 Okay, good morning everyone. It's really delightful to be here. I'll tell you why. I was supposed to be at the first hands-on school that took place in India in 2008. I was a post-doc at Los Alamos back then. Harry knows this painful story. I did not get security clearance to travel to my own home country to participate as an instructor at that first hands-on school. So I'm truly delighted to be here finally. It took what, six years? Eight years? I'm not good at math, as you can see. So I'm sorry I missed the first week. I had to be in Leo for the stativist meeting, but better late than never as they say. The title of my talk is Hydro in Parentheses, Dynamics of a Self-Propeled Camphor Boat at the Air-Water Interface. And this work was primarily done by Dr. Satish Akela and Dr. Dheeraj Kasing. They are post-docs in my group. They did all the experiments. I'm the fellow who gets to stand in one corner of the lab and clap and encourage them and get to give the talks. It's very unfair because I'm not the expert on this problem. Satish and Dheeraj are, they should be giving this talk. We received a lot of theoretical guidance from Ravi Singh, who was then a student. Now a doctor, he works at Google Labs now, doing a different kind of science, and Professor Shreyas Mandre, who is a very dear friend and a close collaborator at Brown University. So, just so you know the faces and we are not headless personalities, that is me and that is Satish, who is currently somewhere in a queue on campus. And I want to start off by giving you a brief introduction of what we do in my group. So our group's research interests lie in both fundamental and applied, experimental, non-linear and non-equilibrium physics. This comes from a shortcoming of one of my own limitations. When I was a student like you, I was very limited by my imagination. So I took it upon myself that I will only do research and stuff I can see with my naked eye. I don't study stuff I cannot see. So that pretty much limits me to classical stuff. But there is a rich spectrum of problems still waiting to be understood in classical, non-linear and non-equilibrium physics. And the specific focus of our research group currently is in interfacial fluid dynamics involving flowing soap films. And what I will discuss today with you and we will do experiments together the rest of this week on camphor boards. We also study amorphous solids, particle rafts, hydrophobic particles that sit at the air-water interfaces and behave like solids, aggregates and granular media. In the last four years I have gotten into biomechanics, particularly these days we are busy studying the evolution, stability and energetics of the human foot. So you will find that I wear these funny looking shoes because I am running an experiment on myself for the past three years. And finally, just to keep my sanity, I keep a problem to myself. I do not collaborate with anybody on it. And I work on, nowadays I work on fluctuations in wind and solar photovoltaics because we have only one planet to live in and we have to care about it, it matters. So if you are interested in any of these other topics, please feel free to catch me at any free time, coffee break, lunch, dinner and chat with me. And I also want to spend a minute introducing my campus. You can see we also have a beautiful beach and you are all welcome there. And we are a brand new graduate university, international graduate university situated in Japan, which means English is our language of communication. 50% of students, research staff and faculty have to be non-Japanese. So we are a very international place. And we are all of four years, four and a half years old. I am one of the founding faculty and we are adding seven faculty every year. We are about 50 faculty right now and we are expanding. So we want to double our faculty size to 100 by 2023 and eventually reach 300 faculty. We only have a PhD program. So if some of you are looking at applying for PhD abroad and you are interested in interdisciplinary sciences, then please do take a look. Also, since we are expanding fast, we are also constantly looking for post-doctoral researchers and technical staff. So in the intermediate term, you again have opportunities and once you are ready to apply for faculty jobs, again take a look at us because we are hiring seven faculty every year. So you should be looking at us constantly. So outline for the next one hour. I am going to keep this talk very simple and approachable, which means first I will describe what is the phenomenon we are going to work on experimentally this week. And I will explain the phenomenon without the mathematics. Mathematics is a language which condenses the idea in minimal information, but with minimal symbols, but rich in information. But the same can be explained in a descriptive manner as experimentalists especially first learn by just staring at the phenomenon. We can into it from observing. And this is a very old phenomenon. The first recorded experiment was in 1686, but it still has modern relevance. So why should we care about this experiment today and I will explain that also. Then we will go into