 In this lecture number 8, we continue our discussion on spreading on liquids. We began talking about spreading from liquids last time and this time we hope to extend that discussion into spreading from solids on liquids. To have a quick recap, let us go back a few slides and from this example it was quite clear that when we look at spreading of benzene on water, we get an initial spreading coefficient of about 8.9 Ergs per centimeter square whereas, the final spreading coefficient represented as S final works out to be equal to minus 1.4 Ergs per centimeter square. The benzene present in the form of film on water lowers the surface tension of water by about 10.4 dynes per centimeter and therefore, we have this final spreading question turning out to be negative. In the final state we may say that benzene has stopped spreading further or if it has already spread over the surface, then it responds by retracting into a flat lens with a monolayer of benzene covering the surface in between this lens and boundaries of the vessel. The reason for this is the fact that benzene rings tend to get slightly oriented against water in the form of monolayer and this oriented benzene monolayer turns out to be less favorable for spreading and benzene would rather choose to form a lens and not spread over the oriented benzene film. Here where some of the magnitudes of initial spreading coefficient values, we see for the lower alcohols S is about 50 dynes per centimeter for octanol it drops to about 36.8 for benzene and toluene it is about 9 and 7 respectively. For normal octane it is a miniscule value just enough for spreading plus 0.22 for carbon disulfide it is indicative of no spreading minus 7.6 and one of the strongest tendencies not to spread is the spread by methylene iodide with S equal to minus 26.5. We take another example here of amyl alcohol on water. So here also we notice that any initial spread is followed by retraction. What it means is that the monolayer of amyl alcohol on water surface is not energetically favorable for further spreading of amyl alcohol and this is reflected in the final S value coming out to be negative. So we look at these calculations a slide later, but the important point is that the hydrophobic chains of oriented amyl alcohol is less favorable for spreading of amyl alcohol. Amyl alcohol rather prefers to strain the form of a lens and here also we see certain principle of surface energy minimization being obeyed. First the tails hang out in air at the lens surface in every case. Second the area of this lens is minimal. So we see surface energy minimization being obeyed here. Secondly the area over which the amyl alcohol has to face tails is least in the lens form especially compared to any flattened film form. So the very extent of this lens is minimized so that the oriented hydrophobic tails offer minimum area to the liquid within the lens. So continuing from that background this is what we had initial floating lens spreads out in the form of a flattened film and then final energetics not being favorable leaves a monolayer all the same at the rest of the surface and contracts into a lens which is in equilibrium with the monolayer on water surface. What we see here is that CH3 groups are somewhat lesser in polar character compared to the amyl alcohol and as a result of that amyl alcohol coheres to itself more readily than it would adhere to its own oriented film. I hope this is clear to you. So the initial spreading cohesion works out to be about 44.3 dyns per centimeter. The final spreading cohesion is about minus 2.0 dyns per centimeter. In the third example we have carbon disulfide when we look at spreading of carbon disulfide on water the initial spreading cohesion is gamma WA which is 72.8 minus gamma OA which is 31.8 plus gamma OW which is 48.6 that is minus 7.6 dyns per centimeter. So the lens of this oil actually would not spread on water but there is a monolayer of carbon disulfide with a film pressure of 2.3 dyns per centimeter which does extend across the water surface. So you have to understand this that even though the spreading cohesion is negative you can have enough affinity between the molecules of CS2 in water so that the water surface would get covered with a substance like carbon disulfide. So if you lower the surface tension of water by virtue of this invisible monolayer of CS2 by 2.3 units this value 72.8 would drop down to 70.5 there is practically no change in the surface tension of oil and interfacial tension between oil and water. So the final spreading cohesion comes out to be minus 9.9 dyns per centimeter. What has happened here is that by lowering of the surface tension of water by carbon disulfide the spreading cohesion has become further more negative. So from minus 7.6 dyns per centimeter when fresh surface of water is exposed to carbon disulfide when a monolayer spreads it depresses the surface tension of water and the spreading cohesion decreases from minus 7.6 to minus 9.9 dyns per centimeter that is even less favorable favorable for spreading. We could sum up our general finding here. Initial spreading cohesion is when we bring one liquid in contact with another. If that is not favorable for spreading then what would be the effect of saturation or mutual saturation of the two liquids mutual saturation of the two liquids makes final spreading cohesion less favorable for spreading than what