 from Senator College, if he's going to tell us about the work on, should switch. Yeah, you have it right. His work on bacterial robots. Ah, it's a lot. All right, good. Good afternoon, everybody. And so what I wanted to talk about today is not what I'm doing in my hands-on session, but it uses a lot of the same techniques that we use in the hands-on session. And it uses things that are tabletop experiments, everything that I'll talk about is a tabletop experiment. Using simple things. Here is a physicist's bacterium. I've given it my name. But it has a little gear motor in there spinning this helical flagellum as a model of things like this, like this is a rotobacter's theroids. This is from a movie by Howard Berg at Harvard. And this type of microorganism uses a rotating helical flagellum to propel itself around. And I published a study in 2013 in PNAS with Harry Swinney that I'm proud to say has more than 50 citations. Using the same techniques I'm teaching you in my hands-on session, right? So the idea here is that we aren't playing at science. I'm not pretending that you can use these techniques to do science. You can do science with these techniques and find interesting problems that people didn't think to do. People have asked Harry Swinney, how do you come up with ideas for projects? And his comment is, there's no end to physical phenomena that you might study if you're creative. But you've got to pick the right problem. That's the skill is picking a good problem. I had helped picking this problem because my postdoc advisor in Texas, it occurred to him, and we were discussing this about bacterial swimming, that nobody had ever done a macroscopic test of a theory that had been around since the 1950s. And it was low-hanging fruit is what that's called, and he asked me if I wanted to be involved in it. I said, let's see, I get to build a robot and measure these forces and torques, and I'll explain the fluid that it's in. I'm all in, right? This is going to be fun. I'm going to have fun doing this. It'll be easy, too. It'll be very easy. Well, several years later we published a paper. What seems easy isn't always easy, but that's the way it goes. But that's only one of the types of projects that I do in my lab. All of these are tabletop experiments because I'm at a four-year college. I work with undergraduates like Tyree. I have to have projects that are within the skill set of an undergraduate. I drive them harder than they understand because they don't know any better. They haven't been to graduate school yet to study things like these are E. coli swimming. This is Hapong Zhang, the postdoc I mentioned. This is live bacteria E. coli swimming. This is where we were trying to understand the swimming of these microorganisms and realize we could make a test using a macroscopic measurement. I also study internal waves in the ocean using particle image velocimetry, which is the image you see over here. Here's a movie of a slope moving just slightly in a big fluid motion, but there's a laser sheet taking a slice out of the fluid flow and take a movie, turn that into the velocity field via particle image velocimetry. These internal waves in the ocean depend on a vertical variation in the density of the fluid. It's denser at the bottom of the ocean because of temperature and salinity differences. It gets less dense as you go up, and it supports the type of wave in the bulk of the ocean that we have no real contact with unless you're an oceanographer. There are sea surface manifestations of it you might recognize, but you didn't know what they were. But they may be important in the global ocean circulation pattern, where this is the temperature of the ocean here, and you see the Gulf Stream coming up the eastern seaboard of the United States transporting heat over here to Europe, so it's much warmer. Maybe we don't like it right now, but it's much warmer than it would be otherwise at this latitude, right? Similarly, we can use Taylor-Couet flow. This concentric rotating cylinder system is a model of things like a protoplanetary disk, accretion disks. If you imagine taking an annular ring out of that, that would be the Taylor-Couet fluid, where, again, I've got a vertical variation in density. It's salter at the bottom than it is at the top. It's fresh water, and we get a unique pattern in that fluid flow that you don't see in a uniform fluid. But these kinds of things are using the same kinds of techniques that are in these hands-on sessions. I just published this paper in 2016. Same sorts of things. Taylor-Couet flow, fast Fourier transforms, maybe I needed a faster camera occasionally, did spectral analysis and things like that. And these are the students that have been working with me in my lab, very happy to have projects to work on, do fun and interesting things, so that when they go off to graduate school, they can impress their PhD advisor about what they know. But I'm only going to talk about the bacterial swimming part of this as a part of what I'm working with with Dan Goldman, who's interested in robo-physics, the idea that by building these simplified robotic