 We have your slides, yeah, first page and yeah, okay, go on. Hi everybody, I want to talk about continued modeling of electrophoresis and zeta potential of air bubbles in pure water. Hydrophobic water interfaces like air or oil water interfaces are negatively charged. One evidence is that micro bubbles suspended in pure water move towards the anode under the exposure of external electric field. Micro bubbles are very fine bubbles and appropriate for the investigation of the air-water interface electric charge because of the reliant stagnation in the electrophoresis cell observation error. The source of this charge is under debate for several years and the molecular explanation can't explain it very well until now. One interpretation proposed to explain this negative charge is accumulation of hydroxyl ions at the water surface. Another is presence of trace amount of surface active charge purity and another potential mechanism is anisotropy of intermolecular hydrogen bonds at the air-water interface. With focus on the potential effect of charge transfer between water molecules, the core speculation here is that asymmetry in hydrogen bonding between water molecules lead to a charge transfer from hydrogen accepting to the hydrogen donating water molecules. In the symmetric environment at the bulk water, this effect demise. However, this is not true at the anisotropic surface of water. Here we have the volumetric electric charge profile at the air-water interface and that is obtained from Poiet-Au linear scaling density functionalatory based simulations. They use Willard and Chandler formulation to obtain the charge profile which defined the instantaneous density fluctuation of the interface. This profile shows that there is a substantial negative charge density of approximately 2 angstroms from the Gibbs dividing surface in the waterfiles. It is notable that Gibbs dividing surface is where mass density reaches to its hot value. The air-water interface is made rough by thermal fluctuations that smear out properties computed related to the Gibbs dividing surface. However, the instantaneous interface does not include contributions from fluctuations in interfacial position and is at each moment in contact with airfiles. We intend to use the continuum model to check how much charge transfer is responsible for negative charge at the air-water interface. Before proceeding to the continuum model, I give a review on basic concepts on electrokinetic of charge particles. When a charged particle immerse in an electrolyte solution is subject to an external electric field, the particle moves toward the particle moves due to the imposed electric field and the relative motion between the particle and electrolyte is developed. This phenomenon names electrophoresis. Electrophoresis mobility turns to electrophoresis velocity divided by external electric field magnitude. The shear or slip plane is a hypothetically location near the surface that separates the mobile surrounding fluid molecules and ions from the immobile part attached to the surface. In other words, counter ions or charge in the shear plane acts like they are part of the particle and that one's outside of the shear acts as if they are part of the surrounding fluid. The zeta potential is defined as the electric potential at the shear plane. It is common to use a zeta potential for indicating amount of charge carrying by the particle, but only to the fact that the reported experiment data are electrophoretic mobility we would prefer to use a platter to avoid double incorporating viscosity in our model. In this question, you can see how the zeta potential can be related to the electrophoretic mobility. Argovan, sorry, I had a question on the previous slide. The viscosity here is the bulk of viscosity. Yes. Okay, it's the bulk of viscosity. So, due to this fact, the point that you said, we avoid calculating zeta potential because we get rid of using bulk or any other viscosity profile here. If we use electrophoretic mobility, we get rid of using viscosity. Sorry, what is the thickness of the shear plane? Can you repeat the... What is the size of the region that you call shear plane? Shear plane is a hypothetical plane, but it is different in several electoral lights. And one of the books that our model do is to estimate the location of shear plane for the air bubble interface. I mean, do you have an estimation? Yeah. About 3 angstroms. Okay, okay. Location of shear plane in our model is fitting parameter. We run our model for several locations of the shear plane and calculate the electrophoretic mobility corresponding to each of them. Thank you. At hydrophobic interfaces, the fluid velocity is not assumed to vanish at shear surface. This arise from lower friction force that hydrophobic surfaces exerted on fluid. This makes slip boundary conditions an appropriate choice for fluid velocity at the shear plane. The slip boundary conditions is identified with the slip length, which is defined as where the linearly extrapolated tangential velocity profile of the fluid vanishes related to the interface. Our continuing model approach is very similar to standard electrokinetic treatment utilized in the charge collades, incorporating the balance between electrostatic and hydrodynamic stresses imparted on the collade. Once a stationary fluid flow and electrophoretic particle current is established, the air-watching interface model as a flat plane that makes sense while thickness of the charge region is a small comparable to the bubble radius. And this plane is extended in z direction while external electric field exposing in x direction. The electrically-deriving fluid flow is governed by