 So, in general how would you quantify this partitioning relationships? Suppose, we are talking about solid water interface saturated soil. Now, this is how you will define KD parameter what is CS concentration of contaminants which are getting solved onto the solid phase and CW in this solution in the solution form. So, if you take the average of these two this is nothing but KD it is always defined as milligrams of contaminants per kg solid of the soil mass or the porous media. What are the units of CW this is the milligrams of contaminants per liter of water of the solution why I use the word water here because contaminant is dissolved in the water phase. So, to create a certain molarity you take 5 grams of a salt and dissolve it in 1 liter of water. So, for CW we always use the word milligrams of the contaminants per liter of the water clear. The second phase is water vapor. So, having see what is the significance of solid water interface the contaminant is getting distributed in solid phase and water phase. Now, look at this situation here the contaminant is getting distributed in vapor phase and water phase. So, third phase is included into this. So, the complete matrix would be solid water and water vapor interface meaning thereby if I extend this model further KD if I know what is the amount of gas what amount of concentration which are getting added on to the gaseous phase divided by the concentration of contaminant in the solution phase this becomes your Henry's constant. Now, Henry's constant is nothing, but the constant which is normally used in gas law. So, for the most of the time when contaminant migrates in the soil mass or out of the soil mass most probably the porous media will remain saturated. However, when you are talking about contaminant migration in unsaturated soil mass then this type of vapor water interaction will come into the picture is this ok is the gaseous phase of the contaminant which is getting adhered on to the solid surface. So, that is how you are saying that the certain amount like camphor what will happen if you have camphor. So, camphor may not get dissolved in water, but the moment it sublimates it goes and gets adhered on to the surface of the solids. So, the gaseous phase of the material which is getting adhered on the solid surface see partitioning is taking place always from the solid form or from the liquid form or a solution form. So, this is how you will be defining these numbers with respect to liquid phase what fraction has got adhered on the solids what fraction has got adhered on to the gases. So, putting these two together is a three phase system all right we can do lot of other things when we use these parameters like contaminant concentration in geomaterials can be obtained. Now, this is what again defines the fate of contaminants in the geomaterial. Now, if you talk about the total mass in unit volume of the geomaterial this is how it can be computed you have density of the porous system multiplied by C s plus theta w theta w is the volumetric moisture content of the soil mass multiplied by C w the concentration of contaminants in liquid phase plus theta g gaseous phase multiplied by C g. Now, there is a boundary condition that if soil is saturated what is going to happen your theta g is equal to 0 where theta g is the volumetric gas content or the vapor content. Now, have you ever studied what is the value of theta the volumetric moisture content volumetric moisture content is defined as saturation multiplied by porosity the bulk porosity. See this is in fashion these days we do not talk about gravimetric moisture anymore we talk about volumetric moisture. So, saturation multiplied by porosity will give you theta value. So, if saturation is 1 fully saturated soil theta is nothing but equal to porosity. What is the need of defining theta value because porosity can be measured very easily and more precisely by using all your TDR FDR techniques, but gravimetric analysis is always very empirical and not much reliable. Another problem is you have already disturbed the matrix of the soil by bringing the soil sample into the laboratory. So, it is not the in situ condition of the moisture. So, that is the reason everybody is trying to use theta values these days that means volumetric water content as theta w volumetric vapor content or gaseous phase content as theta g where theta is saturation and porosity multiplication of the 2. So, then this equation will reduce to C T equal to density bulk density of the system multiplied by C s plus porosity multiplied by C w. Now, tell me one thing what is the application of this equation? If you want to find out what is the concentration of contaminants present in the porous media you can simply substitute these values the density and the porosity and you should know what is the C s and C w phase and hence you know the C T value. Now, this is the practical situation with which you normally deal with in most of the professional activities. So, this is what is known as concentration determination in porous system or the fate of contaminants. Now, if C T tends to 0 what is the implication of this? No contaminants what is the meaning of that? Either no contaminant gets trapped into the porous media or there is no sorption process going on in the porous media. So, again there are two things which you should not forget to apply clear what it indicates either the contaminants are inactive or the porous media is inactive or the time given to the system is so less then nothing gets retained on to this and so on. There can be so many combinations and permutations of this type of a phenomena, but in normal situation what would you prefer as a as an administrator not let us say as an engineer or a scientist C T should be 0, C T should not be 0. Why I say administrator? Suppose you are the chairman of municipal corporation what do you expect everywhere? Completely clean land C T is always 0 clear of course in a hypothetical situation or C T should be a very high number that means the soil mass is never going to release any contaminants in the geo environment. Now, if you are somewhere in between the life is precarious. Now, these