models of nature, we learn fundamental principles about how nature works. And he makes an analogy that when we built steam engines, we really didn't know what we were doing. We didn't have thermodynamics when we built steam engines. We figured out when we tried to optimize steam engines, we don't understand the physics here, and then we figured out thermodynamics. And so he thinks the same thing is true about building robots to do this type of measurement. Okay? So the specific problem, here's that rotobacter spheroidus. I'm loud. There it is. Maybe it was just me. Don't trust me with technology. All right. This is rotobacter spheroidus. Let me go back. Here he is again. He's swimming around with this helical flagellum. He's been fluorescently labeled so that you can see what he's doing. That is apparently a very difficult thing to do is fluorescently label the flagellum of a bacterium. But here he is, and he's swimming around in apparently sort of random motion, right? He's just swimming around. And they have no brain, right? This is a prokaryote. This type of swimming has been around for a long time. What was that? The length scale here is about, well, let's go back to this slide. I was just about to get to that. Imagine about a one micron wide body, about five microns long. So we're talking micron length scales, something like that. And the cartoon of what I'm talking about is an ellipsoidal body. I won't actually model that, not the ellipsoidal body. Just the rigid helical flagellum, and you may say, well, is it really a rigid helical flagellum they use? This is an amazing structure in and of itself made of flagellum. It can take on different conformational shapes depending on pH, depending on rotation sense, and all sorts of things like that. But to first order, it's a rigid helix when it's swimming around. And I say rotary motor here, driven by a rotary motor. Do I mean a rotary motor? I mean a rotary motor. So here is an artist's conception of what's going on. Here's the cell wall of the bacterium. Here is a motor protein complex that was only relatively recently identified. 20-odd motor proteins. You can see the EM image over there. And it uses a stream of protons, typically hydrogen ions, to drive this thing. And each time an ion passes through the channel, it causes these motors to change a little bit and ratchet the motor. It's like a stepper motor like I use in my hands-on session. Drive this thing around sometimes as high as 100 times per second. So it really can spin quickly when it's in motion. And it's just amazing. I love these images. These are cryo-electron tomography images. I don't actually know how they make those. But the amazing detail, the structure of that motor, these are just pretty pictures to look at. The slice through the middle of it. And just this is the 3D rendering of this. It's even more detail. Incredible detail for something that's a couple billion years old, right? This is conserved across a lot of types of bacteria and really interesting structure in and of itself. And this is from Lew et al. I think it's in the journal Bacteriology. And here's a video showing how this would all work for this flagellum, right? Here's that motor working stream of ions through it, causing it to ratchet it around, driving the hook, which attaches to the helical part of the flagellum. And off it goes, spinning this thing around. A lot of bacteria actually have multiple flagellum. And somehow or another, they synchronize their motors such that they can bundle all those flagella into one basically larger flagellum. And that's why it's legitimate for me to think about just a single flagellum in this type of swimming. And so that's the background. But I want to do this in a tank on a tabletop. And I want to do it right if you've been to my session. You know that I have to worry about this Reynolds number thing. But if you've never studied fluids, here's all you have to do is solve this equation. Have at it. This is the Navier-Stokes equation. It's a velocity field equation. What appears, and it's been non-dimensionalized. There are no units here. It's been non-dimensionalized such that the Reynolds number appears here next to the viscous term. And that is important because the Reynolds number, one way we can think about it is the ratio of the inertial to the viscous forces in the fluid. So that in the world where we live, here's Michael Phelps swimming much faster than me in a pool as opposed to a bacterium over here, where the Reynolds number in our world, when I swing my hand around, I create turbulence, it's high Reynolds number relatively speaking, this little bacterium, that because of its length scale, here's a micron there, he lives in a viscosity-dominated regime. So viscous dissipation completely dominates what's going on. And in terms of the Navier-Stokes equation, that means we can throw away the acceleration in the nonlinear term, which is really the hard part. You have this nonlinear partial differential equation in the Navier-Stokes equation, and we get to throw away all the nastiness. And so it presumably life is going to be easier because