 So, we begin with this second module devoted to measurements. In a sense the introduction was to build up an understanding of the theoretical concepts and the practically important applications, that we must now graduate into measurements. And we look at certain aspects of work of addition and then consider the surface and interfacial tension measurements. To begin with, I would raise this question for you. In the backdrop of what we have seen so far, if our task is now to estimate the work of addition between a given liquid and a solid and if the situation corresponds to the weighting of the solid by this liquid, then how do we go about this measurement of work of addition? You would know at once that because this liquid weights a solid, we cannot hope to make measurement of an equilibrium contact angle. The contact angle will be necessarily 0. So, that relation between work of addition and the contact angle and surface tension per save would not be applicable. So, we need to think of something different. We have to contrive our measurements such that we should still be able to work in the ambit of the theoretical framework, the approach of which had been outlined earlier and we should still be able to derive this quantity work of addition from the measured contact angle. In the situation we look at is corresponding to a judicious choice of another liquid. So, we evolve our theoretical analysis down to consider a system where two liquids are to be analyzed while they are in contact with a given solid. So, here is the way to go about this task and what might appear as analysis similar to what we have been doing especially in the later parts of introduction module. We would see continuing here, but by virtue of the relevance of this system to many practical applications and measurements, I decided to club this section in the general discussion of methods and measurements of this module 2. So, what are we looking at? What is our system? Let us say we skip a few slides and go directly to the situation where we represent with the help of a diagram what system we are looking into. We have the given solid S over here like earlier the liquid in contact with the solid in the lower part is represented as that capital L by that later capital L, but we have replaced the air above this liquid by the other liquid denoted by capital M and that liquid will be a liquid that we got to choose. So, the only difference in this diagram and the one we had begun with in the method of virtual displacement of the three phase contact line is in M replacing E. Like earlier we would have surface tension replaced by interfacial tension between the two liquids L and M. So, gamma L M acts horizontally and the inclination of this plate with the horizontal is angle theta such that the interface now is planar right up to the contact line the three phase contact line here between L M and S. So, that being clear we go to the analysis. Like earlier when we take this system of two liquids in contact with the solid we have F S M S as equal to F S L S plus gamma L M cos theta. In your minds you can imagine F S M S is being the precise replacement for the surface tension of solid which would be or interfacial tension of the solid S with the liquid M above. And F S L S replaces the interfacial tension between the solid S and liquid lower liquid L. So, it is the same balance of forces, but written in terms of energy for solids. Now we have these two situations when we talk about the work of addition let us say we have the solid in contact with given liquid L and we go from here to the solid S separated from the liquid L. Likewise we can have liquid M on top of solid and then we have the separation of the solid and the liquid. We are replicating the thought extent which goes into the derivation of Dupre's equation. So, if we have the total interfacial energy of the system in this state minus what is there present here that will be the work of addition of the liquid L to solid S and similarly for liquid M with respect to solid S. So, we return to the slides with that clarification and we find that W S L is now equal to F S AS the free energy per area of the solid in contact with air plus gamma L A that is the surface free energy per area of the liquid or surface tension for the liquid gamma L A minus F S L S the interfacial energy for the liquid L in contact with solid S. And likewise W SM is equal to F S AS plus gamma M A minus F SM S. So, far everything is fine we make certain observations and for clarity maybe you can also add in your mind some more subscripts for theta in equation 12 because that is for two liquids L and M in contact this theta is even better expressed as theta subscript L M that is for the two liquid system. As I remarked earlier our liquid M is chosen such that this theta L M is measurable. The difficulty we had to overcome was presented by the fact that the liquid L would actually weight the solid. So, theta L would not be non-zero that is why we had this new situation constructed between two liquids. So, that now we have a theta L M which is measurable. Now if we could work with these equations such that W S L which cannot be obtained from Young's equation could now be inferred from the other measured values. So, we play with these equations a bit first we subtract the equation 14 from equation 13 that gives us W S L minus W SM is equal to gamma L A minus gamma M A plus F S M S minus F S L S we have gotten rid of the free energy per area for the solid F S A S. Now using this first equation that is the energy balance for the two liquids in contact with the solid this equation 12 for S M S F S M for F S M S as shown over here we have for F S M S gamma L M cos theta plus F S L S and that F S L S cancels with this F S L S when you substitute for F S M S that gives you W S L minus W SM is equal to gamma L A minus gamma M A plus gamma L M cos theta this is the left over term when you substitute for this difference F S M S minus F S L S remember this theta comes from the two liquid contact with the solid. So, it is the theta subscript L M that is a measurable one. What was the concentration in choosing this liquid M? How did we decide upon this liquid M? One thing it should give you a measurable theta in the two liquid contact system that is one second concentration was that M should not actually weight solid S which means if we