designing the experiment briefly. Most of the details will be in the lab and then imagine analysis. What quantities do we measure? And finally the results. What are the different modes of this motion of the cell propellant particle? And then understanding the modes of this origin. As I mentioned the emphasis will be on physical intuition rather than the mathematics. The experiments you will be performing together with us have not been published yet. So these are not hot of the press. They are still baking in the oven. So you are going to be working on stuff that I am still thinking about. I will point out unsolved problems along the way each worthy of investigation. Some of them are worthy of becoming PhD problems. So if you are looking for a PhD project you will have plenty of opportunities. And if you are interested please come look me up, talk to me. I am happy to share all the literature and all details I know. And I have no expectation of collaboration because I am a vegetarian so I cannot say I have other fish to fry. I have other grass to eat. But if you are interested please let me know. I also noticed a poster yesterday from Zanjan Syed Mola'i. So this is very closely related to your poster. So what is the phenomenon we want to look at? What you are looking at is a Petri dish sitting on a light tablet like a TV monitor or a computer screen filled with water, distilled water or mineral water. And you see this black dot over there. That is the camphor boat. I will explain what a camphor boat is shortly. It is floating on the surface of water and it just moves by itself. So that is the phenomenon we are interested in. Stuff particles etc when floating on the surface of water it is natural for them to move when the water is itself moving. Here the water is not moving it is static and yet this particle is moving by itself. And this is not the only motion it shows. It can show some other type of behavior also. It will remain static for a long time and suddenly jump to a new position. So it is not just one phenomenon. There are different facets, different varieties of this motion. So this is the phenomenon we want to study. This is not a new phenomenon. As I list here, it was first reported to my knowledge in the year 1686 by Dr. Haydia. I do not know who he or she is. And you can see from 1686 it goes down to 1869 when it was finally understood. So it took 200 years and not for lack of effort and these people were not stupid. You see some of the most illustrious names in the Annals of Science listed there. Sir Benjamin Franklin who was an American statesman and a very famous scientist. Alessandro Volta after whom the unit for electrical potential differences named Volts. Lichtenberg of the Lichtenberg figures. Giovanni Battista Venturi of the Venturi effect in fluid dynamics. Jean-Baptiste Biot of the Biot-Sabbat Law. And Charles Tomlinson you may not have heard of but he was a fellow of the Royal Society. Finally it was explained by Fandaman Sprucher and later immediately after Lord Rayleigh himself worked on this when he was researching the effect of surface tension. So as I said this problem occupied some brilliant minds over nearly two centuries and many in science had to. I can tell you a story about how did people decide on the fixed points of thermometry 0 degrees and 100 degrees Celsius. It took a Royal Society commission of 35 people about 15 years to decide that even Newton made a mistake there. So there is a story behind every effect that we study in the textbooks and it helps to learn what were the difficulties they faced. Because it's not just us who face difficulty when we do science. They faced it too. It's a very human process. And if you are interested in the historical introduction I suggest you look at this paper. If you would like a copy I am happy to post it on Google drives to all the literature that I am citing here. I have copies I can share it with you through Google drive together with this presentation. And this one I do not have because it's in French which is all Greek and Latin to me French is Greek to me. So that I do not have but I have an English translation that was provided by Charles Tomlinson later. So the effect that you saw the video of the basic mechanism starts with this concept of surface tension. So what is surface tension? I took this image from this website because it does a good job of explaining the phenomenon. In a liquid we have molecules that are all packed in some disordered configuration and they are all interacting through atomic or molecular bonds. They could be covalent. They could be ionic or something else. But the point is when a molecule is in the bulk of the liquid it sees neighbors in all directions. But when a molecule comes to the surface half of the neighbors are missing on the other side the other phase. So the bonds that you see in red along the surface they lead to higher energy. As a result the surface behaves like a stretched membrane with surface tension which opposes the distortion. It wants to minimize the surface because being at the surface is not a very happy state for these molecules. So they cannot avoid it so they will