 Partitioning relationships, partitioning could happen from solid to water phase alright. Saturated soils, pores are filled with water, CS is the concentration of the solids, concentration retained on the solids, CW is the concentration of the contaminant which remains in water clear. So, this is the KD parameter. So, imagine if I have 1 gram of clay and if I dip it in a solution of some molarity, some concentration of cations, how many cations have got sobbed on the clay particle can be obtained by detecting the CW from the initial concentration by using the ICP or Atomic Absorption Spectrophotometry. This is okay. So, CS is the sorbit which is sobbed on the solids and CW is a sorbit which is remaining in the solution at Eclutium. The second one which is quite intricate and difficult to simulate in the laboratory condition would be water vapor. Nature does it very beautifully. It is not easy to create interface between water and vapor in the laboratory circumstances. You must have heard the Henry's law, right. So what is CG? Here we use CS upon CW. This is CG upon CW. But the guys who are working in the field of climate science, aerosols, air quality analysis, for them I hope you realize the water vapor interaction is going to be extremely important. So, CG is the concentration of the gas which is getting sobbed on the solids divided by the concentration of the sorbit which is remaining in the liquid phase. So, we have solid water or we have water vapor, two types of interaction. Then you can compute the total mass per unit volume of the geomaterial by using these relationships, okay. So, theta W is the volumetric moisture content, theta G is the volumetric vapor content, theta is the volumetric moisture content which is equal to saturation into porosity. This is a gas component. This is the fluid phase component and you know this gets converted into when you are talking about no gaseous phase, this gets converted into the concentration of the solids, concentration on the solids and concentration which remains in the water solution. This is how the partitioning is defined. Do not write down this equation. You just understand, you get a chance to work in this area, you will learn it automatically. So far so good. I hope you are realizing the intricacies associated with environmental geomechanics henceforth. We are still attempting it. A good example of this would be gas hydrates where we have a three-phase system and you lower down the pressure or increase the temperature and the decoupling takes place in the material. Well, so to start with determination of sorption and desorption of geomaterials. Normally batch tests are done or column tests are done. Batch tests are you take some material, few grams of soil or geomaterial in a powdered form, why you have made powder so that all the particles contribute to the process and then put them in a solution which is in a beaker or a container. What is happening is that you are allowing 100% interaction between each and every particle with a solution. So this is the best possible form of studying contaminant, geomaterial interaction or the immobilizing agents. Unfortunately, this type of situation is not going to occur in the field. Why? Because the soil mass is in compact form. So all the surface of the grains is not really contributing to the interaction. Because when you compact it, what happens? A substantial amount of the surface of each grain gets hidden by next grain. So it does not come in contact with the contaminant directly. So that means if you are doing batch tests, you are going to get something which is very extremely lower value of the KD parameter. So what people do is they do batch test, sorry column test. So you make the columns and let contaminants pass through them and then see how much has been solved by the soil column or the geomaterial column. Now this is going to be realistic because in nature also you have soil beds but unfortunately this is a very time consuming process. Why? Because the permeation through the compacted soils and the geomaterials is time consuming, clear and extremely expensive. So this is going to give you a very lower value of the KD. But yes, these are the two tests which you can do. Whatever parameters we get from batch test and the column test, somewhere in between we have to select the right parameter for doing our mathematical model. So these are the two bounds of the KD parameters which you get by conducting laboratory experiments. This is where you can use centrifuge modelling also and I will show you some of the results which our group has published where centrifuge was used to obtain the KD parameter from the column test. We can also do these tests in the field. We can do field modelling test. There is another method which is known as distribution coefficient which can be obtained because of the presence of organic content in the soils. So the soils which have higher organic contents would have higher distribution coefficient. So there is a empirical relationship which has been given by KoC equal to KD multiplied by 100 upon Oc. So KoC is the organic carbon normalized adsorption coefficient and Oc is the percentage of organic carbon which is present in the sample. Do not write these things. These things are available in the