now we have a linear equation. Well, it turns out life is not so easy. But what I need to be able to do in, let me go back, let me match the Reynolds number, which I'll show you how I do that in my tabletop experiments, but I'm going to digress. I'm not going to talk about Taylor-Collett flow, but I will talk about G.I. Taylor, he's not recognized for how amazing he is with all the things he did in his career. I didn't know that until I looked it up. He's the grandson of George Boole of Boolean Algebra. He studied quantum effects in single photons in like 1904 or something. He did that. He studied turbulence and weather. He studied propeller blades and learned how to fly. Seminal figure in solid mechanics and in nonlinear dynamics. He invented a boat anchor because he liked to sail. It's still used today. He studied in World War II air and underwater blast wave. He was a member of the Manhattan Project. It's a pretty good career. One of 10 VIPs at the Trinity test, which of course that's unfortunate that that ever happened, but he got in trouble sort of for accurately estimating the highly secret blast energy of the Trinity nuclear test from just the pictures. Where's the leak? Where's the leak among the US intelligence? No, he just looked at a picture and did a ballpark estimate of what the blast energy was, right? So it's good to be smart. And he was seminal in micro hydrodynamics as well. In the 1950s, early 1950s, one of the first people thinking about how does a spermatozoa with its flipping tail, how does it move itself at low Reynolds numbers? And he has a paper that's still very well cited starting that. It was 83 when he published his last paper that was seminal in understanding thunderstorms and electro spinning. So yeah, that's a pretty good career. But the reason I bring him up is I want him to convince you that low Reynolds number is different than our world, right? He's got what here is a little Taylor-Couette cell. So there's some Taylor-Couette and what we're going to do. It's got a handle. He's going to hand crank it. And let's see what happens at low Reynolds number. I think I need to click directly on him. Do you get him to go? Nothing surprising here, right? No big deal. That's not the way my espresso works, right? So... That's important. I thought when I first saw this video they just played it backwards. There's no way. It just can't work like that, can it? Low Reynolds number world is very, very different than our world. And the reason I wanted you to see this second part was he's saying that the motion of the boundary you saw immediately, as soon as he starts moving the boundary the fluid starts moving instantaneously. The acceleration term, the right-hand side of Navier... or left-hand side of Navier-Stokes is gone. There is no acceleration meeting. Things happen essentially instantaneously. When a bacterium stops rotating its tail it stops within a microsecond. They've measured this, right? So it just stops immediately. Viscosity dominates what's going on. And so I published previously a study about bacterial swimming using robots. But what's new and different about what I'm going to be talking about today is the influence of getting that bacterium near a boundary and those long-range and somewhat surprising boundary effects that come into play. And what happens for the bacterium, this is from Laoga at all and this paper will keep coming up, but bacteria near a surface will swim in circles. It was known. And they're tracing out these trajectories of live bacteria, small-scale measurements. And they can see that. And we have a basic physical understanding of why this occurs. So let me unpack this a little bit for you. Remember that you haven't seen this before. One of the first things I want you to see here and remember throughout the talk is my coordinate system. Where X and Y are in the plane parallel to the surface that I'm talking about. Z will be the vertical coordinate over here, right? Z is moving into or out of towards the boundary. So if I look at a side view of the bacterial head here, their bacterial model is about as crude as mine. It's a sphere for the head. The part of the sphere that's rotating because the head must counter-rotate relative to the body in order for this thing to remain torque-free because he's free swimming. So the part of the sphere that's closer to the boundary feels the drag of the boundary more than the part away from the boundary. And therefore, it feels a net force this direction. Conversely, the flagellum, here's the side view and then edge on looking down the helix feels a force in the opposite direction. So that's what this FX1 and FX2 are. They are forces in opposite directions. There's a net torque on the swimming bacterium. He swims in a circle. We know the basics of this. The basic physical mechanism is understood. The details are where it's going to get complicated. So anybody at low Reynolds number can be represented. It's a linear system, 6 by 6 linear system, a big coefficient matrix multiplied by the three components of velocity and three components of rotation. If you know the matrix elements, if