were to take this solid and the liquid M they would give you a non-witting or equilibrium system. In other words the contact angle M would make on S theta M would be non-zero ok. So, when we inspect this equation W SM should be obtainable from Young's equation from the major theta M. So, once we have theta M this can be substituted the surface tensions interofficial tensions and the two liquid contact angle are all measurable. So, that means the only quantity which remains to be reduces what we wanted the work of addition of given liquid L for this solid. There are certain practical consequences for systems of this sort. First to take note of is the following that in any extent of this kind if a liquid is already present on the surface of a solid and if it has to be replaced by another liquid this can be a very very slow process. For instance here one may say that to begin with in our extent the solid would be in contact with the given non-witting liquid M. Even then the waiting liquid L would take possibly a long time to displace this non-witting liquid M from the solid. And you will realize from what we discussed in last couple of lectures that this is the source of hysteresis. Even if the liquid M does not wait the solid the high surface energy of the solid is likely to pick up whatever is in contact with it of M and they thereby reduce the otherwise high surface energy. And when liquid L comes in contact with such M covered solid it would have to displace M from solid that could take time. And even very very thin layers of M over the surface which is now invaded by L will be able to clear M only so slowly that the advancing contact angle will be much larger than the receding contact angle. So, hysteresis of contact angle in such systems can therefore be quite large. Talking about a generalization in practice one may have to think of a liquid like L displacing liquid M from a solid in a system which is a powder or a fine capillary system. Even though the contact angle made by liquid L theta L is acute and the displacement of M by L would be possible it just could be a slow process. Given the particles or the capillary systems crevices one could guess that these time scales can be typically large. Since the free energy of the system however is lowered in the process with larger FSMS being replaced by a smaller FSLS which you can see from this equation 12 because cos theta is positive and only then that spontaneous displacement of M by L will be possible. Such replacement of liquid M by liquid L would be theoretically possible, but it could be slow and sometimes it could be so slow that it will have consequences in practical applications like in oil well flooding. Eventually of course, all powder or capillary system will become spontaneously weighted with L, but to make the time scales manageable for practical viability of process one may require to apply a pressure difference to force liquid L to occupy solid S and such situations are common in the oil recovery scenario. Enhanced oil recovery will have umpteen number of such examples of different degrees of inventiveness. So, I just have this application to site and you can think of many other systems where the two liquid systems would be involved and in which the first liquid will have to be replaced by the second liquid. Workup addition could be calculated from measured theta L M and theta M. This has already been expressed theta M being known WSM is gamma M A into 1 plus cos theta M and therefore, we can determine WSL. Over here we must emphasize one particular precaution which is kind of generic whenever you deal with two liquids. Over here the two surface tensions gamma L A and gamma M A and the interfacial tension gamma L M must be for a system where the two liquids are mutually saturated. L should be saturated with M and M should be saturated with L before the surface and interfacial tensions are measured. Otherwise you could expect spurious results and that of course, holds also for the contact angles measured. Now here we change the gears we look into the very practical aspects of the interfacial science and engineering. The experimental methods and the theory behind these various methods we begin looking into the measurement of surface and interfacial tensions. I am sure some of these methods are known to you from school level chemistry and physics. However, it should become quite clear when we look at couple of methods that there are many aspects of measurements that one is not aware of sometimes after even prolonged academic exposure. This kind of sends a message also across the board for all interfacial science and engineering measurements that we have got to be extremely cautious in our measurements. Before we make any measurements it is necessary to clean the surfaces involved very thoroughly. These preparations can be laborious and demand patience. Even slightest contamination could alter the surface and interfacial tensions significantly. Here I may add also a precursor to what will be postulating later that what appears like gentle magnitudes or gentle changes at the level of surfaces can amplify into very significant values when viewed in bulk terms. All differences in surface tensions could actually make a very large difference in the bulk terms. So, we got to prepare all the solids and liquids involved. This diagram tells you little bit about how to prepare a liquid surface. You may make use of a jet of cleaned air directed at the surface like shown here and this fine jet of clean air would be able to push the impurities at the surface downstream towards this end. And here a fine capillary attached to a pump would be able to clear off the impurities which are accumulating downstream. So, a fine capillary attached to a water pump can be used to suck off the impurities from this surface and if that is done for sufficient time the liquid would be expectedly clean. Hopefully ready for the surface tension measurements. However, there is no need really to be complacent about our measurements yet because even liquid surface are notoriously known to adsorb impurities and some impurities may be harder to remove than by just this action of a fine jet of clean air. So, what do we do? If there is a chance that there is a small level of impurities still adhering to this liquid surface and it can produce gentle looking changes in the surface