try to minimize the exposure to the surface. Which is why bubbles like soap bubbles etc take up very perfect spherical shape because it's the minimal surface. Now at the surface since we have only half the neighbors it increases the energy at the surface and therefore the forces are acting on the molecules. It forces the liquids to adjust shape to expose the smallest possible area. The symbol I will use for surface tension is gamma. Its units are energy per unit area so milli joules per meter squared or force per length milli newtons per meter. Now the surface tension is what we call an equilibrium construct that means everything is more or less static on average. But things can change when you take stuff out of equilibrium so I will explain what it means to take stuff out of equilibrium. If I take a drop of water on a surface leave it on a surface forever assuming there is no evaporation it will just retain its shape. There may be molecules moving about within that but on average over the observational time scale it remains static. But suppose we consider a different situation this situation which I clicked yesterday morning in Venice as I was waiting to board my train. This gentleman is making soap bubbles that is a very non-equilibrium process. And that soap bubble look at it it is fluctuating so its surface area is changing constantly. So that is the non-equilibrium construct. So what happens you have surface tension on the y axis and the concentration of something on the x axis. What is that something that something is a surfactant molecule or an amphifile. An amphifile is a peculiar molecule in that it has a hydrophilic head which likes to stick its head in water. And hydrophobic tail which heads water so it will stick out of water. So they will form they will go on to the surface like this the head is sticking into the water and the head is sticking out of water. So when I introduce so soap is made of amphifiles. So if I introduce very small quantity of soap maybe I have a very few number of molecules sitting at the surface. I keep increasing the amount of soap I add to the surface of water say a beaker of water. It keeps increasing at some point the whole surface is crowded with these molecules. If I introduce more of these molecules they cannot sit on the surface anymore. But they do not like going into the bulk because the tails hate water. So what they do is they form these ordered structures we call micelles. The micelles the hydrophilic head sticking out into the water and hydrophilic tails sticking in so that they do not meet the water molecules. So now suppose I have a soap film. So I have a soap film and it has these hydrophilic at both the surfaces of the soap film I have these amphifilic molecules sticking out. So the head is sticking into the soap film and the tails are sticking out. Now suppose I suddenly stretch this soap film I have created fresh surface new surface. But that means that I have suddenly decreased the number of if I keep the number of amphifile molecules fixed there are fewer amphifile molecules per unit area. So if I divide the total number of molecules by the area if I increase the area the concentration has gone down. Then this the molecules that are in the bulk like these micelles will then come to the surface and populate and surface tension will go back to normal. So the amphifiles introduced at the surface change the surface tension right. So when I stretch the soap film during that stretching the surface tension has is changing because the number of molecules is kept constant but the area is changing. And it takes some time for the molecules to come to the surface and again bring the surface tension back to normal. So when I had dilute concentration of these molecules I had some high surface tension which was close to that of water. As I kept increasing the number of molecules on the surface it came down and then this is called the critical micellar concentration or CMC point. There basically any excess molecules I add will go into the bulk and form these ordered structures ok. So now if I am past this CMC point the critical micellar concentration point and now I stretch the soap film the micelles will come up and they will again bring the surface tension back to this point. So it may go ok. So that stretching and the time it takes for the molecules from the bulk to come up to the surface is a non-equilibrium process that is what you see here. He is creating the soap bubble he is dipped to filaments in soap solution and then he is using the wind air he is basically pulling it like this and it creates a bubble. But while this bubble is not spherical it is fluctuating with the air currents and so its surface is constantly changing as a result it is always in a non-equilibrium condition ok. So again to recap it when the soap film is stretched the anaphylic molecules from bulk come to the surface to occupy the newly available area. But during stretching the molecules are at the surface are not evenly spread then surface tension is not the same everywhere it is the surface tension varies with the location. So if I take a gradient which is basically this