you know them all, then you're done. And for every different object, it would have a different set of matrix elements. However, for what we're doing, these matrix elements are going to vary as a function of boundary distance. And that's going to create some complications. I put this here. This is a note in the paper where he has labeled these different matrix elements. And the bottom line is any w, generally, should be smaller than any miy. Because in what I'm going to talk about, there's only going to be y-direction rotation for most of it. We'll do a little bit of x-direction rotation. But m should be much, much bigger than w, so I should be able to ignore w's. And I'll come back to why that's important in a little bit. But then you can figure out your forces and torques. And that's what I did in my previous paper. But now I want to do it, measure the thrust, torque, and drag to determine the flagella's propulsion, see how it's affected by a nearby boundary, and then I want to compare. I'm not going to satisfy this. I'm not really going to be able to compare it to Lauga's theoretical models, at least. Maybe when I have more data can do comparison to numerical models, but not yet. And I'll talk about why that's difficult from his theory. But I did want to say my titles are getting cut off a little bit and maybe I'll unplug and re-plug in and I think we'll pick those up. Why do the macroscopic experiment? Why not just do microscopic measurements? So this is what they have in their paper. Full numerical models here. Approximate model there. These are data points. Those are data points. Those are fish. I don't know what those are. And I'm not really sure what they tell me. Now, Lauga, Howard Stone, and Howard Berg are all on this paper. And if you know anything about these people, they are giants in the field. So I don't tell them I put this slide up, but I'm not really satisfied with this data. And I can do better. And I have done better in the one-dimensional problem of just a rotating helix where that big six-by-six matrix becomes two-by-two with only three unique matrix elements. And I can figure out what those matrix elements are just like. Only rotate but don't translate. And I measure the force in the torque and that tells me what these two matrix elements are. It's just a linear system. And then likewise, I can translate but not rotate. And I can pick that up. I can determine those three matrix elements, which in the literature, the theory that was generally used was called resistive force theory. And resistive force theory says imagine zooming in on the flagellum, picking out a little length considered as a tiny little rod, a thin rod, figure out the forces and torques on that thin rod, integrate over the flagellum and you can figure out what your matrix elements are. It's really not difficult to do. The only problem is it's generally wrong. Because if you look at my data, which are the red data points here, and these are the theories, there are two different resistive force theories here. This is for thrust. This would be one of the matrix elements essentially. Light hill of resistive force theory, gray and Hancock, the errors are order of 100% in the regime where we really care because bacterial flagella tend to be over here. So we're looking at thrust, torque and drag non-dimensionalized in some way. You don't need to worry about that. As a function of the flagellum's wavelength over here, so this is lambda dimensionalized by the helical radius. And of bacterium's tends to be here. Torque is okay for light hill, bad for gray and Hancock, gray and Hancock propulsion a little better than light hill, but they really don't get it right at all. And so I can make very precise measurements macroscopically with a lot of work to track down errors and things. You can do this measurement. Here are two different numerical simulations, slender body theory that worked pretty well and matched what I did in the experiments. High precision measurements. They're not all over the place. And that's what I want to do for the case of the swimming near a boundary. So back to this matrix. How do I do this here and what can I do? Well, the first thing, these are Lauga's expressions for the matrix element, but the thing is he used resistive force theory to get these matrix elements. And I already know that resistive force theory doesn't work well, especially when you're close to another body. That's why the reason back here that resistive force theory did so poorly was because as the turns in the flagellum get close to each other, they interact with each other. Nearby boundaries have a long range influence on other solid objects in the fluid, and therefore, it made these expressions wrong to a large extent. And so these expressions that he drives, he uses a resistive force theory, but I don't really believe them, but we'll see. Maybe his numerical model will work, but it involves all that, and there's some i's and j's in there, something that are these expressions, but we'll see what I can do. So the first experiment I'll do is I'll kill off everything else except rotation in the y