tension. How do we ensure that we get rid of these impurities too? It is here that I would expect at least some of you will be able to visualize what might be there on the next slide. You know how we visualize flows in our fluid mechanical work. We make use of fine particles or dyes. When we want to visualize the fluid dynamics in the gas flows we may use a streak of smoke and following how the smoke progresses will be able to get an idea about the nature of flows. In liquids like water we might introduce a dye or we might introduce very finely ground aluminium powder which would permit you how the liquid flows or yet another visualization aid which is used is finely ground fish scales. So, these tiny shiny particles would also follow the fluid particles and help you visualize the flows. What has that got to do with the cleaning of the liquid surface to ultra pure levels? Thinking about particles we have some contact point in the discussion that we had in the kinetics of spreading. Remember the Langmuir stuff in which a layer of liquid was covered by talc particles and by immersing an inclined plate which is pre coated with the liquid of which spreading we want to study we would be able to visualize how the talc layer gets pushed by the spreading liquid. So, there we had an example of surface flow visualization how at what rate the spreading of the given spreading liquid on the substrate liquid occurs. Here we must make use of our knowledge of interfacial or surface energies and the generic principle that I have been trying to convey to you is that the system always tries to minimize the free energy most of the arguments can follow from there. So, if there are certain surface impurities here which need to be captured by this fine capillary and they are not actually being carried completely that is the reason why we need to have some intervention here. We can think of spreading on this surface a finely ground talc powder which is prepared in a special way such that our method of preparation of this powder necessarily imparts it a very high surface energy. And if that is achieved then whatever impurities are present here would be getting adsorbed on such high energy talc particles and then those talc particles will be easier to push with the help of this fine jet of air and would be also easier to collect by this capillary pump system. That is exactly what is shown in the next slide. We use a small quantity of ignited talc which is magnesium silicate heated for 4 hours at red heat. So, if there is any greasy material adsorbed on the powder this would get removed and when you sprinkle a small amount of this talc powder onto the surface of the given liquid it will be able to adsorb most of the impurities there and improve also the efficiency of their capture by this capillary. This is just to give you an idea as to the level of detail which can go into the simple looking formulae which you always remember from what you studied about methods of surface tension or interfacial tension measurements. Some of which will be quickly revisiting in the following slides. But before we do that let us also address the preparation of an interface between two liquids. How do we clean up an interface? Liquid L in contact with liquid M, it could be oil water combination, generic representation oil water combination. It is basically a two step process. First we take the heavier liquid and we clean it up just the same way as I have described here. So, first siphon off the surface layers push by a fine jet of cleaned air then sprinkle it with a small amount of ignited talc powder and prepare the heavier liquid first. So, it is a clean surface now on top of which you could add the lighter liquid. If you want to be extra careful you could prepare the lighter liquid in the same fashion separately. That cleaned up liquid could be placed on top of this heavier liquid and prior to doing that you could still make use of talc particles at the surface of the heavier liquid prior to pouring the lighter liquid and then you can use suction at different points to remove the interfacial layers. That way you will ensure that the interface will be now really clean and would not be affected by different values for or lower values of surface tensions or it interfacial tensions. So, that is the way one one goes about in preparation of the liquid surfaces. The question naturally then arises as to how one prepares the solid surfaces. After all while measuring the surface or interfacial tensions we will have apart from the liquid or liquids at least one solid. Now, how you prepare the solid surface is obviously dependent on what method you are using. So, we will deal with the details regarding the preparation of solids as we address each individual method. So, we expect to deal with a couple of methods today here. The first one is what is known as the ring method. Visualize maybe with the help of this diagram a ring which has the cross section shown by these two circles here. These two field circles are part of a ring and not shown the other part of the ring just the cross sections indicating the ring is immersed in liquid. And you connect this ring to certain external device so that this ring could be lifted out of the surface of the liquid. When you show an intermediate position like this by virtue of the surface tension of the liquid you would have the different menisci as shown here. One over here another here which should be identical for identical rings and then the meniscus here, here and here. What we do is we take this ring slowly out of the surface of the liquid. At some point as you are lifting this ring the surface tension which is trying to cling to the ring will be overcome by the upward pull that you apply on the ring. If we can measure that vertical pull then we should be able to determine the surface tension. Surface tension determines the force required to detach this ring from the liquid. This is one of the oldest methods of measurement of surface tensions. There are obviously number of variants which differ slightly. You could have for instance the ring attached to an arm of a balance and you could counteract the force surface tension force acting on the ring by the weights in the other pan or in another variation we have this ring attached to a very light beam carried on a horizontal torsion wire. Constraints for this torsion wire