the partial derivative of the surface tension with the distance it will show me some characteristic change. That is a force technically it is a stress but for our purposes we will think of it as a force and it is called a Marangoni force. And this Marangoni force is at the heart of the self propulsion of camphor boat ok. So what happens in the case of the camphor boat? Let us say I introduce this red disc which is the camphor particle at the air water interface. The camphor is a waxy hydrocarbon it is what we call a van der Waals solid van der Waals forces are much more weaker than covalent bonds or ionic bonds. So the camphor particles can easily break if with the hand most hydrocarbons are like that. So those of you who are from India know what camphor is very well because it is regularly used in the temples. Those who are not from India you know moth balls or naphthalene balls that you use to protect clothes at home it is the same material. What these materials do is they undergo what is called sublimation at room temperature because their atomic or molecular bonds are so weak. The fluctuations in temperature are enough to knock one atom or molecule out from the solid. So this solid can go directly from this material can go directly from the solid to the gas phase it does not melt into a liquid ok. So when I introduce a camphor disc on the air water interface the camphor molecules are moving into turning into gas and they spread along the surface. So these are not amphiphilic molecules they are just camphor molecules their camphor is not the surfactant it is it does not have this amphiphilic structure. But when it spreads along the surface it reduces the surface tension locally ok. So the camphor will spread out like this radially outwards uniformly and it will reduce the surface tension. So there is a gradient in that means the concentration of camphor molecules is changing as I go from the center of the camphor particle out towards the edge of this petri dish ok. So there is a gradient that means there is a force. In fact the force is same along all directions so it is like taking this bottle of water tying ropes to it and each one of us pulls but we pull with the same amount of force. So the bottle will not move anywhere but suppose one of you is stronger than the other and pulls with slightly higher force then the bottle will tilt towards that person. So fluctuations in the air will or air currents will lead to fluctuations in the evaporation and that breaks the symmetry. And the camphor disk will slightly move to one direction and that will amplify and that changes the spreading of camphor into this comet shape. When it turns into this comet shape it just starts moving by itself and we will see this we can visualize it ok. So that is the basic mechanism and it took 200 years to come to this point. So you have the camphor disk and basically the gradients in front so the force in front is different from the force in the back as a result the camphor moves along a particular direction. So if you look at it from the side this is the top view from side view you have the camphor disk and you have this camphor material that is oozing out onto the surface. And it has a longer tail on the back than it has in the front it is moving in this direction. So and stuff gets from out from the camphor molecules get out from the disk onto the surface and then they have to eventually evaporate or dissolve. If we are using camphor it will evaporate if you use camphoric acid which is what we will use because it is more stable it will dissolve ok. So it will get out. So there is a flux an influx of the camphor molecules from the tablet onto the surface and out flux either through dissolution or evaporation from the surface and this moves ok. So any questions at this point please feel free to ask questions. There are there is no such thing as a stupid question there are only stupid people. That is what I was told when I was a post-doc by my advisor. So no questions you understand everything then I do not have to talk anymore ok. So let us now the cute photographs are over now we will get into movies. I come from India Bollywood is a big industry we love movies right. So let us visualize this mechanism what I am going to show here let me first explain the mechanics. So I take this is not a camphor board that is moving about I take a tablet we stick a needle to it. So it goes and touches the surface and it stays put and because it makes it easy to visualize we have a camera. So you have a light tablet you have a petri dish over it with water and then with a needle the camphor pellet comes down onto the surface and we have a camera above and we are imaging at a high speed and we have seeded the water with tiny glass spheres which are neutrally buoyant. So they just go around in the fluid all over the place but sometimes they come to the surface when they come to the surface they are swept away by the camphor molecules that is how it looks. So it is a real effect. So you see that the camphor is getting out so the particles are here you see that the particles seem to be moving in slightly that is basically because