direction. That's axial rotation of the flagellum. So I'm going to rotate the flagellum, and I'm not going to do anything else, and if I measure the force, f y, the thrust force, then I can pick out this matrix element, so I measure the force, vary the rotation, the slope of the line should be linear is the matrix element. Should be able to do that. I can do the same thing. I can rotate in the y direction, measure the torque, and pick out that matrix element, and then jumping ahead a little bit. I could also just move in the y direction, drag it up, and then I pick up the matrix element over there, and I also have a body that mounts perpendicular to the other body, so I can do some x direction rotation instead of y direction rotation, and the reason I want to do that, especially first of all, I want to measure that perpendicular force. So the flagellum is going to be rotating this way, trying to drive the flagellum this way, but it feels a force perpendicular to its motion due to that increased drag at the bottom of the flagellum that's closer to the boundary, and I want to actually measure that. Nobody's actually ever measured that macroscopically, and I can do that, and then I can see, is this matrix element, I mentioned it should be much, much smaller than these other matrix elements, and we'll see if that's actually true. I can do that with an Arduino board, a $10 DC motor, and my setup there. The most expensive thing that I'm going to use is this silicone oil that's right here. So this body, here's my acrylic body, and my flagellum, it's probably been out of this oil for five minutes, because this is not water, kind of looks like water, but I need to keep my Reynolds number much, much less than 1, right? So my fluid needs a huge viscosity, 100,000 times the viscosity of water. It's pretty expensive. You could also use, as G.I. Taylor was using, glycerol, you could use syrup. It will work for low Reynolds number stuff. When I was at a conference, sure, it's density of water. So yeah, same. Yeah, it's 0.98 the density of water. So yeah, the kinematic viscosity is also 100,000 times the viscosity of water, too. Yeah, it's a weird substance in that it's sticky and slippery, and I don't know what to make out of that, but it also has a pretty low surface tension, so it leaks into everything. Drive you crazy, it leaks into the body and then burns out your motor. Because if that hits your gearbox, this has a 300-to-1 gearbox on it, this little motor, and if that high viscosity silicone oil gets in there into the right gear, it'll just burn it out almost immediately. But that's how we do it. That's how I can scale my problem up to a 10-centimeter robot. And I don't have to deal with the complexities of making a small-scale measurement. There's no reason for me to do that. All I have to do is scale my fluid dynamics up and believe in Reynolds number scaling, and I can do that. But like I said, that's probably the most expensive part of it. So the parameters of my flagellum, I'm currently only using one flagellum right now. It's pretty close to the sort of properties of a bacterial flagellum. Not as long as bacterial flagella typically are in this case, but this is how we do it. We say, okay, the radius of the helix is r, and we use that as our typical length scale. That's about six millimeters, a quarter of an inch for those Americans in the audience. The filament radius is an important parameter. Bacterial flagella tend to be very, very thin, thinner than this actually, but that's okay for what I want to do. In the paper that I published in 2013, we used thinner wire in building this helix. Lamb does the distance between these crests, and we express that in helical radii, and then there's the overall length, again, expressed in helical radii, so it's all non-dimensionalized. There's no units involved. Fluid dynamicists hate units. We always want to get rid of them. So here is an action again, and about here, if you saw it before, there's a bubble right there. It's rising buoyantly. You can't tell in the time scale of the movie that it's rising buoyantly, but it will eventually come up to the surface if you wait long enough. There is an action. Okay, so how am I going to do all this? How am I going to measure my matrix elements? And what are the devices that I'm going to use? So over here, again, here's my coordinate system now. My boundary is this vertical boundary. That's the z direction. X is coming out of the plane. Y is along the axis of the flagellum. The propulsion is going to be upward, vertically upward. And I have a stepper motor up here, exactly like the one I use in my hands-on session. I use this torque sensor to make my force measurements. All of my measurements will be made with the same torque transducer, which is an interesting little device that has two shafts in between as a little filament that emits a magnetic field under a torsional load. And that gives me, I have some hall probes in it that give me the torque as a function of, I mean the voltage as a function of the torque applied to that inner shaft. I put that in there. I rotate my flagellum. I move the