 So, the first thing is the specific surface area of the geomaterial, pore warning activity that is the land activity. It talks about the percentage of free lime which is present in the soil mass, cation exchange capacity or the value, liquid to solid ratio L by S, pH of the soil solution. Now, what is your feeling? If pH varies both sides of the you know normal value or neutral value, what should happen to Kd? It will remain same or it should change or it should change because both sides of the pH equal to 7 either pH less than 7 or pH more than 7. The tendency of the system would be different. More aggressive the environment, more acidic the environment, the chances are that Kd will be less because the system itself is unstable under more acidity. Buffer capacity of the sorbent temperature grain size presence of other ions. Now, this is what actually gives rises to the competitive sorption which I was talking about dimension of the ion and its valency ok. So, when you say presence of other ions there is a sort of a competition going on between different cations that which one should get adhered for which is going to get a chance to get adhered on to the clay or the solids. Their ionic strength valency organic contents particularly iron manganese oxides. If you have more ion than oxides the cation exchange capacities are going to be less is it not. And hence the distribution coefficients are going to be less the carbonate content. Carbonate content if it is more in the soil mass the soil mass becomes passive and hence these parameters will get affected accordingly. Let us talk about now batch sorption test. Take the geomaterial in the powder form and add contaminant in the solution form. This interaction is allowed for a certain duration with continuous stirring. And the factors which are important or which influence this interaction would be liquid to solid ratio and interaction time. Now, if C i is the initial concentration of the contaminant in the liquid phase C e is the concentration of the contaminant in the solution after time interaction time is to be recorded. After a certain time interaction time is to be recorded by sampling the solution frequently. And the C s is the concentration of the contaminant which is solved. Now, this is the equation which gives you C s. Now, if you know C s this will be nothing but initial concentration minus C e. So, what is C e the concentration of contaminant in the solution. So, this divided by C e will give you inverse of K d clear. Because C s is the concentration of the solids divided by C e is nothing but C w. So, this way you will be getting if you plot C e with respect to time for different l by s what you will notice is that after certain time the concentration which is remaining in the solution remains practically constant. Now, this is the equilibration time or this is the interaction time. So, the question which you had asked you have to establish for each contaminant porous system what is the equilibration time beyond which the concentration in the solution is not going to change. Once you have got this time you can go ahead with your test. Now, comes the concept of isotherms. So, the first isotherm isotherm word is a miso number here please understand isotherm is normally used for the equal temperatures, but it has nothing to do when we talk about the concentration profiles. So, linear isotherm is given as L r where C s equal to K d into C e. C s is the concentration on the solids C e is the concentration of patterns or contaminants in the solution phase. This is one way of defining it another way of defining is a Langmuir isotherm L m. So, this is how this equation is given C e upon C s equal to 1 upon K d into B C e upon B B is a unknown. So, if you are using Langmuir isotherm by doing lot of experiments you have to establish for a given contaminant porous media the values of B. So, that you can use this B values and you can use this equation to get K d parameter. The third one is known as friendlish isotherm F h where log of C s equal to log of K d plus some coefficient n inverse of that multiplied by log of C e. Now, in this form you have to plot the results on y axis you have C e C s on x axis you have C e. So, if you plot using linear isotherm you will be getting these type of relationships. If you use Langmuir isotherm you will be getting this type of relationship between C e by C s and C e. So, the slope of this line will give you 1 upon K d slope of this lines will give you K d. Here n parameter can be obtained. So, the intercept on the y axis will give you log of K d and hence you can obtain K d value. So, these are different techniques of plotting the results which you get from the batch experiments. Now, the question is which isotherm I should select? What you are noticing here is for the same experiment for the same test results the trends are different and what you notice is that F h that is the friendlish gives the best possible fit. There could be a situation where L r gives you a better fit or L m gives you a better fit. So, you have to plot all the three types of isotherms and justify that why you are selecting a certain type of isotherm. Once you have selected this you can get the value of K d directly. Is this part clear? And of course, these two isotherms are named after the researchers who have proposed them. These