they are coming from below the dish and once they come to the surface they are quickly expelled and here they are not moving that is where the camphor has evaporated. Here we used camphoric acid so it has dissolved. So there is an out flux of camphor from here and it spreads and then it dissolves ok. You can look at it from the side so yes 50 microns plus or minus 10 microns these are yes. These are hollow glass spheres it is a very excellent question. Glass is more dense than water so it will sediment right. So he is asked trying to bluff me because how come how can glass particles come to the surface. So these are hollow glass spheres filled with the gas so that they can control the density. So the density is slightly higher than water it is 1.03 ok. Here we are looking at the same effect but from side. So I have a laser sheet that goes through the it cuts through the petri dish that is the camphor boat you see over there. This is basically a mirror effect that you will you will notice what it is. But basically these speckles you see are the glass particles and this the camphor is spreading along this direction ok. So let us look at it. So ignore this above part that is basically a mirror effect at the interface. But the point is the camphor does not spread out of from the disk from the tablet onto the surface in isolation. As it is spreading it is pushing it is trying to drag the fluid with it. So these particles are slowly migrating up and then as the camphor spreads out like a jet they are being pushed like this and then they come back. So there is convection in the fluid below. So if I were to take a long exposure of this video and watch it you will see two huge vortices over here ok. So we had taken this video for an experimental imaging technique that we call particle imaging velocimetry. Unfortunately so who knows Yogi Berra here not the Americans who knows Yogi Berra. Yogi Berra if you do not know you should know he is my favorite baseball commentator and he had one of the finest one-liners. So the one that is relevant here he says theory and practice are the same in theory. In practice they are different. So theoretically speaking this particle imaging velocity technique should have given us what we had hoped to measure. But in practice we could not do it. So we had to go to other methods which we pulled out the data that we wanted to but it is still an excellent way to visualize and qualitatively understand what is happening. Now what you realize because most of the dynamics is at the interface right and there is this mirror effect which we can get rid of. But the dynamics is actually limited to a one millimeter layer which we call the boundary layer in hydrodynamics. If I want to image one millimeter with this it is a little difficult but we can do it with another technique. Anyway so the point to note here why what is the take home message from this video. We learned that the camphor particle does not behave like that in isolation. If I were to leave the camphor disc on this table it will not move around by itself. It is moving in response to the forces it is setting up on the water surface. And in the process it is disturbing the water which acts back on the camphor particle. So that is why I put hydrodynamics because up until now people studied the dynamics of camphor goods. But what is the effect of the water below? What happens is the merengoni force that I talk spoke of or the merengoni stress is trying to move the particle. There are viscous forces in the water trying to hold it back. So there is a balance that must come. So that is the basic mechanism. Now why should you sit here and listen to me for one hour? It is good I am glad that you are sitting here and listening to me but I have to give some reasons. And why should you continue to maintain interest in it? This is a very old system as I pointed out but it continues to maintain relevance in important unsolved problems in basic and applied science even today. It is a very simple system with which to study these questions. In statistical physics how many of you have heard of active matter? All of you. So for those who have not when we study basic statistical mechanics let us assume this is a jar containing neon atoms. I pick neon because it is a monatomic gas it is an inert gas it does not react. Life is simple. Let us say it is sitting at room temperature 25 degrees Celsius. The atoms are moving about in this jar randomly in response to thermal fluctuations which are set by the room temperature. Now that is the kinetic energy. So when we study basic statistical mechanics of such a system the energy is set at the scale of the container that is the scale. But suppose I look at a bunch of these scamper boards where the energy is not at the scale of the Petri dish it is at the scale of the disk which is 3 millimeters or I could make it 1 millimeter or 500 microns. Then and if I throw a bunch of them and they behave and they interact with each other the statistical mechanics that went into describing the neon atoms is not the same as the one I should use for this because the energy is at the microscopic level not at the container