 In the previous lecture we started discussing about how to modulate surface tension. So, we were discussing about that how to generate gradients of surface tension maybe by generating gradients of temperature for example, which is known as thermo capillary or marangoni convection. Now, to generalize let us say that there is a free surface for the time being let us assume that the free surface is flat. In our next chapter we will see that I mean how to modify this if the free surface is itself curved, but for the time being let us assume that there is a flat free surface for simplicity. So, let us take a small element dx. Now, on this small element let us say here the surface tension coefficient is sigma. Let us say that the width is 1, width equal to 1. So, this is sigma and let us say that here the surface tension coefficient is sigma plus d sigma. Why this is sigma plus d sigma? Because maybe there is a temperature variation along x because the temperature variation there is a surface tension variation. So, sigma has changed from sigma plus d sigma. Now, we can write so there is a imbalance of sigma and sigma plus d sigma. So, that may be balanced by a shear force which is tau into dx into 1 where 1 is the width. So, we can write from the force balance that is sigma plus tau dx is equal to sigma plus d sigma that means tau is equal to d sigma dx. So, we can write this as d sigma dt into dt dx. So, you can see that how a shear stress can be generated because of surface tension gradient and this stress can be the driving influence for the fluid flow to take place. So, this is one effect that we discussed in the previous lecture. This is just a continuation. Controlling surface tension by surfactants also is a possibility. So, surfactants are short forms of surface active agents are compounds that lower the surface tension between 2 liquids or between a liquid and a solid. Molecules are attracted by interfaces. So, you can create an assembly of molecules which are adhering or attach to the interfaces and there are several applications of surfactants like in emulsification, in detergents like in soaps, in missiles and so on. So, basically adding surfactants is a way of controlling surface tension by creating a concentration change by making a change in concentration by adding surface active agents. Controlling surface tension hydrophilization. Now, this is a very important point to discuss in many microfluidic devices. The substrates that we are using are originally hydrophobic like for example, PDMS. We will discuss about this like polydye, methyl, siloxane that it is inherently a hydrophobic substrate. Now, these hydrophobic substrates may need to be hydrophilized. So, how they can be hydrophilized? There are certain possibilities. So, the fundamental principle is attaching polar groups or non-polar surfaces. So, commonly what is done this process is routinely done in our labs that is we have oxygen plasma treatment or plasma activation. The surface reacts with reactive molecules. So, you have gases like oxygen or you can have water these can be ionized and so basically you can attach polar groups on surfaces and these polar groups can impart hydrophilicity to the substrate that is the fundamental principle. Now, this particular principle I mean it is good to use it is quite cheap. So, in labs it is very convenient to use but one of the problems is that it is not long lasting. So, the hydrophilicity that has been imparted will go away if you leave it beyond a critical time. So, it depends on how long you are doing your experiments. If you are doing experiments over a period of time over which the hydrophilicity remains then that is fine but otherwise you have to go for a permanent treatment. So, permanent treatment is coating with the hydrophilic material for example, PTOX is a material. So, you can make a coating with the hydrophilic material it is long lasting it is not a short time solution like oxygen plasma treatment or plasma activation but it is costly. So, I mean this is of course quite obvious that any process which is not long lasting will not be that expensive but process which is long lasting is expected to be expensive. Controlling surface tension by electrical effects this is a very very important concept and we will discuss this in some details. So, if you recall that in one of our introductory lectures we discussed that how to make a droplet move with the help of electric field and today we will discuss the science that how that can be possible. So, let us say that you have a electrode just look at this schematic on the top of the electrode there is a insulator. So, typical insulator is a dielectric material and what is not shown at the top because it is a very thin layer is there is a thin hydrophobic layer on the top of the insulator. I mean that is important because you want to form a droplet on the top of that. So, if it is not hydrophobic you do not expect a droplet to form right. So, you you typically have electrode on the top of that an insulator and on the top of that a thin hydrophobic layer. Typically like I mean the insulator even in silicon technology SiO2 can also be an insulator and you require a hydrophobic material for that case very strictly because SiO2 is actually not hydrophobic it is hydrophilic. So, you require a hydrophobic layer on the top of that. So, very commonly like insulators I mean many common insulators or dielectric layers are like periline for example, I mean there are several different types of materials even you