option process will be a inverse phenomena. So, here if you use the words like C s l what is C s l the amount of contaminants which is present in the sorbet after desorption phenomena. And C e l is the equilibrium concentration of contaminants present in the solution after equilibration time and C s is the concentration of the contaminant which is getting solved. So, using this expression you can get C s l and then again you can use the same equations. Only thing is the parameters will get changed by L. So, this is the leaching or the desorption phenomena. C s l is leaching, C e l is leaching and so on. And then what you have to do is you have to establish the equilibration time for leaching. That means, for different L by s if you plot what is the value of C e l with respect to time. Now, C e l is nothing but the equilibration concentration of contaminant in the solution. It is very easy. You can dip your electrodes take the solution measure the concentration of a contaminant and then again you have to find out after which time practically there is no change in the C e l value. That means, even if the leaching is taking place nothing leaches out much into the solution phase and hence this is the most critical value. So, this again becomes your equilibration time. So, once you have got this equilibration time the leaching should be done only for that period. And by using these isotherms again you can get the parameters associated with leaching which is K d. So, you know sorption coefficient you know desorption coefficient. This is part ok. It must be giving you a feel of how these parameters are obtained nothing more than that. You need not to worry too much do not try to remember these equations and all. Only thing is you should understand that given parameters how you can obtain what is desirable and how it is obtained. Now, just to give you an idea about the C e c and K d interrelationship I have included some minerals for a soil where quartz and montmornaite both are present. It is a typical marine clay and what you will notice is that the C e c varies from 49 to 57 and the K d is 3000 to 3600 about. However, if you have quartz and orthoclase like your white clay kaolin where the cation exchange capacity will be very very small and then K d will also be very small. So, what is your conclusive remark by looking at these values? Even if the mineralogy is not favorable clear the surface area itself is contributing towards K d up to a certain extent. You got this point. So, even if you are working on a passive soil where the minerals are not very active the fineness itself is good enough to give you more parking lots for cations to get power simply. On the top of this would be the mineralogy where the tendency of the soil is to catch more and more cations onto it and then you can correlate C e c and K d directly more C e c more K d. So, a day should come where just based on K d you should be able to characterize the soil mass and its activity and reactivity towards the environment that would be the ultimate in our subject clear. So, if you think of a situation like any type of a soil any type of contaminant and you have a matrix of K d values. So, looking at the K d values itself you can say that this seems to be a combination between clay and this type of a contaminant and that can be you know very much useful to the professionals. Now, another interesting thing is if you plot K d as a function of L by S what is Neha was asking L by S is nothing, but a sort of a moisture content. So, this could be in the gravimetric moisture content form liquid to solid form or even the volumetric moisture content form. So, they are all similar L by S is nothing, but W and W is equivalent to theta clear. So, if I plot this what you will notice is if L by S is more more mobility is there and hence K d will be more. Some other important relationships are if you plot K d with respect to time now this is nothing, but the interaction time. So, more the interaction time more K d clear similarly K d versus P h. Now, this is what I had asked you sometime back that what is your intuitive feeling that if P h changes look at this just about 7 it touches a minimum. So, in the acidic ranges K d happens to be varying too much for a given type of a porous media soil system. However, this curve cannot be generalized so easily. So, this is one of the trends which somebody might have got for his or her experiments and on the you know basic side that is when P h is more than 7 the influence on K d is not much. Exactly that is what I have been telling you because this is the acidic environment where system itself is very unstable. So, what is going to happen in the long term is not very known and mind you all these experiments have been done for less than 24 hours. So, within 24 hours degradation of the porous media is ruled out, but the biggest challenges the parameters which you are getting in the laboratory how you are going to delegate them to the field situations and one of the challenges would be how to talk about the P h changes on the K d parameter. Well, there was another philosophy that which was proposed by Dr. Naidu in 2006 what he tried to do is he tried to link electrical conductivity with L by S. So, I am sure you will agree with this that if liquid to solid ratio is more what will happen to the electrical