boundary around. So the flagellum holds still and the whole tank moves. I have a translation stage that was intended for a CNC machine. These are cheap. You can buy them online. And I can get accuracy order of .01 millimeters with it pretty easily, pretty cheaply. Move my tank around very precisely, because most of the action, most of the change in the propulsive characteristics, change in the matrix element, is going to occur over the first centimeter or so as we move this guy around. So thrust and drag measurements, same thing. I'm going to put him in the fluid. He's going to try to swim up. He's constrained. And that's an important point. There's no translation upward. He hits the torque sensor, get an applied torque. We can convert that into a force. And that'll give us the propulsive force. Move the tank around. That's with my translation stage. And I can measure that propulsive force as a function of boundary distance. And then drag. I take the whole thing, the whole apparatus and move it up and down. And I can get the drag force with no rotation. So velocity, no rotation. Rotation, no velocity. I can pick out matrix elements. And so let's take a look at what I can do again, right? Why I'm making these measurements, right? Rotation in Y, but no rotation in X or velocity in Y. I do each one of these independently and I can pick out these matrix elements and look at the data as a function of boundary distance. But each boundary distance for each of these measurements requires multiple measurements from the torque sensor. That's the torque signal up here. And sometimes an experimental problem is an opportunity. We previously took movies of the flagellum rotating and used PIV to pull out the rotation frequency. But we realized that our torque signal oscillates at the same frequency as the rotation rate of the flagellum. So now all we do is we analyze this with an FFT to get the rotation rate of the, a fast Fourier transform of the torque signal itself. We just take the one measurement. And we plot this data out. I claimed it should be linear. I claimed that the force as a function of rotation rate should be linear and up to some scatter is linear. The error bars are about the size of the data points. It is, but it's the tip of the flagellum. Yeah, we're feeling as it's rotating around you'll see if you go back Well, it's actually look at, if you look carefully at the body itself he's oscillating a little bit. And that's because I think Yeah, yeah. And also if there's any misalignment of the helical axis too then it'll Right, well yeah, so the any misalignment of the flagellum I know when it's out of alignment because I'll get I actually see it moving a little bit. It's wiggling around due to imperfections in the flagellum. I do my best. Yeah. Yeah, yeah. Yeah, yeah. But it's always there. No matter how well, no matter how well I align this guy, I always see just a little bit oscillation and I have to try to minimize it in my signal. I'm not trying to be a giant. But the thing I want you to realize about what I'm asking my undergraduate students to do is the range of forces that we're talking about here is 3 to 15 gram forces, right? So there's a lot of extraneous control, controlling all extraneous sources of forces on that bacterial body is important. We have to get the wires arranged, right? Oh, track down that error, get inconsistent results. It's a challenging experiment. The idea is simple. The devices are simple. We're using an Arduino board sending a voltage to this motor. Everything is really straightforward, but it's getting the precision that we need to get good results. And that's what was true from my paper in 2013 as well. We spent a year and a half getting data through all that data away because we figured out all the mistakes we were making and we just started over. Clean data after that once we figured out our experimental methodology. It was tricky. So let me show you what the normalized torque here, and what I'm normalizing it by is the value out here, say, by this data point. So I've measured torque as a function of boundary distance. So each one of these is a linear plot and we pulled out the slope and we put it here. And we divide all these values by the slope value out here with the torque. So we see something that I can fit with an exponential. That's called T-L-A-R. That looks about right. There's no reason for me to do an exponential fit. Other than it gave me, I could do a spline fit. Give me enough parameters so I can fit anything. Exponential fit seemed to fit the data. So we did that just to kind of guide your eye. But like I said, you see that all the action is in here, right? We see a 30% increase in the torque as you get close to the boundary. So the matrix element is changing very rapidly as a function of boundary distance. And this really this functional form really doesn't fit what Lauga has. It's pretty hard to unpack what it should actually look like as a function of boundary distance. But it's I don't think it's this. And I need to do more work on that in making more direct comparisons with his data. So that's our torque values