scale. So that changes the physics. So active matter is basically an area of research that has started in the last 10 years and is currently in progress we do not have all the answers yet. If you are interested you have a simple system with which to explore those questions experimentally. Hydrodynamics I say viscous merengoni propulsion. So you have this particle it is moving about on the surface due to surface tension gradients or the merengoni force and there is viscosity acting. Look at when this paper was published Eric Lauga and Davis 2012 not more than 3, 4 years ago but you will notice that this towards the end of the talk I will give you a question. But you notice that this paper came out just 3 or 4 years ago so very recently. So these questions are still relevant. In biology chemo mechanical transduction molecular motors they do not work as the regular heat engines. You do not have a Watson's engine sorry not Watts James Watts steam engine somewhere in my body that does all the work. There are chemo mechanical transducers and the camphor board system is one such example. In materials autonomous motion and self assembly and in soft matter physics. So these are all active questions the experimental requirements are very minimal. So as I said you have a light source you can take a computer monitor with a blank power point screen and you are ready. On top of that you place a Petri dish with distilled water deionized water or this will do mineral water. All you need is a clean surface at 72 Newtons per meter surface tension for water. A camera webcam will do logistic webcam as I learned from Harry. And he also pointed out the virtual dub software which is open source to image. I have done it with smartphones also they are more commonly available these days. And as I said you do not need camphor or camphoric acid. If you use mothballs at home you can use that also the same effect he will see. Matlab for image analysis or if you are old fashioned like me I use image magic with C++ because I hate paying money for software. I am just cheap. So that is all you need. And the quantity you measure is basically the position of the camphor disc. So this is one of the experimental images that Satish took. You see this white circle over here. The white circle is basically a zone beyond which so the red part of the trajectory we are discarding. Why because I told you the camphor is leaching out of the disc onto the surface. It goes up to a certain distance. So if I have a 3 millimeter camphor disc it goes can go up to 3 centimeters. So the effect of the boundary of the Petri dish the wall of the Petri dish on the camphor particle we wanted to get rid of that. Like a free electron we wanted to study what is the hydrodynamics of a free camphor board. So we all our analysis was limited to this region. So all the only the blue parts of the trajectory sorry. Now when you take those positions and you pull out the speed of your camphor board something funny pops out. On the top plot you are looking at the average speed as a function of time in hours. So it starts off at t equals 0 and goes for about 6 hours. So Satish is a very patient gentleman. He sat in the lab for 6 hours and took this recording. I am on the other hand as you will find out this week I am a very impatient man. I want everything done yesterday. I am such a reasonable fellow. So what you notice is the average speed of the camphor board starts off at about 4 centimeters per second. And constantly decreases it changes slope it goes down. But so it is what is happening is the tablet only has a finite amount of camphor in it. It does not have infinite quantities. So with time the amount of camphor that is coming on to the surface is decreasing. As a result the surface tension gradient that I mentioned which is basically the force that is driving the particle is decreasing. As a result this is never in what we call a steady state over long periods of time. It is slowly decreasing its average speed is slowly decreasing. But as it is decreasing if I look at say 8 seconds worth of data in this region I will notice oscillations in the speed. But in this region if I look at say 8 seconds or 16 seconds it is a constant speed. But here for about 1 the camphor speed is 0 on average for long intervals. But at regular intervals it will suddenly jump with spikes. So mode 1 we call harmonic because it is almost sinusoidal. So this is the average speed this is the average speed but this is the instantaneous speed. So here since it is sinusoidal like we call it the harmonic mode of motion. Here it is a steady state motion and here we call relaxation oscillation. I will explain why we call it the relaxation oscillation towards the very end. We will not get into the mathematics of it but I will point you to the literature there. Any questions? Everybody is with me so far? So I told you about early on at the very beginning I showed you these beautiful pictures of Satish where he draws this comet. These are not real experimental systems and this is my illustration which is much more crude compared to what Satish made. The point is this is not some imagination in