can use PDMS as a dielectric layer. So, you have a dielectric layer and on the top of that you may have a hydrophobic layer like say Teflon for example, Teflon is a very common hydrophobic layer. What are the typical thicknesses of this just to give you an idea just a rough idea. Say typical insulating layer thickness will be around say 8000 angstrom and typical insulating sorry typical hydrophobic layer will be around 1000-2000 angstrom like that. So, that will be the I mean these are not hard and fast numbers just to give you a feel of the dimension what we are talking about. Now you can see that like in this figure we apply a voltage across the electrode and the droplet. So, how that is possible sometimes you can sandwich the droplet between 2 surfaces and on the top surface you can have a coated ground electrode like ITO coated electrode for example. So, I mean of course we will discuss about the science but you know as engineers it is important also to know that what actually we do to implement it in practice. So, I am parallelly talking about what we actually do and like what is the science behind that. Now the contact angle theta when the voltage is applied changes and the contact angle changes by this corresponding formula cos theta prime is equal to cos theta plus half Cv square where C is the capacitance per unit area of the dielectric layer half Cv square by sigma Lv. Now we will discuss about this formula in details but like certain things which we can get from this formula immediately. What are the things that we get from this formula immediately? First of all cos theta prime is equal to cos theta plus what a positive term right because it is V square. So, does not matter whether it is positive bias or a negative bias ultimately you will get the same effect provided the magnitude is the same. That means that cos theta prime is always greater than cos theta that means theta prime is less than theta that means when there is a droplet it is becoming more weighting as the voltage is applied that is why this process is called electro weighting. So, why you want to form a droplet? Why do you require a hydrophobic layer? Because you want initially something which is non weighting or less weighting by a voltage you want to make it more and more weighting. So, that is what overall we can see now we will look into some more details. So, there are several configurations possible. One is the open configuration where there is no confining boundary at the top and the other is the sandwiched configuration where there is a confining boundary at the top and these two are the two extreme configurations sometimes it may be possible that a part of the system is unconfined and a part of the system is confined. So, the countertangle changes with the applied potential you can see that look into this experimental picture this is hydrophobic under no potential. So, you can see that a droplet is forming now if you apply electric potential this becomes more weighting. Question is we will look into this that does this process go on eternally that means if you apply more and more voltage it becomes it goes on becoming more and more weighting is it so we will answer this question but these are critical questions not only that is it reversible. So, these are the points that we will discuss. So, the mathematical expression that cos theta prime is equal to cos theta plus half cv square by sigma lv we will prove this but for the time being assume this is known as Young-Lipman equation. So, this Young-Lipman equation can be experimentally tested. So, you can see that there are two interesting observations this red colored line with black squares on the top of the red colored line is a representative of the advancing contact angle that means what you do is that you go on applying the voltage and the contact angle decreases. But you can see that beyond the critical voltage the contact line does not go on eternally the contact angle does not go on eternally decreasing it comes to a saturation this is what is observed in experiments. On the other hand if you reduce the decrease the voltage from the maximum one then the contact angle is getting increased. But you can see that the increase in contact angle is not following the same path as that of the decrease in contact angle with increase in voltage. So, there is some hysteresis these two are very important observations in the electrowetting phenomenon and these observations mind it or not there have not yet been I mean convincing theories to explain this phenomena I mean these are I mean people have come up come across with theories to explain this I will give you some sort of like some summary of what are the explanations given. But these are yet the problems which are yet to be resolved theoretically I mean experimentally these have been observed. But theoretically these are yet to be resolved contact angle saturation the Lipman young law or young Lipman law whatever way you say implies that the apparent contact angle continues to progressively decrease with increasing applied electric potential. However, experiments reveal that the apparent contact angle stops decreasing beyond the threshold value. This phenomenon is called contact angle saturation. What are the possible reasons for contact angle saturation I mean these are some of the possible reasons see all these are like hypothesis I mean it is I mean theoretical foundations have not been strong enough to convincingly pinpoint the entire phenomenon the details of the entire