must be known. When you have a ring attached to a torsion wire then the ring method is referred to as using a tensiometer with this name do now tensiometer. What is not indicated of course here is that this is attached to a light beam on top which is connected to a torsion wire. So, it should be possible to measure the vertical pull required to overcome the action of surface tension. We could now go into the theoretical interpretation of the results. We would equate this vertical pull to detach the ring to the total surface tension force and that will have to address the total perimeter or in this word equation we could say the pull required to detach the ring is equal to the total perimeter of the ring times the surface tension and this total perimeter will have to be taken as twice the length of the wire which makes the ring. The reason is liquid is trying to pull this ring both on the inside over here as well as over here outside. So, the total perimeter will be twice the length of the ring. Small correction corresponding to the diameter of the ring is something which might cross your mind. You will see later that we have to be very perspicacious here in being aware of the corrections that are required in such simple theories. So, having made note of that fact that the total perimeter is twice the length of the wire making the ring and the wire diameter possibly could play a part we can move forward. So, in this simplest analysis the vertical pull on the ring f is equated to the surface tension gamma times 2 times 2 pi r as a rough balance between the vertical force and the surface tension force. And this should be valid at the moment the ring snaps off from the liquid surface. So, this is what is equation that comes to your mind from the school days gamma should be given by f by 4 pi r. We need to worry about how good this method is now. We begin with questioning the assumptions which have gone in implicitly in this derivation. The first assumption was that the surface tension force acts vertically. Look at this diagram this is magnified, but it does not appear actually at this scale that the surface tension would act exactly vertically. This is not just the sketch I have shown, but this would be reality. Action of surface tension would not be exactly vertical there will be certain angle here over here. So, our estimate will suffer if this assumption is not fulfilled. Second, the contact angle is 0. This is actually connected to the first one requires here that the liquid whose surface tension we are trying to measure actually weights the ring method will make no sense if that condition is not met with. You could be analyzing a theoretical picture with no equivalent in practice. So, one has to ensure that the theta is necessarily 0 as is commonly done these rings are made of platinum. Platinum being noble is very easy to prepare you just have to do gentle flaming for enough time to drive away any impurities adsorbed. So, you have to remember that it is not enough to have a good tensiometer in the lab you must remember to take all the precautions and this is practically every time. Every time you use a platinum ring or whatever ring you have to use for a given liquid it has to be prepared in case of platinum is done by gentle flaming before you make the measurement. That will ensure that theta is equal to 0 for platinum, but because the surface tension does not exactly act vertically we expect that certain correction factor will be required. Again this is often overlooked. So, you would expect if I coin this correction factor as beta you would suspect that this beta will certainly depend on the radius of the wire. I tried to give you an idea why radius would matter that is only visible in exact part in that balance. So, radius of wire should come into picture actually one finds that the radius of even the ring that you use matters and lastly the density of the liquid whose surface tension surface tension is being measured that also is important. So, expect this correction factor beta to depend on these two radii radius of the wire radius of the ring and the density of the liquid and understand that this correction factor is coming out of non vertical action of surface tension. So, I like to ask you a question if I am given the correction factors as you will see on the next slide and if they are less than 1 where do I expect to have beta appearing I hope the question is clear. We need a correction factor we given a correction factor that correction factor is less than 1 we understand the correction factor comes from non vertical action of surface tension. So, where do we expect the beta to figure in this equation? If we had to explicitly put beta in this equation 2 where would that be? So, because gamma is appearing with cos theta equal to 1 we know that the that is only for theta equal to 0 or the vertical action we expect that correction factor less than 1 to appear in the denominator. It should have come here in this equation over here in transpose case it will be appearing here ok. So, let us look at the values for pure water at 25 degree centigrade beta is given about 0.93 for ring radius of 1 centimeter wire radius of 200 super centimeter very thin wire. You can see for larger radius of ring of 1.85 centimeter and correspondingly slightly larger wire radius 0.03 centimeters beta is 0.88. Such correction factors will have to be necessarily used and when you actually embark on measurement of surface tension as always you have to be doubly cautious. You must calibrate your apparatus you must calibrate your instrument for measurement. In this case you have to calibrate the ring that could be done by using pure liquids with standard surface tension values known. So, you could take ultra pure water for which surface tension is widely agreed upon as 72 dynes per centimeter. So, you could do that in the range of surface tensions that you expect your liquid will have. If you do not know it a priory even the range then of course a spectrum of standard liquids may have to be used to make sure that the unknown surface tension is reasonably accurate. So, I hope I have emphasized enough the precautions which are necessary in measurement of surface and interfacial tensions. I guess I have to stop because the signal is gone. Next time around we will take up the other method method which is the drop rate method.