 The organizer for putting together this conference, it's really nice to see people after a few years that has been really difficult I guess for everybody, sort of get used to talk to people face to face and see at the eyes and it's actually, I forgot how nice it is. So for me it's also the first conference after, in person I mean after a few years. So what I'm going to be talking to you today is actually moving a little bit from what we have seen before to a little larger scale, moving from 2D, just trying to argue that it's life beyond 2D and a little on a mesoscopic sort of length scale instead of none. But I just try to convince you that this is also interesting. So the title of my talk is Sofa and Slippery and for a few years now we have been looking into compliance surfaces and the effect of surface deformation and how important it is in many different problems. It's actually something that is now for many, many years now, but it's been increasingly realized how significant it is the coupling between the hydrodynamic and elastic field to describe the behavior of a system and to describe this, to talk about this. We have been investigating some microels, just can you imagine of a little ball of a few hundred nanometers that you can put on surfaces and try to deform. And so how this is interesting, how this is important, probably the best reason to argue is in the field of bio tribology, you have compliance surface everywhere on your bodies and on the bodies of the life systems and you can talk about the best known is probably the mangalia articulations and all the joints, but there is tribology everywhere, you probably have been described by many things like doson and others. You have the ocular tribology, the retic cells that are going in your capillary, in your body. All of those systems are actually being confined by compliant boundaries and again the coupling between the hydrodynamic and the elastic field is really important, it needs to be described if you want to really understand what's going on. So our model system again is this polynipon microgel, the chemical the types are not really very important. What is interesting of this system is it can do little, the chemist can do little sort of gel of few hundred nanometers on site and this is particularly nice the polynipon because it's thermoresponsive, so if you are sort of room temperature they are very swollen or hydrated, but if you increase the temperature you go through a lower temperature and then they actually collapse a little bit, they get a little smaller, they get less hydrated and more read if you want. So you actually have a nice sort of knob to control the elastic properties of your system and also an other thing that is nice about this system is that you can actually put it on surfaces. So what I am showing you here is just an AFM micrograph of this little soft particle that has been your self-assembled on surfaces. So on the left is a high temperature, on the right is a low temperature and you can see how different it is, on the left you can really see the well-defined particles on the right is much more difficult to see them, they are there and you can easily get a very high coverage on the surface. You can have a nice fairly controlled layer, a compliant layer on your surface by using this system. This actually is a good model system to sort of play with these sort of materials. The way we have been installing it on the triangular experiment is by using the surface of this apparatus, if you do not know the system, this machine is like a big AFM, you can measure forces between surfaces in a very well-controlled fashion. The typical radii, we use cross-cylinder configuration so it is like a sphere on a plate and the typical radii of the cylinder is about 1 centimeter and you can measure with high precision the geometry of the system so you have, we use interferometry to get a really precise map of the geometry with the resolution of an answer or so. So what you need to retain is that we are able to keep these two surfaces together at a certain separation that we know, we measure it in real time by using interferometry and we measure the normal interaction and the lateral interaction, sort of what you do with the scanning proof microscope. The only thing is at a much larger scale, so a typical contact size is few tens of microns and the typical radii of the contact is a centimeter. We put our micro-draws between those surfaces in the way I just showed you in the previous slide. So we get something like this, it's illustrated here. We use mica surfaces just as a very nice material, you can get more molecularly smooth, very flat, clean mica and you can put then your micro-draws on top of this mica and this mica is glued on the cylinder. All that different of a real, I argue it's not all that different of a real molecular joint, then you have the hard bone that is coated by the cartilage that is lubricated by the synomial fluid, so we're going to be doing sort of the same, we're going to have a hard mica that is going to be coated by a soft layer of 100 nanominus or so of our hydrogel and this thing is going to be lubricated by water. So I am going to talk to you about two things today, so the first thing is what's going to happen on the contact mechanics of this problem and the second thing is going to be about the lubrication of this system. If you just measure the normal force of this system that I just showed you, so it's just approaching these two coated, micro-coated surfaces together, so it's like going from something here where they are separated to something that they are not closer, you