would be implied by the initial spreading cohesion S. So if you do not have initial spreading tendency that will be accentuated further by mutual saturation of the phases. Here we go into kinetics of spreading. One might want to have a feel for the velocity of spreading. So some of the pictures here are supposed to motivate you towards the numbers involved. It is interesting that we do not we do not walk any bit quicker or we do not swim any quicker compared to the other. We walk or swim in water walk on land or swim in water at approximately same speed. Average speed will be about 5 kilometers an hour. Even dog speed of swimming is comparable. There was one record holder a dog named Umrah landed up into top 25 percent in a swimming competition with humans. Speed of spreading of many polar oils is about 10 centimeters a second when translated into kilometers per hour it is about 0.36 kilometers per hour that is about 14 times slower than your average speed of walking or swimming. So you can imagine if you are walking along a long canal containing stationary water at the leading age of which a polar oil is introduced to spread it would be left quite far behind you if you are walking at your average speed. Why is there interest in the velocity of spreading or kinetics of spreading? We have certain phenomena observed which are related to such instances as foam breaking or kicking droplets. When I mentioned oleic acid being placed on a hydrocarbon liquid drop placed in water leading to rather violent action which makes the lens burst into many tiny lenses and a thick layer thicker than monolayer of the mixture forms in between lenses we have this kind of phenomenon. You have also seen probably of a practical consequence will be lots of times water bodies which are polluted tend to have a resistant foam or flot for floating on it giving it a snowy appearance this has to be compared against your observations. See foam or froth is not desirable is especially persistent foam or froth on water bodies is clearly an indication of high level of pollution. One might simply want to break that foam or better steel not have the polluting agents which lead to the foam stability there in the first place. We will see later that even in laboratory or in process equipment where you need to control foam or froth formation and persistence you need to make use of the spreading phenomenon and what anti foam agent you might be able to use could be dictated by the kinetics of spreading. We show in the next figure an apparatus commonly used for studying the spreading rates. We have here a trough in the top half of this figure we see a silica trough containing water and perhaps another oil layer on top depending on where we want to study the spreading kinetics whether at water surface or an at an interface between oil and water. And then we have a camera here a camera here and couple of floodlights making this whole surface clearly visible. You also see a glass plate inclined at a leading end that is used for introducing the spreading liquid. So, this top view gives you an isometric view of your setup. A side view is shown in the lower half. We have the metal framework which covers the entire arrangement including the trough. We have the cine camera mounted at the top we have that inclined glass plate to introduce the spreading liquid. Then we have these two layers in general case where we have about 1.5 centimeters of water and about 1 centimeter of oil like petroleum ether. The total height of the trough is about 5 centimeters and the length is about 100 centimeters. And then we have the floodlights making recording of what happens at the surface possible. The distance between the camera and the surface or interface is about 50 centimeters. In the older experiments cine cameras were used with about 16 frames grab per second. Nowadays we have much faster cameras available and that makes more precise measurement on kinetics of spreading possible. We also see talc particles spread on the surface or interface. They are provide they are able to provide visualization of the movement otherwise we will not be able to track the interface between the spreading liquid at its leading front. But if you have a layer of talc particles and a spreading liquid is introduced the talc particles layer will be pushed and so we will be able to track where the leading age of the spreading front is. We will later see how we use this talc particles there is considerable precaution required in preparing this talc particles. All right the oil like layer that would actually spread can show different kind of stages in the spreading behavior. If you have oil like acetone then there are chances that there would be desorption of liquid from the film. This may cause a drop in the spreading rate especially after about one second. This necessitates that early stages of spreading need to be observed. Typical dimensions of the silica trough are about 100 centimeters by 30 centimeters by 5 centimeters. That glass plate is weighted with acetone or the liquid which you want to which you want to spread on the surface of water or an or at interface between water and another oil. What kind of measurements do we get? Let us look at this figure showing the spreading behavior. If you look at the spreading curve then we may find stages like these. This may be the spreading velocity or the distance versus time. So, you see