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Video 1
Hello all, we have been discussing the concept of vapor pressure lowering which can be well understood using Kelvin’s equation. So, Kelvin’s equation a which states that the vapor pressure on a curved surface equals to the saturated vapor pressure times exponential of partial molar volume of water times change in the pressure across the interface divide by RT. So, the implication of Kelvin’s equations is that above a curved surface the vapor pressure is larger than in the fluid. So if you consider a capillary tube immersed in a beaker of water, the water rises in order to balance the chemical potential and it assumes a meniscus or curved surface like this depending on the interaction between the capillary tube and the fluid. So, this is a typical example of water in a glass beaker or glass capillary so you have a meniscus like this. So, the vapor pressure above a curved surface is u v which will be less than the saturated vapor pressure which will be above the flat surface, so this is the implication of Kelvin’s equation. More than that the vapor pressure even though this is less than the saturated vapor pressure water vapor condenses into water and it accumulates in a capillary tube which we will understand. As there is a pressure drop across the interface, so this is ua atmospheric pressure and this is water pressure. So, there is a pressure drop across the interface because of which there is a change in the vapor pressure. Similarly, when there is a capillary tube which causes a lowering of the vapor pressure. So, you have, say for example, here you are maintaining RH equals 100 percent. So, thenyou have u v sat here in the ambiance, so here the vapor pressure is lower than the saturated vapor pressure u v inside the capillary tube. Even though the vapor pressure inside a capillary tube is lower than saturated vapor pressure, you see that the water accumulates into the capillary tube with time and you see that there is a filling of water within the tube. So, which fills because, a number of water molecules that get trapped in this small cavity, so slowly the water level increases within the capillary tube in order to which is nothing but condensation. So, condensation takes place at a vapor pressurewhich is less than saturated vapor pressure that is the implication of Kelvin’s equation, this has a very important application, important correspondence to our soil mechanics. Because, when you take a soil sample which is kept outside this is initially dry which is the oven-dried, initially at the oven-dried state you take a clay powder, say any clay powder or even soil at oven-dry state if you take and then place it in the cup and in an atmosphere when you leave it the relative humidity of the atmosphere maybe 80 percent or it could be anything, it may vary usually between 60 to 90 are closed to 100 percent depending on the location. So, when you have some particular RH and temperature of the ambiance, then you would see that there is an accumulation of water at the surface of the soil due to condensation. Because, if you consider the force of soil grains hasindividual capillaries you have a number of capillaries attached here which lowers thevapor pressure above this and eventually there is a condensation that takes place at lower vapor pressure which causes accumulation of water at the surface, because of the potential difference from the top surface and the bottom surface there is a diffusion that takes place and water slowly penetrates into the deeper layer of the soil.So, this happens in any type of soil but clays generally the pore size is very small, so therefore easily the condensation takes place and more water will get accumulated. So,the vapor pressure lowering depends on the capillary size, so here in this particular case Kelvin’s equation a simple capillary tube is assumed. Therefore, the pressure drop across the water interface is 2 T s by r surface tension times 2 by the radius of the capillary tube. So, capillary tube diameter or the radius is very important in controlling the vapor pressure and condensation so this is called capillary condensation. This is a very important concept in soil mechanics because this concept is also utilized in the estimation of the specific surface area of fine-grained soil such as Carnuts and other clays not expensive clays like Bentonite etcetera. Because Bentonite generally they have dual porosity system and you have smaller pore fractions that exist this generally used for only for Carnot clays using adsorption isotherms. So, you take a soil sample and you expose the soil sample to a particular temperature and then relative humidity and absorption of. So you would expect that there is an absorption of water molecules around the clay surface and the exchangeable Cations because of the hydration there is waterthat accumulates. So, you would see that the adsorption increases with time for a given RH, and also it increases the adsorption amount of adsorption also increases with an increase in the RH, so using this concept the specific surface area is estimated.