get a number of force profiles as we call it, so this is what I'm showing here. So going from cooler color to harder color means like increasing temperature of course, so when you're low temperature you have swollen micro-gel that is interacting very far away because it's swollen and you have a long-range repulsion that actually kicks in very far away. On the contrary, if you actually hit the system you're going to have a force profile that is much short-range, the particles have collabs and then they see, show, figuratively speaking, much closer. So what you need to retain from this overhead though is that you have a long-range repulsion between these surfaces, so this distance that I'm showing here is the separation between the two mica surfaces and the micro-gel starts interacting a few hundred nanomers away. So there is a long-range repulsion. So now you try to sort of measure the friction force at given velocity, it's really not very important. What we observe, there are a few things, so here I'm showing on black again a typical normal force and on red a typical friction force, so this could be a low temperature. There are a few things that are actually very interesting. The range of the normal and friction forces are really different. This has been seen many times before on this kind of seasons, so you see the normal force much farther away than the friction force. But a second aspect that has been less reported that is not very easy to see here is that the friction force seems to actually get to a level that it doesn't really increase a lot anymore. So in black the normal force seems to be increasing and increasing on red the friction force seems to sort of get to a plateau. And you can see that a little bit better if instead of doing this representation you do it the friction as a function of normal force. And what you can see here, so this will be the black data here that you actually increase and then sort of seems to get to a plateau and we found this actually quite surprising because this was really unexpected, so we were really wondering what is actually going on here. And the answer is actually quite simple and it came from here. What I'm showing here is the geometry that we measure on the system at the same time we are actually increasing the load. So from violet to red it's actually increasing the load. So this is half of the geometry, so the fin is actually symmetric. So I'm not showing the whole thing. But this is what you see when you increase the pressure within the two surfaces. The surfaces get closer together as you expect. But then if you actually shift the point of closest approach sort of to put all the curve together, you see something that maybe not immediately trivial to you. But the mechanic of the contact is not at all trivial. So the thing seems to be instead of what you actually expect, like I'm showing here at the right, let me try to get clear. The hertz sort of behavior, when you're seeing a hertz behavior, a typical hertz behavior is that you press two surfaces together and what you call the actual area of contact sort of increase with the applied pressure and gets bigger and bigger as you can expect. But we're on the center, what we see with this kind of system because you have a long range repulsion, instead of getting a larger area of contact, the system sort of get different in this way. It's just sort of holding a lot of load on the outside and it's not getting a lot closer and it's not really getting larger on the contact area. And the reason is because we have this long range repulsion and the system that I showed you before, that the system is getting stiffer and stiffer when you press that it's getting harder and harder to get in contact. So when you actually put a global normal load, the system instead of actually moving the central region that is much more stiffer is moving, let's say, the outside region that is much weaker. So instead of being growing like this, like the hertz, a contact's not growing like this way. So that has actually large consequences on the behavior of the system because it gets increasingly difficult to actually indent, let's say, to get closer because it's getting tougher. And this is the reason why the friction gets stopped growing. When you keep pressing, just because the system is not getting any closer, the contact is not getting any larger, the system is forming sort of this way. And the region outside of the periphery of the contact is too far away. And as you can see, again, from the comparison between normal and friction force, if you're increasing the approximation of the system in this area, this is not contributing any longer to the friction. It's just the region of your contact that is closer, let's say a few tens of nanometer, that is going to contribute to the friction. So this is the reason why we get to this sort of plateau here. And you can actually, so the main message of this first part is that for this sort of system, you cannot use like JKR or the MT or TRX contact, you need to take into account the effect of a long repulsion to describe the contact mechanic. And if you do that, so that's what I'm showing here is what you will expect. So what I'm showing here is what is the geometry of the system when you actually compress, so this is now a theoretical calculation. Assume that there is a long range sort of exponential interaction between the surfaces as the one we saw on the experiment. So depending on the compliance of the contact, you can get a contact situation that is very different. So here on the dashed line is a system that is an effective modular of one gigapascal. And