phenomenon. So, trapping of charges in the dielectric layer the vertical component of the resultant electrical force acting on the liquid air interface close to the contact line or I mean a limit which is prescribed by 0 surface energy limit. So, these are some of the possible explanations which have been given. But I mean there are still many open questions to be answered contact angle hysteresis as we increase the applied voltage the droplet spreads and the apparent or macroscopic contact angle decreases the equilibrium contact angle at every applied potential during this path is a static advancing contact angle if you assume that the droplet is spreading. So, slowly that each individual state in between is in local equilibrium then like it is a succession of static equilibrium configurations through which the droplet is going and the contact angle is decreasing like that. As the voltage is gradually decreased the droplet gradually regains its initial shape and the contact angles are the static receding contact angles hysteresis refers to the fact that the advancing and the receding contact angles are different as we discussed this is due to random pinning of the 3 phase contact line by microscopic surface defects this is a postulate remember. So, when I say that this is due to it would have been better if I said this might be due to okay this might be due to random pinning of the 3 phase contact line by some microscopic defects like surface roughness physical or chemical surface defects and so on. Another manifestation of hysteresis during electro waiting on dielectric I mean this phenomenon is also called as electro waiting on a dielectric that name is the reason of giving such a name is pretty clear that electro waiting is occurring over a dielectric layer is the existence of a minimum actuation voltage for the droplet motion this is another manifestation of hysteresis. At this voltage the electro capillary force is just sufficient to overcome the surface pinning effects in general for any surface hysteresis is quantified by the difference between the maximum static advancing contact angle and the minimum static receding contact angle without any electric effect this is how the hysteresis is defined the difference between these 2. So, like you know when there is a contact line the contact line tends to move so something which disrupts the movement of the contact line. So, an effect which tries to disrupt the movement of the contact line. So, like for example aspirates on the surface so if there are aspirates on the surface the aspirates on the surface will try to disrupt the movement the continuous movement of the contact line. So, it is a sort of a resistance you can say. So, based on this one can talk about a phenomenon which is like based on electro waiting on dielectrics or in general the electro waiting phenomenon you can have a phenomenon which is called as electro capillary phenomenon. So, electro capillary phenomenon refers to the modification of the surface tension by presence of electrical charge. So, it is a concept which is related to like how surface charge can alter the surface tension or equivalently the surface energy. Surface tension occurs to be a strong function of the electrical potential and is described by the Lipman equation. Now, we have also discussed the thermo capillary actuation right that is creating a surface tension gradient due to temperature gradient and here we are creating a surface tension gradient due to electrical voltage. Now, this is a good time when we can compare these two. So, advantage of electrical electro capillary actuation over thermal counterpart is the speed with which electrical potentials can be applied and regulated with possible characteristic time scales of even less than a few milliseconds. So, the thermo capillary system has a inertia. So, it is it takes a time for the system to get adjusted to the temperature gradient and that is how to generate the surface tension gradient. On the other hand, this electro capillary actuation is almost instantaneous. This also takes its own time, but the time taken is much shorter. Not only that, this is the characteristic time scale is in terms of science, in terms of technology also when you talk about the electro capillary system, it requires integrated electrodes on a microfluidic platform. So, that is very common in lab on a chip based devices. So, it is possible it is often quite straight forward to integrate electrodes on a with a microfluidic system or integrate electrodes on a on chip device. It may not be a microfluidic system, it is in general a chip. So, to integrate electrodes on a chip is much easier rather than to create a design temperature gradient on a chip. So, that makes it possible that makes it possible that you can apply an electrical field to modulate the surface tension and low electrical power may be sufficient in modulating surface tension. So, you energy wise the kind of energy that you need to spend for creating a thermal gradient, you can safely use very low energy as compared to that to create the surface tension modulation through electrical field. Now, I was talking about the Lipman equation. The Lipman equation relates interfacial tension to electrostatic potential. So, you can see here that you have a del sigma del E is equal to minus Q A, where sigma is the surface tension. E A is the potential of a cell in which the reference electrode is in interfacial equilibrium with one of the ionic components of A. Q A is the charge on an unit area on the