courts and you can use them in case you are working on these topics. These are the courts and the information which is available already. I hope you can realize as far as the Indian context is concerned we do not have any guidelines. So these are mostly ASTM standards and the OCED standards. You know what is OCED? Organization for Economic Cooperation and Development. These type of treaties and the guidelines are useful when you are exporting and importing any material from any country that becomes a mandatory thing. If you send a courier through any of these courier agency they will take a declaration from you that this material is not toxic. There will be some 20-page gadget associated with these document which you have to sign and you have to declare that the material which you are sending as a consignment does not fall in the category of toxic material, export and import. So these are the standards and the international norms which have to be followed. The list of the parameters which influence the sorption and desorption mechanisms is big. Whatever comes to your mind can be written here but primarily surface area contributes a lot because surface area contributes to the cation exchange capacity also, pozzolonic activity of the material, liquid to solid ratio. What is liquid to solid ratio? If I take 1 litre of water and if I add into some salt of known weight I can create a solution of certain molarity. This is your 10 plus 2 signs. So this becomes my contaminant. In this contaminant if I add 1 gram of soil, clear? So 1 gram of soil I am adding to 1000 cc of or ml of water. So this becomes liquid to solid ratio of 1000 alright. So what I have done indirectly is I have simulated a situation which is similar to the pore solution. So all the studies I will be doing by using this liquid solid ratio where soil is 1 gram and the solution is 1000 ml. So the more realistic value would be 20, 25, 10 that means 20 times solution 1 gram of soil. pH of the solution, buffer capacity of the sorbent, temperature, grain size, presence of other ions, ionic strength, organic content, iron, magnesium oxides and the carbonate content. This list is very big. I have just given you some parameters which would be influencing the KD parameter directly. Just to remind you why KD parameter is required because you wanted to solve one dimensional ADE. You remember? So unless you get KD parameter you cannot get CT as a function of x, y, z and t. So the batch tests are you take certain amount of soil or the geometry in the powder form, put it in the solution, stir it over a period of time, heat it also if you want and then create different liquid solid ratios and then keep on dosing or sampling out from the solution and see what concentration of chemicals is getting sobbed onto the solid phase. So this is what I was discussing. The CS is the concentration of the contaminant in the sob form which can be obtained by subtracting whatever is the concentration in the solution after equilibration from the initial concentration multiplied by L by S. So this is how we do this test. These tests are extremely intensive to conduct. Each point you might be getting after few days. So there was my student Dr. Pankaj Patak. She did her PhD on this and I think she is one of the pioneers in the subject. She has published three international journal papers in ASC and two patents. That is really remarkable and the patents are in the form of the guidelines which have been created how to perform these tests. You should be aware that there are no guidelines which are available to select the concentration of the chemicals and that amount of soils and we realized from the completely negative results that if you do the synthesis of results properly you can get an extremely interesting idea which can be published in the form of a paper and a patent. So never ignore the results which you get which appear to be incorrect because there is a story behind that also. If you have time and if you sit down and apply your mind you will realize there is something interesting which has happened and which was going totally unnoticed. So at different L by S of the solutions when I take certain soil and when I allow interaction to occur what you are observing here is CE is the concentration of the contaminant in the solution. So concentration of contaminant in the solution decreases over a period of time. Why? Because this concentration is getting sobbed onto the solid phase and hence the sorption is going on. So after certain time what you observe is that concentration becomes almost constant. This is what is known as equilibration time. So for every contaminant and geomaterial the equilibration time is going to be different. So the moment you change the parameters here the equilibration time changes. Just so sensitive. Now how to analyze these results? How to get the sorption characteristics? So sorption characteristics are obtained by using these three mathematical models and these three mathematical models are known as isotherms. The term therm which is associated with this model is a miso number. It has nothing to do with the temperature because these are the plots of concentrations but because the concentration is very much susceptible to the temperature all these parameters have obtained