the continuous line is an effective modular of ten gigapascal. And you can see that the harder system get much closer than the software system. And the deformation in the software system gets stuck much farther away. So when you have a compliance system, the main bottom message for this first part is when you have a compliance system, you're going to get stuck much farther away if you have a long range repulsion. And this is going to make your friction force stop. And this actually actually for us was very sort of unexpected. So that's kind of saying this in this slide. So for the time that is left, now I'm going to go to the second part. Let's talk more dynamic part of the thing. What actually happened when you have this soft, compliant surface and you move one with respect to each other. A good point to start is probably the straight X curve that everybody here probably is aware of that you can see that you have different regime of friction depending upon the mainly the separation of between the surfaces and the speed that you are moving one with respect to each other. So you have, as you all know, a region of boundary lubrication on the surface are very, very close. When the surface are separated by a field of fluid, you have more hydrodynamic lubrication. And actually in this regime, you can have probably two different scenarios. You can have some sort of a hydrostatic generated film. So you put a pressure, you generate a flame, you separate the surfaces. Or you can have a hydrodynamic lubrication in which the film separating the surfaces is generated by the motion between the surface. And that's what I'm going to be looking into today. So to understand this, the people have, this is actually really sort of all stuff that has been going around probably since the work of Dawson in the 1950s. And they put together this sort of interesting diagram in which you can illustrate a different regime that you can see. This is a bit complicated, but the thing that we need to look at here is there are two parameters, one that is related to the viscosity of the fluid and especially to the sensitivity of the viscosity to the applied pressure. So this is what you would call piezoviscosity. And a second parameter that is more related to the elastic properties of the system. So what you need to sort of think of is that to the right is more elastic and to the left, more compliant to the less, is less compliant. Up is more sensitive to pressure of the viscosity and down is less sensitive to viscosity. So you can grow some of what you can identify for regimes. In this corner here you have a viscosity that doesn't change with the applied load and the system is rigid so it doesn't differ. Down here you have a viscosity that doesn't change, but the system is compliant. So this will be what we are going to be talking today. Here you're going to have a system that the viscosity is very dependent of pressure or is rigid and here you have a viscosity that is dependent on pressure and the system is relatively elastic. And this has been the interesting of most of what has been done in the last few years for many, many decades. And this is probably this sort of contact that you are maybe all familiar with. But it's important to understand is that what is key here is that when you apply a very large pressure between a non-conformal contact, non-conformal surfaces, if there is some piece of viscosity, the viscosity of the lure can increase so much that that's actually what's happening in industrial gears and everywhere. The pressure increases so much that you keep the surfaces apart and you deform the contact in this funny way. So this has been an incredibly difficult problem because you have the non-linearity of the Navier-Stokes equation and the non-local character of the elastic field and has been described by many workers probably those on the first line that came out by numerical approximations and by finite differential element calculation. But it has been actually well-studied and it's really probably the most successful thing on tribology of last century. But what we're actually curious about is this sort of regime here. So this is the regime of relevant to a compliant system. And what happened here is that the surfaces are so compliant that you really don't have any change of viscosity. You have an isoviscous fluid, just water. Nevertheless, your boundaries are so compliant that they do deform on their modest hydrodynamic field. And the difficulty of this problem is to solve the coupling between this hydrodynamic forces and the elastic deformation. You have this hydrodynamic equation that are non-linear. You have this elastic equation that are non-local. So the local deformation don't depend only on the local pressure, or the pressure pretty much everywhere. And this is really a hellish tool to solve. However, what is nice about this with respect to the more realistic thing is that you have a viscosity that is constant and the hydrodynamic equations are much simpler. So you actually come a hope for an analytical approach to describe this system. And a few tens of years, a lot of people have been working on that, especially on theory. So I can mention a few words later. But the main thing that to grasp what is the physics of the problem is just follow. If you have a read, let's say a sphere of a cylinder on front of a read surface lubricated by a liquid, and if you are very close and the radii is much larger than that separation, you can use the lubrication approximation and the Stokes equation. And in that case, things are relatively simple. And especially, they are temporarily