interface. Mu is the chemical potential. We will discuss about chemical potential, electrochemical potential, all these things in details when we discuss about electrokinetics. This is just a definition that we are talking about. T is the temperature and P is the pressure. So, at constant temperature and pressure, basically the gradient in surface tension with electrical field or electrical potential to be specific is nothing but negative of the charge and per unit area of course. So, you can see that if you can create a charge on an interface, then that will create a gradient in surface tension or a surface energy with the aid of an electrical potential. Or equivalently, if you have a gradient of electrical potential, then the variation of surface tension with the electrical potential will implicate an equivalent amount of charge stored at the interface. So, charge at in the interfacial location if you can alter the charge, it is possible that you can also alter the interfacial energy or the surface energy. Now, we discussed about the Young-Lipman equation. There are various ways in which one can prove the Young-Lipman equation. Now, here we have put a very simple battery capacitor analogy to derive the corresponding equation. Let us look into that. So, if you look at the system, so you have a counter electrode on which there is an insulator. So, typically we often just draw the insulator, but not the hydrophobic layer. Now, if the insulator itself is a good hydrophobic layer, maybe additional hydrophobic layer is not necessary. But if it is, if there is no hydrophobic layer and the insulator itself is not sufficiently hydrophobic, then it will not form the droplet on the top of that, that we have to keep in mind. So, now you apply a voltage across the system. You can see that the voltage V is applied. So, upon connecting the initially uncharged droplet to the power source which is a battery, a charge delta Q flows from the battery to the droplet and then to the electrode. So, let us assume that there is a charge delta Q that flows from the battery to the droplet and to the electrode. The resultant work done on the droplet electrode capacitor is given by what? So, if there is an instantaneous charge Q, then the resultant work done is V, the potential that is established at that instant when the charge is Q times delta Q. Now, the potential across the capacitor when there is a charge Q stored is Q by C, right. So, you can write in place of this one V Q, you can write Q by C and you can integrate this to get the total work on the droplet is equal to half C into final battery voltage Q square and this you all know. This is how the energy stored in the capacitor is evaluated. So, this VB is the final potential. See finally, it is charged to the potential of the battery, right. So, the potential when you integrate it over the potential, the potential is from potential 0 to the final potential VB. So, that makes it half C VB square. Now, there is a work done on the battery. So, we have talked about the work done due to charging of the capacitor, but there is a there is also a work done on the battery. Work done on the battery is the voltage across the battery times delta Q for the battery. Now, what is delta Q for the battery? A charge delta Q has flown from the battery to the capacitor. So, for the battery delta Q battery is minus delta Q, right. If the capacitor is charged by the charge plus delta Q, then for the battery it is a loss of charge. So, the for the battery delta Q battery is minus delta Q. Now, since the battery voltage is constant, so you can take this VB outside the integral and then the total work for the battery is minus C VB square. So, what is the net work done on the battery electrode system? What is the net work done on the battery electrode system? The net work done on the battery electrode system is the total work done on the droplet and on the battery. So, that is equal to half C VB square minus C VB square first component for the capacitor and the second component for the battery. So, it is half minus 1 that is minus half C VB square. So, this work is done on the battery electrode system. So, this work is done how? This is where the fundamental science is there. This work is done at the expense of the surface energy. So, a part of the surface energy is utilized to do the work. So, which surface energy? It is the solid liquid surface energy sigma SL. So, that means, now sigma SL will be effectively reduced by sigma SL minus half C V square. That is the, this is the essential thing. So, now if you see, let us come to the board to see that what is the consequence because some of the steps are missing in the slide. So, cos theta this was without voltage, right. So, this is the so if you do not recollect how this was there just consider a droplet like this. So, this angle is theta, this is sigma LV, this is sigma SL, this is sigma SV. So, you have sigma SV is equal to sigma SL plus sigma LV cos theta for equilibrium that is what is written here. Now, because of the applied voltage the cos theta has changed. So, it has become cos theta prime. So, what is the cos theta prime? Sigma SV minus sigma SL dash by sigma LV. What is sigma SL dash? Sigma SL dash is sigma SL minus half C V square. This we have just derived by the battery capacitor analogy. So, the remember the insulator acts like a capacitor and you can find out the capacitance. How? Just it is like a parallel plate capacitor epsilon by d. So, if you know what is the permittivity then you can find