and again, this kind of precision versus that kind of precision, like I said, I'm going to get beat up at a conference or something for putting that up. Yeah? What is what is where did you have this like this boundary layer where the boundary How does that really relate to a bacterium? Is that your you're putting only the distance to the boundary but if you normalize with the size of your robot Sure, sure. How many, okay. So my the helical radius is about half of a centimeter. Yeah, you're right. I think that is a better way to plot the data. It's a good point. Yeah, that I really should be non-dimensionalizing this boundary distance as well. It's a good point. Yeah, the divide every or multiply everything by two about because it was a 6.1 millimeter helical radius. I think that would be the appropriate way to do it. And whether this is exactly zero or not, it's tough to tell. It's really hard when the because you've got this acrylic boundary clear fluid and you're trying to eyeball down the boundary to make sure that you're right at the boundary and surprisingly I can't tell often that I'm hitting the boundary as we move our translation stage around. We figured out a way to make that to figure that out though. We tried lasers we tried various other methodologies to get that to happen but I think I figured out a way from the torque signal to determine where we are consistently as a distance to the boundary because with this rapid increase if you're slightly off if there's another quarter centimeter over here you could have been closer then this force would be screaming upward. So it's an important consideration as we track all of these things down. Here these are just spline fits to my data and so what I didn't present on this plot is counterclockwise rotation it's the same here in the torque data but it should be the same for clockwise and counterclockwise rotation in my previous paper but it's not. We were surprised by this result right? Very large difference between clockwise rotation and counterclockwise rotation I told my students I don't believe you I have to see this show me show me in the lab let's do this do it and then maybe I'll believe you that's good to be the advisor but so same thing force free divided by boundary distance same flagellum so again you could multiply by two lots of action early on and you can see we were rastering closer here for these propulsive force measurements and we run into so many difficulties that we didn't get as far this summer as I'd hoped we would but that's the way experiments go but this result is robust there's a huge difference between clockwise and counterclockwise rotation and I got worried when I found this result and I'll tell you why if you look at how we make this measurement over here I am really measuring an x direction torque right? x is coming out of the board my thrust measurement is an x direction torque which says that if there was an x direction torque that should be there according to the mobility matrix is what this thing is called then I've got a flawed experimental design so I was worried about that and sure enough if you look at the x direction torque there could in theory be this matrix element W coming into play and therefore my experimental methodology is just flawed I sweated that for a while and then I thought wait a minute that doesn't make sense because if I flip the rotation rate it should flip the sign of the x direction torque I should not see the asymmetry between clockwise and counterclockwise rotation that wouldn't make sense now it might be affecting my propulsive force a little bit that's possible but it wouldn't have created an asymmetry however if there is a z direction force if I go back then that would be affecting what I see because this is the z direction here if there is an attractive force created by the pumping of the fluid downward if it draws it to the boundary then that would affect my measurement I think that's what I'm measuring and if you look at the mobility matrix again where is the mobility matrix here Laulga writes these down he says that these are zero either by symmetry arguments which he doesn't present because if you integrate over a full period of oscillation then it would be zero however there is supposed to be an attractive force for motion parallel to the boundary so if you imagine that instead of the pumping of the fluid in the y direction I might be picking up this matrix element or something like that I'm not overly sure yeah in both cases I have not done that test yet and yes I would like to do that but when I built these flagella what I did was I had a CNC made to take a groove for me so I could bend the wire around it so doing that requires me to have a CNC laid which I don't have where I'm at but I'm going to do that there's another way I can build these by just wrapping it around tightly around and then expanding it out Kenny Breuier's group that's how they did there Ed Brown that's how they built their flagella for this type of thing so you're right that's exactly I need to do some other tests to figure out does this flip the sign of it I don't know for