conductivity? It will decrease when the concentration of ions is less in on this axis when you move from x to y the concentration of ions is becoming less and hence conductivity is decreasing. So, we wanted to develop a nomograph without doing so much of work just by measuring electrical conductivity which is very easy to measure you just have to have electrode and selective electrode which measures the electrical conductivity and from there I should be getting what is the value of sorption and desorption parameters. So, we trained our methodology for different types of geomaterials, fly ashes, clays, rocks, clays, marine clays, kaolin and so on. And then we came up with a proposal that if you measure EC which can be measured very easily you can directly know the K d and you can also know the K d L. So, both sorption and desorption parameters can be obtained just by measuring electrical conductivity, but this work remains incomplete and I have shared with you the philosophy. Let me quickly go through the column test is this particular about the batch test. So, in short you are allowing interaction of the loose form of the material in the powder form with the contaminants and trying to find out the equilibration time beyond which no more sorption will take place on the solids. And that is the point where you say the equilibration time and you find out what is the concentration sorbed on to the solids, what is the concentration remaining in the solution average of the 2 will give you the K d parameter. And when you are doing desorption test you take the contaminated soil put it in fresh water and see how much is leaching out in a certain time. So, that becomes equilibration time for leaching and within this time you are trying to again defining how much remains on the solid phase, how much comes out in the liquid phase and the ratio of the 2 will be K d L. Now, let us talk about the column test. As I said it will be very difficult to perform column test in the prototype. So, this is modeling exercise which is normally conducted in a centrifuge. You take a small sample where L is the length of the sample and this sample is packed in a container the bottom of this setup there is a water table. So, whatever percolates through this comes out and gets accumulated into the cistern or the standing water table. So, you can dose the system from the top whatever percolates will be getting collected into the outer cylinders. Now, this is where the concept of pore volume comes into the picture. How many pore volumes of the contaminant you have to pour from the top so that something meaningful comes out of the sample. So, this is where you have to define how many pore volumes are present in the soil mass. In any compacted soil mass the biggest question is when it gets completely saturated and when it will start expelling water out from it clear. So, this number PV is nothing, but the volume of the solution multiplied by porosity of the system and this is nothing, but the volume of the sample. So, inverse of the volume into porosity multiplied by volume of solution is nothing, but pore volumes where L is the length of the sample or the thickness of the sample, D is the diameter of the sample and volume is the V volume is the volume of the solute passing through the sample. Now, in this situation important thing would be how much time I should allow for the interaction. How would you obtain this? This is a very big question. I hope you will realize this. Now, this is a relationship which you will be getting the breakthrough curve. If you remember on the y axis this is CT by C naught the concentration which is coming out from the downstream side you collect analyze it in a atomic absorption of the ICP get the value of CT and C naught is the concentration of the fluid which is being put into. So, the normalized CT by C naught value is nothing, but 0 to 1 it will vary. Now, as time increases what happens? CT by C naught will start increasing and it will go up to a maximum value. Now, the moment it becomes close to 0.9. Now, this is where we started washing it. So, you add fresh water. So, that the desorption process takes place. So, this is the sorption process or the sorption breakthrough curve and this is the desorption breakthrough curve. You can go for several cycles of sorption desorption to understand what is the resilient modulus of the material as far as sorption desorption is concerned. See you have talked about resilient modulus for loading static both as well as the dynamic loading. Here we can expose the sample to chemical loading in cycles and we would like to see what is the characteristic of porous media contaminant interaction. Is this part clear? Now, the tail of this graph over here corresponds to something. What it says is up to this much portion of the graph where CT by C naught is almost 0. What is the significance of this? No concentration of contaminant is coming out of sample. That means, if you check out from here this will give you a time up to which the system has a tendency to sorb only. So, this is a sorbing capacity of the material. Now, after this more and more flux of chemicals come into the system and what happens? There is a accumulation of concentration and hence CT by C naught keeps on increasing very rapidly and again you will notice a time comes where further change in CT becomes