out the equivalent capacitance as epsilon by d just like the parallel plate capacitor formula. So, sigma SL dash is equal to sigma SL minus half C V square where V is the voltage that is applied. So, this becomes sigma SV minus sigma SL by sigma LV plus half C V square by sigma LV. What is this? This is cos theta. Any problem here? Sigma SL dash? No, no, no. This has nothing to do with I mean sigma LV has come in the denominator because you have divided all the term by sigma LV not because here there is sigma LV. So, you can see this is the Young-Lipman equation basically. See, this is why I mean we always try to derive things from the fundamental if it is simply possible. The reason is that you see if you do not go through these roots it will give up illusion that the Young-Lipman formula is as a consequence of having a different sigma LV but actually sigma LV is not changed. It is sigma SL that has got changed. So, the contact angle is a manifestation. The contact angle is a manifestation but fundamentally it is the effective solid-liquid interfacial energy that has changed. Contact angle is a manifestation of that change. Electrowetting from an energetic point of view can be described by the following points also. Electrowetting decreases the effective contact angle which is driven by the energy gain upon redistributing the charge from the battery to the droplet. This reduction of apparent contact angle is fundamentally related to the fact that a minimization of the free energy requires a maximization of the capacitance. Now, question is then you can see in the formula what we have written. So, you have half C v square. So, you can well say that well I do not care about the voltage. See why we always in technology in electrowetting see anybody who has done experiments with electrowetting will devote a lot of attention on changing the voltage rather than changing the dielectric. But you may think that okay I also have half C v square in the formula. So, let me make some change by changing the C also. See there are two reasons why we do not or two or three reasons why we do not actually try to play a lot with C, but we play a lot with v. One thing is the square dependence with v. That means changing the v by a small amount will create a large change because it scales with v square. A related point is that because it is v square it is not dependent on the direction of v also. The third point is that changing v is much convenient or increasing v is much convenient as compared to increasing C. Because increasing C how do you do? C is epsilon by D. So, you may say that I will reduce the D, the thickness of the insulating layer by whatever amount that I want. So, that I will have a tremendous rise in the capacitance that is possible in pen and paper, but in reality if you reduce the dielectric thickness beyond the critical thickness there will be breakdown of the dielectric layer. It will no more act like a dielectric layer. So, this is this phenomenon is called as dielectric breakdown. So, it is therefore common possibility that actually you give a lot of importance to the voltage, but not so much of importance to the capacitance for working with this technology. Applying a potential between the droplet and the electrode would spread the droplet as much as possible in an effort to increase the capacitance. So, that is an implicit way that the in which the droplet tries to increase the capacitance, but we are not talking about the increase in capacitance by altering the thickness of the dielectric layer. So, this is the natural readjustment to the configuration. There are different types of electro wetting. So, simple electro wetting refers to the change in the wettability of an electrolyte droplet say something like this due to an applied electrical potential difference between the droplet and the electrode. Schematically it is shown in this figure. So, this is simply electro wetting and what we have discussed so far is electro wetting on dielectric. So, this is a phenomenon which is not requiring the dielectric layer to be present. Electro wetting on dielectric or EWOD which we normally use for technology refers to the electrostatic change in the wettability of a societal droplet resting on a dielectric film coated on the top of the electrode. The change in wettability stems from the electrostatic change in solid liquid interfacial energy that we have discussed. There is a process by which droplet attains its new equilibrium state on application of the external electrical potential and there is a dynamics associated with it. Say let us say you are applying let us say that the droplet is sitting on a substrate and then you are applying a potential. So, the droplet will go through some dynamical states before attaining a new equilibrium state and in the process it will spread. This phenomenon is called as electro spreading. That means it is actually spreading because its contact angle is reducing and there is a sequence of events that is taking place as the electro spreading of the droplet occurs. So, I will show you couple of movies I mean which concern some typical applications. So like where do we use this? Like we have understood the science of this but where do we use this? So droplets can be targeted to localized hotspots for electronic schooling. So, if you have a localized hotspot in a device in an electronic device then you can have droplet which may be targeted to move to a hotspot and you see like when you are talking about a droplet being targeted to a hotspot