initially a certain portion where the transient is there then there is a portion where there is a steady state and finally, there is a depletion and there are transients here. So, in that initial part A the spreading depends on the height of the lens and other mechanical factors. In part B we have steady spreading and in part C we have depletion arising out of desorption and evaporation of acetone. By desorption will mean that some of the acetone will tend to dissolve and enter the water underneath and evaporation of acetone into air will also lead to depletion of acetone in the spreading layer and when this desorption and evaporation become significant the spreading rate will fall off. We can look at some of the values for the spreading question measured for different systems so that we can arrive at a field for what is happening during spreading. So, we see here in the next table the initial S value also against a column where we have the initial spreading question divided by the viscosity of water or in an interfacial system spreading at interface the initial spreading question divided by some of viscosities of the water underneath and the oil on top or petroleum ether as the case is here. So, if we observe closely in this table we find first ethanol spreading at an interface between air and water. The initial spreading rate is measured to be about 53 centimeters a second this is quick. The steady spreading rate is much lower 9.2 centimeters a second and the initial spreading rate divided by viscosity of water is about 50 viscosities will deal with in centipoises and not mention the units, but these are the usual units. In the second entry we see ethanol spreading on petroleum ether on top of water. The initial spreading rate is 27.2 the steady state spreading rate is 6.4 centimeters per second and S by sigma eta which is viscosity of water plus viscosity of petroleum ether that is 25. In the third case we have ethanol spreading on petroleum ether against water when this water is containing a quaternary salt like C 12 H 25 N C 3 thrice plus at a concentration of 10 raise to minus 4 molar. We see now initial spreading rate is 12.8 the steady state spreading rate is 3.4 and S by sigma eta is about 21. Likewise we have values for spreading of acidic acid at air water surface and at petroleum ether water surface the values are 43.2 and 24.8 steady state spreading rates are 10 and 4.8 S by sigma eta 45 and 25 or for acetone at air water and petroleum ether water system. Spreading question is 33.6 and 24.6 steady state spreading rates 10.4 and 8.2 and S by sigma eta is about 50 and 25 here and so on. What do we see as a trend? What can we infer from these measurements? Look at entries 1 and 2 ethanol spreading at air water and petroleum ether water surface. Initial spreading question has dropped from 53 to about 27 S by sigma eta is dropping from 50 to 25 or entries 4 and 5 initial spreading rate has decreased from 43.2 to about 24.8 S by sigma eta from about 45 to 25. Once again we see that when you go from air water to oil water interface the spreading rates are diminishing to about half the value at air water surface. There is one more point to be noted in this table compare entries 2 and 3. Interface is similar petroleum ether water but in one case we use pure water in other case we have the surfactant containing aqueous solution and we see the initial spreading coefficient spreading rate decreasing from 27.2 to 12.8 that is a significant drop. This is happening because the monolayer of the surfactant at the interface can oppose spreading of ethanol slowing it down considerably. So, there is a decrease in the spreading rate from 27.2 to 12.8. The other observation is that the spreading rate initial spreading rate correlates well with this last column S by sigma eta roughly same values at least proportional. In S by sigma eta we taken summation of viscosities of the phases involved the underlying liquid and the overlying liquid but we neglected here the viscosity of the spreading material. Yet there is a reasonable correlation here and one may postulate in view of these essential data that the rate of spreading is proportional to spreading coefficient initial spreading question over some of the viscosities involved. And write this rate of spreading as a constant times S by sigma eta. I already made a comment on the entries 2 and 3 is a surfactant which has lowered the surface tension of water and therefore that first term in expression for S having been diminished the initial spreading question is reduced. We could go further and ask a question why is it that spreading film travels much slower compared to the kinetic molecular movements in the surface. This is for the reason that there is no slippage between the spreading film and the liquid present on each side. If there is no slippage and this is a very general fluid mechanical understanding although there could be exceptions in special circumstances to no slip condition. In general there is no slippage between a spreading layer and the liquid above or below it which means some of the liquid especially the liquid under the spreading layer will tend to get carried will get dragged along with the spreading film. So, one may ask a question how much is the thickness of the liquid that may be dragged by the spreading layer. With this understanding it is now clear to visualize that the resistance to