we have sort of the flow field that we have fit from the data and these are all predictions of the simulation so you see that there is a very nice match between experiment and these simulations. We are able to capture all the dynamics over here. So what's going on? So we get a very simple qualitative picture of what's going on simply by looking at the flow of an individual swimmer. So as I showed you in these Healy Shaw configurations the flow fields that we calculate look like this. The swimmer in this case is moving from this direction to that and the resultant flow field is like so. What you will notice is that there is a flow which sort of pulls things from the side of every swimmer. So these pulling forces naturally have the tendency to create these lines and that's what you are seeing resulting in both these configurations that lines spontaneously form simply because each swimmer is entrained in the flow field of the other. Likewise when you have simply this one wall what you notice is that when there is a solid wall there is this recirculating flow in the third dimension and a flow like so here and if you look in plane this looks like a monopolar field. So you have fluid being sucked in from all directions and consequently what you have is swimmers coming in from all directions giving rise to a two dimensional aggregate which is symmetric in this direction in both the cases. But in order to understand the subtle differences that we saw about the stability what I said is that we can also calculate these forces and talks that result from these hydrodynamics. So in this situation so what we calculate are the forces that pull the swimmers together and we also calculate forces that act in the direction of the propulsion of the swimmer itself. So in this situation where we have the gap to be sufficiently small you see that you know there is sufficiently strong force pulling them in but there is also a very strong force that pushes them in the same direction. So you can imagine as a longer and longer chain forms the force on the middle guy keeps on increasing it's just additive right. So naturally you will have this sort of arrowhead configuration where the middle guy moves faster than the others and naturally you will break off in this play like more. However when you increase this gap the force that pulls in these swimmers together increases significantly whereas the force that sort of pushes them along their propulsion direction reduces significantly. So you can immediately see that once these bands form they are very very stable right. And if you look at a sort of phase diagram which depends on the speed of these particles there are these stable and metastable or unstable lines in both these configurations. You just shift these phase boundaries because all you have changed really is this gap. You don't change anything qualitative you only change something quantitative. Whereas over here a very similar picture plays out when you have this solid wall the forces that pull them in are very strong as are the forces that push them out as a result these swimmers get out of the wall and you get this recirculating motion. And in this configuration the forces that push the swimmers out of plane are extremely small and as a result you get these crystalline crystallites which are just confined to the plane. What's very interesting here however is that there's a qualitative difference because of the qualitative difference in the boundary condition of the flow field. Here the flow field closes on itself. There's a recirculating flow which is what causes these excursions and coming back whereas in this kind of a situation the flow never closes on itself. As a result you only get either these 2D crystals or crystals which are unstable whereas here you get this very interesting vortex stabilized crystal as we as we call it. Now very very quickly what I in the last 5 minutes what I will do is to say that if we think about this from the view point of statistical mechanics this is really a phase separation or a phase transition that we are actually seeing over here. And this phase separation is induced by the flow fields that are set up by these swimmers. In the absence of any boundaries in the absence of any boundaries dynamic interactions are typically destabilizing. They don't give rise to this spontaneous aggregation of swimmers. But in the presence of boundaries this picture changes. So the phase separation here that we see is driven by these dissipative flows rather than something that we can derive from a potential and the kinetic roots that lead to the formation of these aggregates depends on the boundary condition. So if you have a wall you get these aggregates which are very dynamic and keep mixing up whereas if you have this liquid air interface you get crystallized which are extremely stable they don't mix up and so on and so forth. And this flow induced phase separation is I must point out two very interesting features of this. The self propulsion of the object itself is not necessary to cause this. It's sufficient that the particles produce simply a long range external flow field. So even when the propulsion is set identically to zero we still see the fact that you get these metastable lines and stable lines in our phase diagram. And in the absence of any noise in the system any positive value of activity however small spontaneously leads to a phase separation. So a uniform state is unstable to this aggregation and you will very quickly go to this crystalline arrangement no matter what the configuration as long as you have a very small activity. Very very very quickly I want to point out to you that this flow induced phase separation that we have uncovered over here should be seen complimentary to another mechanism of phase separation in these active systems. So called motility induced phase separation. Very quickly the argument over there is that if you have self propelled particles irrespective of how they move whether they and these particles are not immersed in an ambient fluid they just you can think of them really as Wildebeest moving. The phenomenology is that they accumulate where they move slowly and the particle speed itself depends on the local density of the particles so it is low where the density is high so this sort of give rise to a feedback mechanism giving rise to aggregation spontaneously. So like I said the motility induced phase separation which I just mentioned is kinematic in origin it only depends on this how the speed of this particle changes right and then you have these density dependent currents which are due to the collective effects of the particles which lead to aggregation. In the however this situation that we have just uncovered we know very nicely the dynamics that lead to this whole process itself right. So it is dynamical in origin not kinematic and I have also told you that the constituents just need to be active not necessarily motile and this whole mechanism is very sensitive to the boundary conditions that we imposed and as a result you can tune the structures you get by just placing this whole aggregates in different boundary conditions ok. So there are other similar aggregation scenarios in other active matter systems such as active colloids or swimming bacteria which also form these crystallites which look something like that but we think this is a mechanism that is flow induced rather than a motility induced separation mechanism ok and a couple of teasers at the end this is also a very interesting system where we can start thinking about situations where you have leaders not everyone is the same. So if you just throw in one big droplet it behaves like a nice leader so you see that this huge droplet is sort of carrying a pack of very little swimmer droplets behind it and what's more we can put in magnetic beads into those swimmers and guide them and so on and so forth and so you can do interesting leader follower dynamics and when you crank up the density so what are all the things that I have shown you is when density is quite low crank up density there are other interesting effects which come into play because of the dissolution effects and you start to see various kinds of interesting pattern formation like dynamics in this in this system and with that as a teaser I will thank you very much for your attention.