at a constant temperature and hence all these graphs which are being shown correspond to a specific temperature. So what normally is done is you plot CS versus CE just to remind you CS is the concentration which is sobbed on the solid phase and CE is the concentration which is still available in the solution phase. So when you plot these two against each other these are the models which are used. Linear isotherm, Langmuir isotherm, Friendlich isotherm. You just understand how the interpretation is done. What you will observe is out of the three which are very common you can also come out with your own isotherm. So that would become XYZ isotherm. This matter is still the subject is under developmental stage. So if you propose a kinetic process it goes in your credit. So once you draw the straight lines or fit a best fit to the data which you are getting what you will observe with that some of the isotherms do not follow experimental conditions there are some which will follow better. So like in this case what we have presented here the Friendlich isotherm is giving very good results as compared to the linear isotherm alright. So this is how you have to train the experimental data. The slope of these lines is nothing but KD parameter. So here you can observe CS upon CE is KD clear. So once you have plotted these graphs you know the trends take the slopes this is KD parameter. So in most of the cases the slope of the line is the KD parameter. I hope now the methodology is known to you you can perform this test and you can use them. The best example of KD parameter would be in pharmaceutical industry how? I hope you know that the carrier of the medicines or the tablets which you are taking is a claymendal and that claymendal is dosed with different types of medicines. So the moment you swallow it you want to accelerate the desorption process or sorption process. So depends upon the doctor imagine if your colon is full of bacteria what I would like to do I like to insert something which goes inside and attracts everything and then comes out through excreta clear. At the same time if I want to impregnate your body with some chemicals which are required as nutrients. So what I will do I will take these metrics of the claymendals charge them with that particular species of the bacteria, medicine whatever and the best way to inject this would be through your asapagus eat it it goes in your stomach becomes a part of the blood tomorrow. So sorption desorption in the best possible way can be practiced in this manner think about it. I hope you are getting now the applications of how to do this. You must have realized what we will do is after achieving the equilibration in the sorption you take out those samples which are fully contaminated put them in fresh water and as the time increases what happens the contaminants which were soft there will ooze out into the fluid phase and keep measuring them every time. So after a certain time what you will observe the concentration of the contaminants in the solution phase is going to increase and becomes constant. So this is a desorption characteristic and this is what is known as desorption equilibration time. Rest methodology is same you can find out the KD parameters for sorption desorption by using the same isotherms and you can designate the geomaterial contaminant interaction. Many people are trying to quantify this contaminant geomaterial interaction in the form of CEC and I hope you understand that CEC is linked with surface area clear. So why surface area becomes very important because it gives an indication of CEC and CEC gives an indication of KD they are all interrelated with. So you are trying to work on this model so that we can get rid of the conventional soil classification system. Conventional soil classification system cannot be used for environmental geomechanics applications because nowhere you talk about the geomaterials interacting with contaminants I hope you will agree with this, agree. But we have created so many case studies to make you convince that you cannot isolate the geomaterials from the environment, geoenvironment which is either manmade or natural. So this is becoming a very interesting debate in the international fraternity. Can we eliminate all these conventional tests and come out with simple parameters which would define how geomaterial interacts with geoenvironment clear. So once you have done this, this is going to be ultimate Brahmastra that is what people are trying to do. So we have shown here KD is dependent upon L by S different type of minerals are related to KD to CEC. We have shown that how KD changes with time, how KD changes with pH. So these are the subjects which have to be studied further. This is the thesis of my PhD student Dr. Naidu who is a faculty member now at IIT Chennai. He did remarkable work and he was the first one to crack this problem of electrical conductivity of a geomaterial contaminant system directly giving the KD parameter. So imagine if I create some probes or sensors, so sensors will give me directly the EC value and that EC value can I from that EC value can I obtain the KD insorption and KD in desorption. If this can be done, this would be interesting. Now comes the column test. Having talked about the batch test, we create