motion would depend on the viscosities of both water and petroleum ether and because there is no slip the layers will get carried. If we estimate for a monolayer of oleic acid flowing under the influence of an imposed surface pressure gradient of about 5 centimeters per second the water under this monolayer oleic acid monolayer that would be actually carried by virtue of no slip could be estimated to be about 10 microns thick. You might be wondering why it is important to think about this thin layer of water being dragged. It will become clear when we worry about measuring surface viscosities and when we look at different ways or different instruments that we would require in measuring surface viscosities. This drag of the underlying liquid has to be included in our calculations so that the surface viscosities can be determined correctly. There are also other phenomena like tear formation about which we will talk some other time. So, much for the spreading of a liquid on another liquid. We would next like to think about spreading from solids. Spreading from a solid is a phenomenon which shows a very marked dependence on temperature. In fact, there exists a temperature below which spreading from solid at an air water surface becomes practically 0 or extremely slow. So, there is some critical temperature for each solid when you look at spreading from the solid onto water. If you exceed this temperature then the energetic is favorable for spreading. That means, energy is at the triple surface or triple interface which is solid liquid air and the energy of molecules in the solid are of such values that the spreading cohesion becomes significantly positive which means the molecules can leave the crystal lattice rapidly and proceed to occupy the liquid surface. I would like you to think about a question here. The question is where do we expect the molecules from crystal would get detached into the surface film? How would the solid molecules would proceed to occupy the position at the surface of water or interface between water and air? While I planned that question in your mind and answered that in a couple of slides, let us look at this critical temperature that I talked about. The critical temperature for rapid spreading from a solid is indicated here for a CLM acid it is about 233 Kelvin. For C12 acid to 54, go down to the higher carbon numbers C15, C16, C18. We see a rise in temperature critical temperature 266, 278, 290. Oleic acid shows a critical temperature of 221, ethyl permeate about 271. Now we return to that question where would the molecules of a solid crystal leave the crystal from? Turns out it is only at the periphery of the crystal. This is where the molecules tend to leave and why the arguments which explain this and the experiment which can demonstrate this are both fairly straightforward. We have to understand that supply of material through the bulk of water is negligible. This is because the energy barrier will have not only the component corresponding to formation of a hole in the crystal, but also of immersing the hydrocarbon chain or tail into the structured water. In addition diffusion through a liquid medium that is bulk of water is a rather slow process. So, one expects not much transport would happen through the bulk of water. You need certain energy to create a hole in the crystal that will be required in any case, but supposing that is done then the release molecule has to enter rather structured water, associated water. It will have to incorporate the hydrocarbon chain into hydrogen bonded water structure which will be disrupted that will not be energetically favorable. Supposing that even that happens then the kinetics enters into picture this molecule which has entered the structure of water or by disrupting it now has to travel across bulk of water at a very small diffusion rate. So, that rate also will be much lower. How do we confirm that the spreading actually will occur at the periphery or where the liquid solid and air are in contact? A very simple extent could be devised. You could think of spreading from steric acid in water. All you need to do is have solid steric acid in the form of a flat slab flat solid surface. On top of that you just keep a drop of water then observe what happens over time. If you place a drop of water on surface of this piece of solid steric acid you would see that it edges out a shallow ring on the surface and apparently there is no dissolution occurring in the interior of the drop in the interior of this ring. The reasons are clear. The energy that a molecule of solid possesses and the energy at the 3 phase contact line they are favorable for molecules to get released then spread onto the water surface, but not in the bulk. If that is the argument one may one may be able to go further and even think about kinetics of this spreading actually what will be the rate of spreading? The perimeter the extent of these 3 3 phase contact line that would come into picture in our effort to model the kinetics of spreading from a solid into liquid. Before we come to that quantification let me mention a curious case of subtle alcohol. This is a compound of interest in retarding the rate of evaporation of water. Satellal alcohol spreads from a solid at room temperature that would be an advantage. I spoke about need to conserve water in a country like ours where we have lots of hot and arid areas water