are the boundary condition which you have to put in your modeling mathematical modeling is the concept of modeling clear to you know and most of the time C T concentrations are defined by pollution control boards. So, they come up with the norms that in a certain country at a certain location whether the thermal power plant or a rubber manufacturing unit, electroplating unit the permissible concentration of a contaminant should be less than this. So, this becomes third boundary condition. So, you have many constraints for which you have to solve this linear equation and here you can use the concept of optimization, mathematical programming, linear programming, operational research and so on OR NOE and what not and this becomes a good PhD thesis for people who are trying to earn their doctorate. Is this okay? Any doubts questions? So, all of you are now experts in modeling contaminant transport in soil mass. His question is that in these equations C T time is not coming to the picture truly speaking time is inbuilt. Now, I will show you how time gets automatically reflected in this equation because CS and CW both of them are functions of time. So, we always talk about equilibration time beyond which even if the interaction is prolonged nothing much different is going to happen. So, in all these relationships the most important parameter is to establish equilibration time alright. So, when you conduct any test one of the most important parameters would be what is the time of interaction and what happens beyond equilibration period. Is this okay? What is her question is that is there any limit on saturation? See the most simple situation is even saturation is 100 percent because we have been dealing with saturated state of the material in terms of hydraulic conductivity and what not. But the most problematic situation would be when your two phase system is trying to become three phase particularly for unsaturated soil where the saturation is less than 80 percent alright. And as we have been talking about since last so many lectures that most of us locations in the country or anywhere in the world you will not have soil mass which is fully saturated because the water table keeps on either fluctuating or it is much deeper. So, to answer your question let me put it like this that CS and CW or in the words KD parameter itself is a function of volumetric moisture content. Is this clear? So, KD is a function of theta. Now, please tell me one thing if theta is more KD will be more or less. If you have more water present in the soil mass the distribution will be faster or lesser? Faster. Exactly. So, that means higher the degree of saturation your KDs will be very high the sorption capacity of the porous media will be extremely high. Is this the answer is this what you are asking? So, the moment theta changes your suction value comes in the picture the soil becomes unsaturated the contaminant transport starts taking place in unsaturated soil mass alright. Further soil. What about the? Good. Further soil itself is there any. Very good. So, what happens when you go to many malls in Bombay city where they say parking full no parking lot available. What do you do normally? The same thing happens landing does not take place on Bombay airport because of traffic congestion. So, what do they do they keep on hovering the same thing happens to the atoms and the moment they get a chance to get stuck to the soil they get stuck. So, you think of a situation where around the particle there will be multi layers of cations clear. So, the most high valence cation should be sitting close to the atom or extreme end no that again depends upon lot of things that will depend upon the valency that will depend upon the pH and so many other factors pressure and all. So, it is very difficult to generalize anything. So, the easiest way to say is there will be so many parameters which will again guide which cation should come and get parked onto the surface. Suppose a truck cannot get parked in a parking lot, but a motorcycle can be parked very easily. The same thing will happen in this case also. A small diameter cation will have much more easy access to the soil particle as compared to a bigger diameter cation, but then valency comes in the picture. The place reserved for somebody to come and park the vehicle. So, lot of things are there is a black box clear, but I think this much have given you some reasonable idea about what are the uncertainties associated with determination of KD parameters. So, most of these experiments are done with single cation species, but the real life situation would be where multiple cations are coming in the sludge or the industrial waste and hence you have to model a complex solution for finding out its KD parameter. So, there are lot of things to be done yet alright. Any other question? See the easiest path is what? Either the contaminants will get adhered onto the solid surface or onto the gaseous surface because even if they get interaction with liquid phase they will get dissolved again. So, partitioning cannot be from water to water phase. So, it is always with water to solid phase and with water to gaseous phase this is ok. If no water phase is there then what happens? You tell me a solid contaminant unless it vaporizes there will not be any distribution. So, that is what I gave you an example of camphor it will not liquefy it will straight away sub limit. So, that means from solid state will directly get converted into the gaseous phase the entire gaseous phase will get adhered onto the surface of the solids. This is what is known as gas option. So, when you do your carbon dioxide sequestration and all this is what is more important. So, you will be conducting an experiment where you are not interested in soil coming in contact with the liquid phase of the contaminant. All your experiments will be diverted towards how much gas can be retained into the solid phase. How much carbon dioxide from the atmosphere can be squeezed and sequestrated into the solids is this ok. So, there your connotation of Kd will be H, but not from the liquid phase. Incidentally, we have talked about gas option for finding