Video 2
Video 3
The water retention curve is a terminology used in water resources and soil chemistry, in agriculture, etc. So, whereas the soil-water characteristic curve is a terminology used in soil mechanics geotechnical engineering. So, the soil water characteristic or waterretention curve is an important constitutive relationship of unsaturated soils, which is a psi versus water content here I am writing gravimetric. But generally, we use volumetric water content I will explain why in a bit very soon, which forms a very important constitutive relationship unsaturated soil mechanics forunderstanding the flow behavior or for understanding the shear strength of the soils or volume change, etc, this constitution relationship is very important this is central to the entire soil mechanics. So, let us try to understand how this suction and water content are related. If you consider the simple capillary the single capillary tube initially the water may be completely filled or slightly it may have some meniscus due to the interaction between the water molecules and the capillary tube. So, the adhesive forces woulddictate what is an angle that would that it would have it may 90 degrees or it may be less than that. So, when there is continuous evaporation of water that is taking place, so as there is goodinteraction between the water molecules of the pore fluid and the wall surface a good adhesive forces that exist, so water cannot leave even though there is evaporation that takes place or the energy is applied. So, it changes the curvature of the meniscus so thatsome water can be taken out. So, without losing the interaction between the wall surface and the water phase it loses some water molecules some water, so which is negligible. So, there is a point one initial state and there is a 0.2 that is a state here. So further if you wait for some more time or further energy is given, so the energy that is given is indicated with the suction there is negative pore water. As we have seen earlier that if you consider soil column immersed in a water reservoir you would see that there is a rise of water or water content is increasing, but the water pressure within the soil mass above this level is negative, so water pressure is negative this is less than the atmospheric pressure. So, therefore, there is a negative pressure due to the potential drop, so therefore this is the potential that is increased. So, the evaporation is taking place because it is likesuction you are taking a thin straw and keeping it in a juice glass of juice and sucking you are applying energy and then sucking it. When you are sucking this is what is happening water is lost because of the sucking action that is this is a suction pressure or simply the suction negative pore water pressure, which creates a negative pore waterpressure initially. There is no water pressure inside here you would see that there is a pressure that is build up because, u a minus u w if you see here there is a negative pressure that a that is developed here, this is the atmospheric pressure this is the water pressure is lower than atmospheric pressure. If you consider gas pressure the water pressure is negative that is what is indicated here if this is 0 then the minus u w is plotted here. So, the new w is negative here within the water column, so if you increase the suction further or more water is lost. So, then there is a change of contact angle from earlier angle to the new angle, and further water is lost when the curvature of the meniscus increases, there is more water pressure inside more negative pressure within the column so water pressure here is increasing. So, here this is a water pressure corresponding to the second figure and this is a water pressure corresponding to the third figure and beyond that with a small change in the suction, you would see that the with the same angle the water drops drastically and this particular point is called receding angle theta r. So, therefore, one water is slowly lost from the column of water due to the evaporation. You would see that there is a build-up of negative pressure within the water because there is a concave meniscus that is developed and because of that there is negativepressure and more water is lost u w here increases or more negative pressure that is built up within the system within the soil within the water and beyond that, the water simply decreases by decreasing it is level within the capillary. So, this particular point is also called air entry value, air entry value, or air entry suction the suction corresponding to this particular point is called air entry value or air entry suction. So, because until then the air enters into the system but here air has entered. So, we have air here so you have air here so this is called the air entry value. So, that was the most idealized system where you have a single capillary, but when it comes to the soils you have a network of pores that can be idealized as a capillary network like this. So, you have one capillary which is larger capillary here so you have thick capillary here and there is a thin capillary here, there is a thickest and this is the thinnest capillary and in between, you have these 2 capillaries. If you take such a system where the water is completely present in the capillary, so initially the entire capillarynetwork is completely full of water. So, therefore, here we plotted with respect to the volume of water earlier and again we are plotting with respect to the volume of water per total volume of pore space. If you plot and which is we hear x-axis is plotted with respect to the suction are the negative pore water pressure in log scale, then you would see that initially, the suction would be 0because this is flat. So, this is flat so u a is equal to u w or u a minus u w is cos 90 is 0, sou a is equal to u w or u a minus u w is 0 so the suction is 0. So, however, that particular point cannot be pointed because it is a log scale, but a small value if you consider and the corresponding value is equal to 1 this cannot this could