bodies must be probably tailored to cut down on the evaporation losses. Satellal alcohol as we will see later is a probable candidate for this and its favorable spreading is one concentration which may make it a viable candidate. For subtle alcohol the monolayer forms with a surface pressure about 33 dynes per centimeter 25 degree centigrade. If you look at the higher alcohols they will have progressively lower film pressures and corresponding lower rates of spreading. In general the rate of spreading is about 0.8 to 1.0 into 10 to the power 14 molecules per centimeter per second on a clean surface of water. Note the rate of spreading is being expressed in molecules per centimeter per second that centimeter has a reflection on the perimeter. It is clear that perimeter comes into picture and the spreading pressure will come into picture. In fact, the driving force will be the difference between equilibrium spreading pressure and the existing film pressure. So, the number of molecules spreading per second will be equal to a constant times the perimeter times pi e minus pi where pi e is the equilibrium spreading pressure. Pi is the existing one and when we look at the data on spreading that constant works out to be about 2.4 to 3 into 10 raise to 12 molecules per dyn per second. Besides, settle alcohol another example we could consider here in passing for spreading at water surface and you would see later that there is a reason why we should be thinking about spreading of protein films on water surface. If you touch a clean water surface with a solid protein crystal then protein films actually form a monolayer on water surface. You could do a precise experiment to actually find out the molecular weight of the protein. We will go into quantitative aspects later, but here you can visualize that you could take a fine hydrophobic fiber and with proteins already spread on water you might be able to coat this hydrophobic fiber with a layer of protein and you can make actual measurements to show that the spread film of protein on this hydrophobic fiber is actually a monolayer. Once again with rise in temperature the spreading is accelerated considerably. From here we move on to establish possible relation between surface and interfacial tensions. We begin with a treatment given by Gibbs. Gibbs had an interesting thought experiment in which he visualized the system wherein mercury is in contact with water. He considered the interfacial tension between mercury when it is present in equilibrium with water and in terms of surface tensions he deduced that the interfacial tension between mercury and water should be equal to this right hand side here. Gamma Hgw is equal to gamma Hg when it is saturated with water and you consider that surface tension when it is in contact with air minus the surface tension of water when it is saturated with mercury. Again that water is in contact with air. So, his deduction was that interfacial tension between mercury and water is equal to the difference in the surface tensions when the two liquids are mutually saturated. I am sure some of you might have an idea of a similar relation I am not going to name it yet. So, gamma Hgw is nothing but gamma Hg minus gamma w when mercury is saturated with water and water is saturated with mercury. What was Gibbs's reasoning? He argued that on a clean mercury surface with its high surface tension remember about 475 dynes per centimeter that is the value 485 about 485 dynes per centimeter surface tension of mercury. Water would tend to get adsorbed you can understand this. If a liquid has a very high surface tension obviously it will try to minimize the surface energy. If there is nothing else to minimize the surface energy it will simply respond by making itself as compact as possible and a spherical geometry offers one way of doing that thereby area per volume is minimized. But if there are other options the liquid with high surface tension will also explore those options. If mercury is in contact with water it would simply tend to get covered with water. Water with much lower surface tension would then provide an avenue of lowering the surface tension for the otherwise high surface energy of mercury. So, you could look at his deduction. He visualized that if there are two chambers one containing mercury another containing water but connected through this vapour space then in this system mercury will tend to import water molecules from the vapour which will have to be released by the water surface here until it forms a thin enough layer on top of the surface of very high surface energy in the beginning. That way by absorbing water through the vapour space the mercury body will be able to lower its surface tension. He argued carefully here that the film of water that would be present on top of mercury as a result of this adsorption will be facilitating this drop in surface energy. But he also argued saying that it would reach such a thickness that its interior will still be able to display the properties of bulk liquid water. So, it is a thin layer thin and providing the lowering of surface energy of mercury but at the same time at the same time thicken up for its interior to display the bulk properties. With this argument he could arrive at the relation that we just talked of perhaps we can stop here and resume from here next time. So, gives us treatment is the point from where we will begin.