almost negligible and this is the point where you say saturation limit of the material. That means, no further interaction is going to take place between contaminant and porous system and this is where if you add fresh water somewhere here what will happen? The desorption will start. So, this is the best way of doing sorption desorption in a column experiment. This work is also by the way incomplete because of the lack of time we could not do this work completely. Now, coming back to the modeling part. So, another 5 minutes you just try to understand what I have been discussing this is the crux of the whole discussion. You have been utilizing this equation to define contaminant transport in x t domain x is the distance or z t domain z is the distance and t is the time. So, del C by del t equal to di into del square C by del z square minus V s C pi velocity del C by del z die density of the media k d. Now, k d is the principle known or unknown, known Sariqa. They is known upon porosity into del C by del t. Now, there could be a situation where k d is principle known as well as principle unknown. If you are doing field experiments what happens then? It is a principle unknown, but if you are doing batch test then your k d is a principle known. So, you can do both type of modeling forward and reverse modeling that is the beauty of this type of exercise. So, if you put these terms together del C by del t plus 1 that is 1 plus rho d k d by eta this will be equal to di del square C by del z square minus this if r is equal to 1 plus rho dry into k d upon porosity. Now, this r term which is appearing here is known as retardation coefficient. What is the physical meaning of the word retardation? Stopped is it not retained. So, r is the retardation factor which is directly proportional to k d. So, more the k d the tendency of the porous media is to retard the contaminant transport clear. So, in the same time the system is getting more and more retardation the contaminants are not going to flow out easily and hence k d will also depict a dynamic phenomena. I think somebody was talking over such as you are asking about the time dependent situation. So, because r is a parameter which includes k d and k d is going to be time dependent by virtue of these qualities you can do time modeling for contaminant transport. However, if you do the centrifuge modeling where you must be using this law I am sure for a given model p is the prototype m is the model suppose this is sample a. So, you can say that Tp equal to T model of a into na to the power y and if I am testing many models I can generalize this equation like this and if I take their log form this is what it is going to happen. Now, if you look at the previous graph which I have shown you the BTC the breakthrough curves for sorption desorption which one is more steep sorption or desorption desorption. So, what is the meaning of this? If I find out the y value it will be more for sorption or desorption. So, when your y term is 0.5 is very fast it is less than 1. So, that means, for desorption the scaling law would be Tp equal to Tm n to the power 0.5. So, this is how you can establish the scaling laws for the entire exercise. So, what is the moral of the story? The moral of the story is all this was done to understand how contaminants and geomaterials are going to interact and this interaction can lead to all this what is possible. So, at the end of the day if I know DI, if I know VS, if I know KD, porosity is known, del C by del T can be monitored by doing experiments and then I can work out what is del C by del Z. That means, rate of change of concentration at a given depth means distance and you reverse this problem if del C by del Z is known I can find out what is the concentration migration at a given point at a given time, two applications. The third one is if del C by del T is known del C by del Z is known I can get the metal properties also. That means, contaminant transport equation can also be utilized for characterization of porous media. The fourth application would be if you know the porous media, if you know del C by del T, if you know del C by del Z, you can use this equation for obtaining what type of contaminant transport is taking place, advective diffusing. If VS is over with 0 what is DI? If DI is 0 what is VS and so on. So, these are 5-6 combinations which can be worked on by using ADE and the biggest question was how to get the parameters. So, this is what we have discussed in details. So, with this I finish chemical characterization of geomaterials and then hopefully from next lecture onwards I will be talking about thermal characterization, electrical characterization. Now, one question still remains in my mind is we have been talking about environmental geomechanics. So, where is the mechanics component coming into all this and that has to be realized. So, if you concentrate on the very first lecture I have been talking about that we are not talking about the mechanical forces, mechanical stresses directly. We are talking about the stresses which have been ignored till now like thermal flux, electrical flux, chemical flux, combination of these fluxes along with mechanical stresses which are going to act on the system. So, that is where actually you require the concepts of environmental geomechanics to solve a problem in total or details.