the droplet essentially should be designed to move by the shortest path. So that the process is the fastest. So, this process this type of designing or optimizing the path of a droplet given a source and given a sequence of electrodes this is typically done by using optimization algorithms in computer science. So, I mean in this particular application you have actually in interface with computer science and in general electrical sciences with the fluid dynamics. So, you can see here like in this here that you have several electrodes. So, some electrodes are switched on and some electrodes are switched off. Now I will tell you that by electro spreading you cannot make a so by spreading of a droplet by a change in voltage that itself may not be good enough to make a droplet move why let us draw a schematic to understand. So, if you have a droplet and you apply a voltage then what will happen it will spread like this it will become like the red dotted line, but the contact angle will change equally on both sides. So, that will not give a net driving force. So, on this side if the contact angle is theta 1 and on this side if that is theta 2 and theta 1 and theta 2 are the same then there will be no net driving force because driving force is related to the contact angle. However, if you now subject one part of the electrode one part of the droplet to a voltage v 1 and another part of the droplet to the voltage v 2 where v 1 is different from v 2. So, there will be a differential of theta 1 and theta 2 and that can drive the droplet in a certain direction that is the basic principle by which you can move a droplet by using an electric field. So, that is what is done in the movie that is being displayed here. So, you can see that a droplet is jumping from one electrode to the other. So, some electrodes are activated then some are deactivated then some are again activated some are again deactivated like that. So, it is basically a pair of electrodes over which the droplet is moving successively and those pairs are switched on and off switched on and off like that with a particular voltage. Now droplets can act as I mean there is a typing mistake it should be bioreactors droplets act as bioreactors to achieve rapid biochemical reactions. So, you can so let us look into this movie which is there in the right. So, we have got the movie that there are two droplets these droplets are moving and these droplets are coalescing together. So, again look into the movie. So, you can see that there are two droplets I mean these are actually coloured with two different eyes. So, one droplet can carry a reactant A another droplet can carry a reactant B and droplets have large surface area by volume ratio. So, when these two droplets merge then A and B can quickly react to form C. So, this reaction can also be a biochemical reaction. So, therefore it is possible to make use of droplets as bioreactors. Now we will so we have discussed about how to modulate surface tension by electrical field. Now we will discuss that how to modulate surface tension by light by using optics. So, we have discussed about this. So, I will talk about like two basic mechanisms by which we do by which it is possible. So, one is by making a substrate by making an alteration in the substrate liquid interfacial phenomenon. So, there is a optical modulation of the surface potential through the use of a metal oxide semiconductor. We have discussed about this earlier in the context of the design of optofluidic valve and we will discuss about the detailed science of that. So, if you have say a metal oxide semiconductor a titanium dioxide or zinc oxide semiconductor coated on a surface then if you shine light you will light on the top of that then there will be immediate electron hole reaction starting to take place. Because the band gap of this titanium dioxide or zinc oxide typically 3.2 electron volts it corresponds to the energy that comes from the ultraviolet light. So, there will be a change in surface energy state because the surface charging state will change either there will be excess holes or excess electrons. So, that is one possibility by which you can have an alteration in the interfacial energy. There is another possibility that you can dynamically manipulate the liquid front through interfacial evaporation and condensation. I will show how that is possible facilitated by focus light induced excitation of suspended photothermal nanoparticles. I will show that how that is possible. I mean this has been reported in one paper earlier in nature materials. So, strategy one optically modulate contact angle through surface coating coat the surface with a direct semiconductor oxide upon irradiating the coated substrate with ultraviolet light electron hole pairs are formed. These pairs can reduce and oxidize the species that are adsorbed on the surface. Recombination of electron and hole is a competing reaction based on the relative rates of oxidation and reduction and excess or depletion of charge can be generated at the surface and that can change the effective surface energy and the contact angle. Now, out of many materials why do you use titanium dioxide or zinc oxide as a coating? These are stable in aqueous solution since the surface sites do not react with water. The band gap is 3.2 electron volt which corresponds to the wavelength of light in the UV regime. The PZP that is called as point of zero potential varies between 4 and 5 pH. So, the surface is positive for pH less than 4 and negative for pH greater