reversible. That means that the system, when you go forward and then you want to go backward, everything is too reverse. And that immediately implies that you cannot have a normal force. Let me try to get clear here. You have the hydrodynamic interaction between this non-conformal contact. And the question is, what happened when I approached and I moved? Is there any possibility of getting a normal force that is going to help me lubricate and generate a lubricant film? And the answer is that in the axisymmetric geometry, free it, the answer is no. And you can actually calculate it. You're going to get a pressure field that is going to be anti-symmetric. So this will be the pressure generated when you move the sphere with respect to the surface. So it's going to be a negative pressure in the bad words and a positive pressure in the front. And then the interval is going to be zero and you have no net lift force, no net normal force. So this is just mathematically but again, it's very easy to see how it goes. You have a thing that is symmetric. Stokes equation is temporarily reversible. If you go up, let's suppose that there is a normal force. If you go up this normal force, when you go back to go down, and there is no way that the system know what is left and right. So it cannot, the only situation that you have for going up forward or going down bad words that is zero, just by symmetry. However, when you have a surface that is deformable and this is what you have here. Let's say that with our case, you have a real solid with a soft solid on top. You are going to have a symmetry breaking. The symmetry is going to break. The system is going to deform. And you're going to pass goes from a pressure field that is anti-symmetric to a pressure field that is not for the anti-symmetric. And if you do the integral of the pressure field all over the contact, you are going to start generating, obtaining a finite difference from zero lift force. Most of the time I have, I'm just going to be talking about lift forces. They have been looking to this from a theoretical point of view for a number of seasons. The oldest paper that I know related to this problem was the 93 by Tsukimora Liebler. They did a very nice sort of perturbative analysis so that means very low perturbation of the system, very low deformations. And they got this expression for the expected lift force, one thing that is proportional to the square of the velocity and is proportional to the inverse of the cube of the field between the surfaces. This problem was much, much further investigated by Tsukimora Liebler a few years ago. And they really went through a lot of solitude of differences. And this is a really nice paper here. They went through a solitude of differences and they got to the same sort of scaling law. The lift force is going to go to the square of the velocity and the cube, inverse cube of the field. And it's also going to be to the inverse of the your model line, which means that if your system gets softer, you're going to have larger lift force and the opposite, which is sort of kind of interesting. This is valid only for very small perturbations and for just elastic response. However, people has been looking into much more much more complications. And the main thing is a message for these parts that you can have generation of a non-inertial lift force that is going to have you separate in the surfaces. The fluid that's going to come in, it's going to lubricate your surface. It's going to be very good for the moving part. So the people in the Netherlands, they have been looking now into the influence of not only the elasticity, but the viscous elasticity of the system. And they have shown that the presence of a dissipative part on your model line has also a role to play. And in particular, if your system is very dissipative, it just passes you the details, but it's going to have a detrimental effect on this lift force. So this is the lift force that you are going to measure and this is a ratio of times some sort of a number here that tells you how fast you are stimulated the system. If you go very fast, so it's essentially elastic. So you have a large lift force, but if you go slower and you go closer to the system, to the time the system can react, the effect is reduced, however it's always there. And these people also in the Netherlands has looked at the opposite case of not very small perturbation, but a large perturbation, which actually is very relevant. So in the theoretical part and model in power has been a lot of work being done on the experimental part probably where I've got a little bit lagging behind. For the sake of the time. So there are not that many experimental words that have been emerging so far. So this is one that we published a few years ago was like we didn't know what we were looking at, but we said we were looking at exactly this problem and lubricated polymer. So this is not our mercury gel jet, just a polymer on the surfaces. And what we saw when we were measuring the force, the stress as a function of velocity is that this thing increased by a model that we are just not detailing today. But what was surprising is that at high velocity the force was going down the system was getting separated. So we got this without knowing, we got this evidence of this lift force that we could actually describe by the model that I just showed you before. So we look at this in much more detail with our microgel. So that's what I'm showing here. I'm just gonna talk about this in the last three minutes that I have. Two words in black is what you see at high temperature and what you are seeing