our mind you can actually visualize it in the experiment itself. So what we did was we now we use a different kind of glass particles again before you pop the question I will answer it. These glass particles are naturally buoyant they have a specific gravity of 0.25 that means the ratio of density of the glass particles to the density of water. So they are only one quarter as dense as water so they naturally float on the surface. So let us say you use talcum powder or Johnson's baby powder it will work you do not need fancy particles they will float. Decorate your surface with these particles and put this camphor particle and you will notice that the camphor boat when it moves it will create a whole particle free zone. This particle free zone is where the camphor molecules are spreading out. So it gives you a clear way of visualizing what is not clearly visible with just the camphor particle going around in the water. But by using these particles you are able to see something else something more. So in the first mode the harmonic mode you will see this long electrical shape. So this dark gray region is the particle rich region and this light gray region is the particle free region where the camphor is sitting. As the disk is moving so this disk is moving towards the top left corner it is leaving a trail behind it. And you notice that so sorry so this black plot is the speed. If I get the area of the particle free region which is basically telling me something about how much of camphor there is. Remember I told you that you do not have infinite amount of camphor right. So with time the amount of camphor on the surface is decreasing. So this gives me a measure of how much camphor there is on the surface at each instant of time. And from that I can plot the area of the camphor which also oscillates together with the speed. So the camphor concentration is oscillating. In the steady state we picked a region where there were some slight changes. But you will notice that this is between 4 and 4.5 cm per second but this is between 2.4 and 2.6 so there is only 0.2 cm per second. And then when you look at this relaxation oscillation regime this part of the plot is taken from the point when the camphor particle was just sitting stationary. I will show you the movies also. It is just sitting stationary and slowly the camphor is spreading and it pushes the glass particles out of its way. It increases to a certain size and then suddenly jumps to a new place ok. So we have another way of visualizing. So the second measurement is using the decoration of the surface with these hollow glass particles to pull out an estimate of the area of influence of the camphor. So here are the movies. See the oscillations. You do not see the oscillations in this you actually pull out do the image analysis you will pull it out. Satish actually highlighted the camphor free area the hole with in green in fluorescent green but that is how it basically looks ok. But in the steady motion you if you compare this you have a large comet in steady motion the area of that comet has decreased ok. And once we move to the relaxation oscillations the particle is sitting static. But slowly the hole is increasing in size and suddenly it will jump and then it goes to a new position and then it grows again slowly ok. So clearly the amount of camphor is playing a role but the amount of camphor is controlling the force or the surface tension difference. So the next thing that Satish immediately hypothesized was well this is because of the surface tension difference. So instead of waiting for 6 hours he is an intelligent kid he does not he is not lazy he just wants to minimize. I am going to do this slightly differently I am going to change the surface tension of water by introducing some material like soap for instance. Here he used a material called sodium dodehyde sulfate SDS. And by providing meter dosage he did not have to wait for 6 hours to get to mode 3 he got it in the first 2 minutes. So here you have this pure water with camphor the same case you get the harmonic the sinusoidal oscillations. And then he changed the water surface tension from 72 dynes per centimeter to 68 dynes per centimeter and immediately it went steady state. When he changed it to 65 dynes so reduced it further it went to relaxation oscillations. So the Marangoni force is directly related to the surface tension difference and since the board speed depends on Marangoni force we have one more quantity. This and now we are getting into the relaxation oscillations for that you need some two competing time scales. So one is the time it is taken for the camphor to leach onto the surface the second is coming from the amount of time the camphor board spends at a given location. Why because if the camphor board is moving it may not be leaving giving enough time for the camphor to get dumped at that position in space. So when that means that the board speed also must matter so there is a coupling between these two. And this coupling is a source of the non-linear oscillations especially in the third mode which we see more pronounced the relaxation oscillations. This can be