than 5. The flow may be specially modulated through selective coating and UV exposure. This will allow a local control of flow velocities without any fringing effects. Not only that, so you can have a special control. Not only that you can have a temporal control by switching the light on and off. So, you can have a time dependent and position dependent control by patterning the surface and by switching the light on and off. What is the basic mechanism? The water molecules in vicinity of the TiO2 surface tend to adhere to the surface. Ultraviolet radiation creates surface oxygen vacancies at bridging sites resulting in the conversion of Ti4 plus sites to Ti3 plus sites. This is the basic chemistry that takes place. This new Ti3 plus sites are favorable for water adsorption. That makes this hydrophilic. Now you can make an electrical analog of the system by considering that what is the voltage that is being applied across an equivalent capacitor. The voltage is H nu by E where E is the charge of the electron. So, then that is the equivalent voltage. Capacitors, there are two capacitances. Two capacitors in series one is called as Helmholtz capacitance which is because of the electrical double layer formation that we will learn in the electro kinetics and there is a capacitance called as Mott-Skottky capacitance. So, based on these two the CH is typically much greater than CSC. So, the CSC dominates because these are in theory. So, based on that you can calculate that what is the capacitance, what is the potential. If you know what is the capacitance and what is the potential then you know what is the equivalent surface energy. So, it is ultimately the energetic that is dictating the phenomenon. So, now in terms of order of magnitude analysis that energy will give rise to a change in the surface tension. So, then you can say that like if you scale the viscous force with the surface tension force actually these are orders of magnitude. I mean this colon which is displayed wrongly in the slide it is actually order of magnitude. So, the viscous force scales with the surface tension force and from that you can get a scale of velocity. So, if you can create a surface tension change of 0.01 Newton per meter if you have a height of 1 micron of the micro channel if you have length of 10 micron and the dynamic viscosity 10 to the power minus 3 Newton second per meter square for water you will get typically the velocity of the order of 1 meter per second which is quite significant. So, that is one possibility. So, the model of the story is you create a change in surface energy and the change in surface energy establishes a velocity scale which can be established by a order of magnitude comparison between the viscous force and the surface tension force. Strategy 2. So, you can see in this strategy what you have you have nano particles photosensitive nano particles in the fluid. Now, you actually shine laser light. So, when you shine laser light the local temperature will increase because the nano particles what the nano particles will do these nano particles can be metallic nano particles silver nano particles or this can also be nano particles made of carbon nano tubes whatever I mean these are these can be nano shells or nano tubes instead of nano particles. So, these particles will absorb the energy from the laser and that energy will be transmitted to the liquid once that energy is transmitted to the liquid the liquid will get evaporated. Once it is evaporated it will flow in this direction see the cartoon this the liquid become vapor and this vapor when it comes to the interface this will condense. So, it will form droplets and that droplets will add to the previous liquid and that will change the contact angle. So, basically the vapor in the relatively cold air condenses into droplets in the form of liquid layer interface. The droplets coalesce with the original bulk liquid body and the liquid air interface advances because once the droplet coalesces with the bulk liquid then what happens is that the contact angle changes and the contact angle actually decreases. So, that gives a greater driving force and this starts moving. So, this is again a beautiful phenomenon. So, if you combine this phenomenon with the surface coating surface coating is a surface phenomenon and this is the bulk phenomenon. So, you can combine the surface phenomenon with a bulk phenomenon. So, by using the optical technology here the optics is coming from laser. So, it could also be UV source or any other source. So, from that actually the nanoparticles are here the passive media which are accepting or absorbing the energy that is coming in the form of light and that is getting transmitted into heat almost instantaneously and that is giving rise to extrapolation and condensation. So, what are the major tunable parameters? The light illumination power, the laser power, the micro channel dimension, the photosensitive nanoparticle concentration these are the parameters which can be tuned to alter this phenomenon. So, it is possible that by using light one can create a change in surface energy, one can create a change in the bulk also that will eventually translate in the form of a change in contact angle and these two technologies either individually or combined together can give rise to an optical modulation of the interfacial phenomenon. So, it is possible to modulate the surface tension optically. So, we stop here today and we will start with a new chapter from our next lecture. Thank you very much.