sure but yeah it's interesting but this is what oh it goes away away from the wall yeah for sure yeah well and I realized that well like other experimental problems it isn't yes I did there's no difference far from the wall so yeah it's a good point but yes when we get 7, 8 centimeters from the wall it's some and you know you reduce you reverse it you get the same value you don't get some weird value because I do have to worry about because of gravity involved in here in these small forces we have counterbalance weights over here to get it neutral and there shouldn't be any reason but we we're still tracking it down it's an early result that happened you know 3-4 weeks ago yeah Logan they do but for a different reason though when they do that that phlegelum unbundles it's bundled it unbundles and takes on a different conformational shape for most I would just kick it so how much force you have to kick could randomize the orientation of the body better so it could still be important especially there at the surface they do pick one direction typically when they go the other thing yeah that reversal but yeah but what I realized though let me go back the curves well if what I'm saying is true what I could do though is subtract this curve from that curve and they give me another matrix element in one measurement the other thing I can do to test this is reorient my torque sensor and see how that and play some games with which direction the forces being the torque sensor axis is whether it's parallel or perpendicular to the boundary but that would be tough to do tough to do with the precision you need to subtract this from that but maybe so maybe we can do that and pick up this other matrix element that's coming into the the measurements so that's how we did that so future work there's a lot more to be done to try and contribute to this problem the boundary I really want to make more quantitative comparisons to the Lagos theory because it's a bit tricky so there's two things about his theory one was that he has these complicated equations but he also did two things he did the free swimming case and he did next to the boundary and I think I can look at his expressions and try and figure out what the functional form should be as a function of boundary distance there are lots of other things I can do with my low Reynolds number setup bacterial flagella synchronize through more or less unknown mechanisms we don't know exactly what it is there's a lot of debate with these types of things whether hydrodynamic interactions are all you need to synchronize but I can do some macroscopic tests where I don't have Brownian motion problems once you can all think that Brownian motion thermal effects are really really important but I have a system with no Brownian motion that's the one big difference between my setup and the real world of a bacterium is no Brownian motion in this the other thing that Dan Goldman and I are working on is another very simplified robot at low Reynolds number which is a three-link swimmer lots and lots of theory by Hatten and Chauset and various other people that goes back to Wilczek a physicist who in his spare time besides winning Nobel prizes for his high energy physics created the field of geometric mechanics thinking about the three-link swimmer and getting rid of all the actual physical equations about the geometry of the problem and sort of group theory kinds of stuff and it's really interesting what you can try to do and what Dan did he did this in granular material here is his three-link swimmer this is what I'm talking about there's just two angles for this three-link swimmer and get a couple of servo motors is what my student is doing right now I'm going to go and test these theories about three-link swimmers at low Reynolds numbers because people can write down what they think the topological phase space is between angle one and angle two you get what they call height functions where if you trace out a gate a repeating motion of this three-link swimmer in this space all I have to do is figure out the area and I can figure out the rotation and distance traveled without knowing anything and so whether these expressions Dan, what he did was used small motions to map out these height functions in granular material because there is no equation there's no navier stokes for the granular material but we want to do that in a tank of silicone oil that's the wrong way I'm not going to talk about that and so yeah, this is a hat in Cho Set and Yang Ding that's worked with him before and we're going to be doing that as well using these low Reynolds number macroscopic experiments using techniques and devices that are orders of hundreds of dollars except for my expensive silicone oil which is about $100 a gallon I don't know how to translate that in euros per liter but that's four liters of silicone oil for $100 US yeah, it's about the same 20 euros a liter 20 euros a liter, thank you but could be done more cheaply so it's all the same sorts of techniques the things that we talk about here to do real science and have fun doing it that's the idea alright yeah, question