expressed as a pair of coupled ordinary differential equations and it links to the this camphor board system to the system of non-linear oscillator in the theory of self sustained oscillations. So this was first studied in the mid to late 1800s goes with singing arcs by Blondel in France and Henri Poincaré later Balthasar van der Poel the van der Poel oscillator. So is a very rich and work by Soviet mathematicians Andronov is a very rich theory. I am not getting into the equations what I want to do is lead questions. So I told you about active matter I showed you the effect for a single camphor board which is the experiment we will do for the rest of the week. What happens if we throw a bunch of camphor boards how will they interact with each other and come up with collective modes like synchronization active matter etc. I told you about viscous Marangoni propulsion. In fact the data that I showed you does not fall in the viscous regime it falls into what we call the inertial regime. So if you are interested you have a paper to write that goes beyond what Eric Lager did called inertial Marangoni propulsion. Can the boards be exploited for self assembly if so how I do not know I do not work in self assembly I do not know much about. But if you have ideas you can pursue it similarly for mechanical chemo mechanical transduction and actuation. Then there is this result I told you I take the camphor board fixed to a needle and introduce it in surface. So at t equals 0 there is a transient there is some time where the camphor must spread. That initial spreading will occur like that before it reaches steady state. If we plot the rim of this the spreading rim as a function of distance from the center which is what you did for your poster. It goes as some function of time for surfactant simple surfactants like soap etc. This should go as time to the power three fourths for volatile surfactants like toluene or kerosene it will go as t to the one half time to the one half. Camphor is not a surfactant it is but it is behaving showing sign of some behave like a volatile surfactant. So I am showing you a log log scale plot for camphoric acid camphor methanol chloroform they all go as time to the one half. Experimentally this is known but there is no theory for it. So if you are interested there is a PhD problem waiting there ok. Why does camphor behave like a surfactant we know it is not a surfactant. There is something peculiar about it that is why it took these very brilliant scientists 200 years to figure this out. They just so happened that they went and stuck their heads in a very peculiar material. There is something peculiar and I do not understand it completely. So I showed you this video the steady flux of camphor is set up on the surface. When there is the steady flux this velocity as a function of radial distance. So I will call this velocity u of r goes as some power law r to the power x where x is a fraction. There are two theoretical predictions that exist. If the dissolution of camphoric acid into water is as dominant as the spreading of camphor on the water. Then theory says it should go as the radial velocity should go as r to the minus. If the dissolution is negligible that is if it has an affinity for the surface u of r should go as r to the minus three fifth ok. Minus two thirds is minus 0.67 minus three fifth is minus 0.6. It is a bit difficult experimentally to settle between these two values. It is challenging but not impossible. So these are the data we used glycerol water mixtures because we were interested in looking at the effect of viscosity. But you will notice this solid line is minus three fifth this is minus two thirds. But there is a more brutal test for settling this and here is the only equation I am going to show. Suppose you have a quantity radial velocity so u is a function of r. It goes as some constant times r to the power x. If I take the logarithm on both sides log u of r I will get sum of log a plus x times log r. And if I take its log derivative the partial derivative this is the a has no dependence on the radial coordinate. So this will cancel out. So we are only left with this right. So the partial of log r with log r is one so x will come out as a constant. So this is the most convincing test of a power law exponent and derivative is inherently noisy measurement. So it is more brutal. When we do that I am plotting the log derivative sorry. I am plotting the log derivative as a function of distance radial distance for camphoric acid and methanol. This is for camphoric acid this is for methanol minus 0.6 here. All the data is sitting close to minus 0.67. So it is minus two thirds is minus 0.667. So you notice this is varying between minus 0.64 and minus 0.7. So this should be minus 0.667 if you. So there is a way to experimentally determine this settle this. Camphor is not behaving like other materials that spread that are non-suffactant materials that spread on the surface of water. It behaves in a peculiar way. There is something about its physical chemistry that I do not understand. If you can I would be very interested in learning from you ok. So let me stop there.