out SSA especially surface area. So, that is also sort of a Kd parameter which you are getting where the gas is getting sobbed onto the solid phase and hence giving you the surface area. If you remember all your mono layer thickness of the EGMG ethylene blue we have talked about is nothing, but the layer of molecules of ethylene blue getting adhered onto the particles and depending upon how much amount is adhering you can find out what is surface area. Now, let us discuss the methodology of determination of sorption and desorption characteristics of geomaterials and immobilizing materials at mixtures. First of all the most easy thing is to perform batch test or to perform column test. You might have heard about these tests I am sure in your environmental engineering courses you must have done this. What is batch test? You take certain amount of the material, geomaterial and mix it with some solution of a contaminant and allow this interaction for a long duration. However, this will fail to simulate geomaterial contaminant immobilizing agent interaction in a realistic manner why? In nature this is never going to happen that you take some soil put it in the solution. There is always a percolation taking place. So, you there is a acid spill and the rains come what happen? This acid has a tendency to migrate into the porous system. So, batch test will not really give you a clear picture of what is happening in the nature. Water column sorry fail to come up with the recommendations regarding generalized isotherms. I will be talking about what is meant by isotherms. What about column test? So, you make a column of the soil or admixture and pour certain amount of contaminants from the top and let it percolate from the other end. So, depending upon the sorption capacity of the soil whatever concentration difference is coming in the outflow can be again quantified as a k d parameter. So, these are typical column test. Column test are quite near to what happens in the nature, but unfortunately column test which are done in the laboratory will depend upon the distorted texture of the soil from that which exists in the nature. So, again they will be giving you very very distorted picture of the real life situation. And they are very time consuming cost intensive. Another thing is suppose if you are simulating a 2 meter long soil column is it possible to make a 2 meter long 3 meter long column in the laboratory of a soil mass that to undisturbed is not so possible easily. So, you have to live with uncertainties and the problems associated with determination of parameters, but it is still we would like to come up with some numbers. So, that we can use them in our modeling exercise. Another problem is whenever you are doing column test the permeability is a very big issue. So, it will take you for 1 meter long column how much time it will take for permeation if 10 power minus 11 meter per second is the permeability of the clay. How much time it will take you to complete one test your M Tech will be over definitely by that time. So, this is where actually people are resorting to centrifuge modeling. This is a good example of how centrifuge modeling can be done. Dr. Naidu had done extensively this type of studies for his PhD thesis where he has established isotherms utility of some nomograms for selection of a material. Unfortunately, this paper is not published yet it is in the press. Accelerated physical modeling using a geotechnical centrifuge is a good solution for finding out absorbing and desorbing characteristics of porous media. I will show you in the later half of the lecture how the results can be utilized. So, it seems that the laboratory tests are not going to be very reliable. So, it forces you to conduct these tests in the field allow interaction between the soil and contaminant in nature, but you know what are the difficulties involved clear. Of course, this will give you a real life situation real life picture, but then very cumbersome process. Similarly, you can do field modeling test where you model the contaminant migration into the soil mass, use some pre-established numerical models and find out from them the KD parameter. So, it becomes a very long exercise and third one is whenever you are working with highly organic material is what is known as KoC method. So, KoC is nothing, but the organic carbon normalized adsorption coefficient. That means, if you have a soil for which the organic content is very high, find out the organic content of the material. Now, what is your gut feeling because of organic content the KD will be more or less more. So, what is that you are doing over here? Yeah, you are normalizing with respect to 100 percent. So, even if your OC organic content is 100 percent KoC will be equal to KD. So, KoC will always be higher than the KD parameter because of the organic contents present in the soil mass. So, it is a simple logic which is used to determine the KoC for the organic soils. Normally, this method is not utilized so much, but then this is one of the techniques of determining the KD parameters. This is part ok. So, ultimately people come back to batch test and the column test to get some reasonable picture of you know what is happening. It is very difficult to do in situ and the field test. These are the codes which are available in literature. ASTM American Society of Testing Materials has two codes which are available on 24 hours batch test for finding out sorption and desorption processes and ASTM 1988 determining the sorption coefficient for an organic chemical soil and sediments. There is another code which is given by OCED that is Organization for Economic Cooperation and Development. One thing you should realize that environmental geotechnology geomechanics is gaining a momentum because of the organizations like this. It is Organization for Economic Cooperation and Development. Is it not? As the civilization is progressing, there is a requirement for developing the codes which are going to be helpful in taking major decisions. So, this is how in 2000 they have come up with a guiding guideline determination of soil adsorption, desorption using a batch equilibrium method.