be 1 only at you have u w is u a or u a minus u w is 0. But he because it is a log scale that cannot be represented here this cannot be1 this could be small value here. So, when there is evaporation that is taking place because we have seen that the pressure drop across the air-water interface is inversely proportional to the radius of the capillary tube. So, the pressure drop in the larger capillary tube or the thicker capillary tube would be smaller, therefore water will be lost first from the larger capillary tube and followed by this tube and followed by this tube. So, as they approach the receding angles corresponding to the receding angles the water beyond that it drops and this is the point this particular point, say, water drops beyond this particular point. So, this is this particular point corresponding to the air entry value and beyond that, the water content decreases drastically and when or after some time you would see that all other capillary tubes would be empty, but thinnest capillary still contains some water so that water is remaining here and even some more suction is applied or some more negative pore water pressure is developed then also you havesmall water. So, this is the relationship that is shown between water content or volume of water park total volume, so this is nothing but theta. So, this volume of water part total volume is theta with respect to u a minus u w or if you consider gas pressure, then it is simplyminus u w in log scale this is considered this is a unique relationship for a given material. So, if you consider a soil column in a water reservoir, so then you would see that there is a rise of water or the water content of the soil mass increases with time water contentdecreases with depth. So, you would see that there is up to here the water content within the soil mass will be equals to the saturated water content. So, here in case if you consider volumetric water and this volume of water by total volume. So, this is a nothing but porosity times porosity is the volume of voids by total volume times Sr is volume of water by volume of voids. So, this is n Sr so when degree of saturation is 1 that is fully saturated case equals to porosity and interestingly beyond that also up to some particulardepth the water content equals to the porosity or Sr equals to 1 degree of saturation equals to one up to the second depth Beyond that the water content decreases from theta, so let us understand why this particular soil mass can be idealized as a number of capillary tubes. So, this is 1 capillary tube this is a bigger capillary tube this is another capillary tube, so this is a thinnest capillary tube this is a widest capillary tube and this is in between. So, if this is immersed in a water reservoir, so then you would see that the capillary raise would be smallest in this particular capillary tube and highest in the thinnest 1 you would see that capillary rise is would be highest in the thinnest capillary tube and this would be medium. So, this the condition when you have 3 capillary tubes together when they are immersed in a water reservoir so this is a condition. So here if you see at this particular section atthe free water surface level you would see that the water content within this pore space or the capillary tubes water content is completely full. So, this is fully saturated capillary tubes in this particular case. So, if you consider the volume of the capillary tubes at this particular section is equal to the volume of water. If you ignore the surface of the capillary tubes or walls of the capillary tubes, so above this up to a particular depth, at this particular level where the capillary rise into the larger pore larger capillary tube. Here also it is the same volume of the capillaries equals the volume of water, beyond that if you consider any section the volume is less than the volume of water. So, up to this particular depth, the water content remains the same as below this level also, below the free surface also water content how much you have the same water content you have here.So, similarly here also the water content in this particular zone will be the same as the water current in this particular zone. So, therefore, this is called air entry suction head, air entry suction head is the point corresponding to the suction where air enters into thelargest pores of the soil sample. So, here if you consist if you consider this whole soil mass consists of only 3 capillary tubes, so then the air enters into the largest capillary tube here so that is air entry. So, here this air entry head which can be h AEV is equal tois nothing but the suction corresponding to suction corresponding to the soil-water characteristic on a which is on the saltwater characteristic of. The suction corresponding to which the air enters into the largest pore of the soil system is called the air entry section, so beyond that thinnest pore still has some water. So, water content here is less than theta s here theta equals theta s. So, if you plot the water content versus the suction head because the negative pore-water pressure the pore water pressure within the soil mass if you see that is positive downward and the negative upward. So, with an increase in the depth, the water content, if you see water content depletes like this. So, at some particular depth beyond particular depth, this is completely dry water content is 0, so this particular height is capillary height capillary rise h c in the soil mass. So, if you consider the soil mass a one pore structure, if you consider saturated state thisis the condition of the water phase within the soil mass where you have nearly flatmeniscus. So, the point corresponds to degree of saturation versus suction is here as thesuction, here it is written matric suction, matric suction here is nothing but u a minus uw. So, the matric suction that corresponding matric suction is a close to 0, but this is logscale so this cannot be 0 this is a very small value, here it is a small value as a suctionincreases to one particular value.
Video 4