the Stokes equation, where a tau is a viscosity profile across the interface, u is the velocity profile and is external electric field and rho e is a volumetric charge profile that is obtained from the simulations. This equation is solved with a slip and no stress boundary conditions in the bubble fixed frame while the corresponding slip length and accurate position of the shear plane, the shear surface is treated as fitting parameters. Dividing the obtained velocity of bubble by magnitude of external electric field, we can calculate the electrophoretic mobility of air bubble. In this part, we present results of our model assuming that the viscosity across the air-water interface would be equal to bulk-water viscosity beyond the shear plane. This plot is the electrophoretic mobility considering mentioned viscosity in the model versus different positions of shear plane across the interfaces. And we plotted four slip lengths, one, two and three nanometers. By contemplating that position of shear plane could be from zero to approximating two nanometers. Takahashi obtained the electrophoretic mobility of air bubble immediately from experiment as minus 25 times 10 powers minus 9 mesh per square over volt second and assuming that three nanometers be true reasonable choice for a slip length, the best fit value of electrophoresis mobility predicted by this model is equal to minus 8 times 10 over 10 powers minus 9. It's magnitude is 68% smaller than the experimental one but it is 25% better than past similar works in the literature. Across the air-water interface, viscosity varies from somewhat around zero at air-files to one millipascal second at water-phase. Thus, the viscosity alters remarkably across the interface between a few angstroms where the charge profile is also negative in that region. We intend to obtain viscosity profile across the interface from the self-diffusion coefficient profile and from Berners-Allpaper. Then using a sex angstein formula to obtain viscosity. Come on, we have three minutes at most just for you to manage your time. Okay, thank you. Using this viscosity profile in the model, the minimum value of electrophoresis mobility for a slip length three nanometers reaches to minus 16 times 10 powers minus 9. That is 20% closer to the experiment. It shows that the viscosity profile has a crucial role in all results. However, this self-diffusion profile that we use for calculation of the viscosity profile is a respect to Gibbs dividing surface. However, it smears out the results and doesn't give accurate results. We want to progress our work by calculating the viscosity profile versus the instantaneous position of the surface to get more accurate results. Thank you for your attention. Well, thank you very much. We have time for questions if there are any questions. I have one if possible. I have a question about the A bubble. I mean that if we have something instead of the A, some other sphere, has it any effect in your calculation? Any other bubbles? Like an oil. Drops or solids or everything, a sphere. I would like to know where the air bubbles are in your research. Air bubble is... the electric charge is obtained for the air bubble and the experimental value that we are comparing our model results with it. It's obtained for air bubbles. I can repeat the question before I go on. The question is if instead of air you have something else, like the electric sphere. Reza, correct me if I'm wrong. Then where in your model the fact that instead of air you have a solid sphere like the electric enters? Where does it enter in your model? That's the question. In the charge profile. Just you are borrowing the charge from the air. That's right? Yes. Exactly, that's right. Repeat your last sentence. Everything is the same. Just you have a different value for the charge density on the sphere. Charge profile and viscosity profile and also the slip length. These things will be different. The thing is that the argon doesn't solve for the electrostatics. The electrostatics come from MD simulations by Ali and Marco Polini. Basically they... Marco Polini, I said. Emiliano Polini, right? Oh my God, sorry. Then basically we use that as an input because a row is more of a quantum nature that has to be obtained through basically a test used as an input here. If you use the electric sphere I think you have to repeat MD simulations bring in a row as an input parameter so we don't try to solve a Poisson equation for electrostatics because this is not what we want here. I think Ali can correct me if needed. Okay, that's good. I have actually a question from Ali. Are your voids negatively charged, Ali? That's a fantastic question and in fact they are. Okay, that's good. Yeah, we'll talk about this later. Can I just... Ali, is it time for a question or comment? Yeah, I think. It's a quick comment for Ali Rajapur, Edgar Roldan and Roman Belosov because they're all working on related things about spatial dependent diffusion constant first passage time. And so one interesting question and a challenge here is being able to infer the correct spatial dependent viscosity profile. What Argovan is doing now is a bit of a hack which is using the D of Z and inferring from Stokes-Einstein relation which may or may not be correct. But anyway, it's an interesting problem to think about given the other problems we're working on. So maybe we can get together and talk about that after maybe not... Well, some other time because I know it's late for today's session but at some point, right? Maybe we can arrange a group discussion about that. Absolutely. I'll just see Roman Stokes There are going to be two talks now so the next one is going to be Roman