there is the separation between our micro surface at different velocity. And you see a clear evidence, our emergence of this lift force that is going higher and higher with velocity. However, when we decrease the temperature, this effect is much, much less important. This is because the system is getting swollen and it's getting more dissipative as I just showed you two slides ago and the effect is much less important. In the experimental part that is a problem is that actually I'm just gonna illustrate it here. In the theory CC, you can fix your surface to say the feeling is this thickness and everything is fine. For an experiment, you are telling it to apply the load using a spring and you have to keep your surface somewhere. And if you think about it, the fact that you are having a lift force that is emerging between your moving contact is gonna make that the actual load that you are applying with this spring here is gonna be changing when this surface actually be moving pushed by the lift force. So you really cannot really keep, usually you do not keep the field constant that is what is modeled by the theories. And you cannot really keep the load constant either because it's just changing, everything is changing. So that complicates things a little bit. So the thing that we try to do is just to impose a feedback loop and because we can measure the separation, we can impose a feedback loop to actually keep this gap fixed and this is sort of what we did to sort of be able to match our experiment with the theories. And just to make a long story short, we could verify that we have a lift force that actually scale more or less well with the square of the velocity. And if you take into account the fact that you are compressing your layer and the elastic model is not really constant, again you can look all of this paper. We also verify that this lift force goes more or less by the inverse cube of the separation between the surfaces. So with that I just, I think I just took all my time. I just wanna say that last few years a number of papers has shown the emergency of this lift force on soft matter or soft system. So this is an example of a particle moving by a decorated tube, sealing the moving by a soft surface or something done with a scanning probe microscopy. And with that I just finished. I just wanna conclude with this, is that in both cases, the static and the dynamic, finally the conclusion is that if you wanna keep friction and wear low, just wear and keep the surfaces apart. And with that I just wanna thank you for your attention. Stay on message. Rest in town, yes. Thank you. For the second part, I think it's just a quick clarification, but that case where you said there was a cancellation of the normal stress, so there was normal force, was this for, so I take it there's no applied load? In that. It says very small temperature, you can't occupy very small loads as long as you don't deformalode your geometry. Okay. But actually what I was meaning is just the lift for the force generated by the hydrodynamic field. Okay, I understand. Okay, thank you. I'm gonna apply a load. Thank you. Stay for the system you're looking at. The stresses are so low that you don't need to worry about piezoviscus effect or the material, the fluid doesn't have a strong piezoviscus effect. It's water. It's all, it wasn't, it was pure water. Okay, then very, very little piezoviscus. Okay. Okay, so this is why it doesn't matter. Okay, have you seen people examine this for more systems, hydrocarbon systems where you do have piezoviscus effect and is that map still valid, the Johnson map? The system I was trying, this is the description now, it's much more complicated and you have to go to probably the decision that does and this sort of people much more elaborate. But for a soft system with hydrocarbon people yes, the things that with soft complying bonders you cannot really get too high pressure because the contact is getting larger and larger. And people has to look into those sort of lubricants and they think we're fine. Like this, that's example I quickly show, they work with glycerol and all hydrocarbons and things was very fine. But again, mega Pascal pressure system. Thank you. Thank you for a very nice talk. So I have this question that, so if you apply vertical oscillation to this contact then the hydrodynamic force might increase the adhesion to your tip. Would it be possible to increase the vertical force? The F that you were measuring? Well, usually in this kind of system the adhesion is really very low because you have this strong repulsion. Even if you do this sort of oscillation you don't really get any adhesion. So that would not change anything? Actually, it will change the response. One interesting thing about doing oscillation is that people are even able to measure the rheology of the elastic properties of the material without touching it because you start vibrating your thing and you measure the response. The deformation of the surface is gonna talk to your probe even though you're not touching it. And you can really look at what's going on and this is the work of Elizabeth Charley and others. You can really see what's going down there if you do this oscillation that you suggest. The talking between the hydrodynamic and the elastic you can see it on the response on the cantilever. It's gonna tell you what's gonna happen down there. I found that really fascinating. So you can do a rheology without touching. And Elizabeth Charley has done a lot of that and it's really fascinating. Not to do with the adhesion though. More questions? For the remote questions? Go back.