a column here, something similar to the falling head per millimeter test which you normally do. This is a sample which is sitting on a porous stone and the whole system has been mounted on a base plate where we have two more concentric cylinders. What we do is we fill up the inner cylinder up to a certain point with the contaminants, they percolate through the sample. Whatever percolant comes or the leach ends come, they get accumulated in the middle cylinder. In case they overflow, they will get accumulated in the outer cylinder. So these are the typical column tests which are done. This is where we use the concept of the pore volumes. How much volume of the solution should be added which will ensure that the contaminant is passing through the sample and saturating all the pores. So this is a philosophy we created like number of pore volumes is equal to volume of the soil divided by volume of the physical volume of the sample. So if you see this term where the porosity has been multiplied, so porosity is volume of voids multiplied by total volume of the soil sample. So truly speaking, this is nothing but volume of the voids. So number of pore volumes are volume of the solution divided by volume of voids. So if volume of voids are unity, I have to add 5 times the pore solution to do these tests. We get a very interesting relationship like this. I hope if you concentrate on y-axis and x-axis, you will realize that this is also sort of a BTC breakthrough curve where we have Ct by C0 increasing with time first, this is a sorption process. And at this point, if I start desorbing, washing, I get the tail of the curve where Ct by C0 decreases very fast with time. We did this test in centrifuge, we saved our time and this was the first of this kind of the study which was done by somebody Dr. Naidu where we established the breakthrough curves in the centrifuge for a soil contaminant system. And you know how to get the KD parameters from there and what we have done is we have used this information to solve one-dimensional ADE. This is the form of the ADE, you remember del C by del t equal to diffusion coefficient del square C by del z square minus Vs into del C by del z minus the density of the porous media Kd upon porosity del C by del t. If I take this term over here, this will become del C by del t equal to di del square C by del z square minus V upon r del C by del z and 1 upon r here also, where r is equal to 1 plus rho dry density Kd upon porosity. Porosity can be determined by using porosimeters, mercury intrusion porosity meter MIP the best possible way, density of the porous media is known. If Kd is known, retardation coefficient can be obtained. So, by conducting these tests, you can get Kd parameter also and once you get Kd parameter, you get r parameter also and now you can solve the ADE. I hope you have understood the whole story. So, just out of curiosity what we did is we did centrifuge modeling of sorption desorption process. I think, I think you are doing a course on centrifuge modeling. So, the big question was can we model the phenomena in centrifuge and what happens in the prototypes and we model the time. TP corresponds to prototype, TM corresponds to model, N is the centrifugation effort. So, if I say that TP equal to model N to the power y, this is what is going to give me the complete picture. This is how we were doing this modeling of sorption desorption mechanisms. And what we observed is that we got for sorption, we call them as scaling parameters, scaling factors. So, for sorption process which is a slow process, if you remember, if you see this graph, you will realize that sorption is a slow process, contaminants getting assimilated with the surface, but desorption is very fast. If you see there the desorption time factor is 0.5. So, these are the interesting things which we did a lot is to be done in this area. I hope this discussion of today must have given you an idea about where we are, where we could contribute to the knowledge and what needs to be done further. The practical utility of these type of work is extreme and I hope you can realize that if you have to safeguard the environment against its contamination, many times you have to come back and fall on this equation and predict what is the impact of our activities on the geoenvironment, which if you remember, we discussed in the beginning of the course under the realm of EIA, Environmental Impact Analysis. So, because of any industrial activity, the waste is generated and if I am dumping the waste somewhere, anybody is going to ask me a question, what is the impact of this waste in the near fields and the far fields over a period of time. So, when you answer all these questions, you have to resort to the mathematical modeling. But as I said, it is very easy to resort to the mathematical modeling provided you know the coefficients which are unknown. And in order to get these coefficients, you have to do a long journey, you have to create your own setups, you have to derive the expressions, you have to analyze the whole situation and those parameters have to be plugged in over here, the suitable boundary conditions to get the answer. So, this is where we are, I hope people like you will contribute further and the subject grows much, much, much.