4.2. Incorporating Thermal Forces

So this is again the thing that we discussed in last class. When this kind of thing happens, moisture content in the soil is changing as a result emission will change. The partition constant is changing, this is changing. This experiment is done in the lab where it shows that there is a chemical called dibenzofuran and this is experimental data. When the mud is dry and this is the model, the blue line is the model that shows, and then at some point we dry the surface by sending in dry air, okay. So the water content increases. The water flux increases because it is now being dried and then the water increase and then everything is dry. During this period, you see that the flux drops down. The flux for the dry period is down here, dropped down several factors okay. Then again when you hit it with humid air, it goes back up here, okay. So this is illustration of this. When the partition constant changes, the flux changes, okay.

This chunk discusses how the moisture content in soil affects the flux and the partition constant, which quantifies how substances partition between phases. When the moisture level in the soil changes (e.g., due to drying with dry air), the flux—the rate of mass transfer—also changes. In the experiment mentioned, when the soil is dried, initially the water content and flux increase, but then the flux drops significantly during the drying phase. Finally, when humid air is introduced again, the flux increases. This demonstrates that as the soil conditions change, particularly moisture levels, both the partition constant and the mass flux are affected.

Think of a sponge that can soak up water. When the sponge is dry, it can absorb water quickly (high flux). As it soaks up water, it expands, making it harder for additional water to seep in, which reduces the rate of absorption (low flux). When you try to dry it out using dry air, the moisture content changes dramatically, leading to lower absorption rates. If you then blow humid air on the sponge, its ability to absorb water improves again, demonstrating the cycle of change.

When you have a surface and you have to measure the flux and it is difficult for you or it is unreliable for you to enclose a surface, you need to still measure the flux and we do it by what is called as a gradient technique or a micrometeorological technique. I am just going to talk a little bit about it, aerodynamic technique. It is also called as a gradient technique. So, for example, you can do this inside the sediment soil, right, I can take a gradient. If I know the concentration of pore vapor at if there is a difference, I can use = − .I can use solution of this equation to calculate what is the flux if I know the diffusion coefficient okay. Basically, I am using a gradient to calculate a flux, yeah.

This chunk describes how to measure the flux when enclosing a surface isn’t feasible. Researchers utilize gradient techniques, measuring concentration differences of pore vapor at different depths to determine flux. By applying a mathematical relationship that uses the difference in concentration and the diffusion coefficient, they can calculate the flux. This method is especially helpful in sediment or porous media.

Consider trying to measure how quickly a smell spreads through a room. Instead of enclosing the room, you might place scent-detecting devices at various points to observe how the scent concentration varies from one point to another. By understanding how the concentration changes across the room (the gradient), you can work out how quickly the scent is traveling (the flux).

What we are taking advantage of here is that we would like to see if there is a vertical component of the fluid that is going in the upward direction, Yes, this is convective mass transfer right. This is convective mass transfer and therefore we are trying to take advantage of the convective mass transfer component in the z direction to see what is the concentration difference and we will also see if we can somehow measure the net flux based on that concentration difference at a given location, okay.

This chunk explains the principle of convective mass transfer, where turbulent motions carry material upward. Researchers focus on the vertical component to understand how different concentrations are distributed within that flow. In particular, they measure concentration differences at various heights to infer the net flux that results from these convective currents.

Imagine a pot of soup on a stove. As it heats up, the hot liquid (representing fluid) rises to the top and cooler liquid moves down. This rising and sinking creates a current, much like how pollutants or moisture can move through the air or soil. If we wanted to measure how quickly spices dispersed through the soup, we could observe their concentration at different points to understand the overall flow of the ingredients (the flux) happening due to this convective movement.

In turbulent this things, the idea is that velocity has a gradient, we already know velocity has a gradient with height and the structure of this gradient is this form usually. It is a logarithmic relation vx is velocity in the x direction, is a function of z, but in this as a logarithmic function of z and the proportionality constant, this is called as v star, v star is called as the friction velocity okay.

This chunk introduces the concept of velocity gradients in turbulent flows, where the velocity varies with height. The velocity in the x-direction is related to height through a logarithmic function. The friction velocity (v*) is significant in this context, representing how the shear stress at the surface influences the flow above it. This relationship helps in understanding how rapidly air (or fluid) moves as a result of surface interactions.

Think of standing next to a busy highway. The closer you are to the road, the more you feel air moving past you from the cars. This is similar to how friction from the surface of the road affects air movement above it. The speed of that air (or velocity) isn’t constant; it changes with distance from the surface, creating a gradient that can be plotted logarithmically.

For that, there is something called as modified Thornwaite-Holzman equation. When you have thermal forces, you bring into this question. There is something called as a Monin-Obukhov length scale. This comes up there also, you can read, there is one page set of things I have put in your, if you are interested you can read it, and if you go and read AERMOD derivations, this morning Monin-Obukhov length scale comes there. This is Lm, this is physically the length scale at which the production of turbulence by buoyancy effects are of the same order of the shear stress.

In this chunk, the discussion moves to how thermal forces, such as those caused by temperature differences, affect measurements and calculations in mass transfer. The Monin-Obukhov length scale (Lm) is introduced as a crucial factor that indicates when buoyancy forces due to thermal effects are comparable to shear forces. This helps scientists understand the stability of the atmosphere and modifies existing equations to better account for thermal influences on flux.

Picture a hot air balloon. The hot air inside the balloon (which is warmer than the surrounding air) causes the balloon to rise due to buoyancy forces. Similarly, in the environment, when areas of air are heated by the sun, those warm areas can start rising, creating turbulence that affects how gases and particles move. Like the balloon, these forces can impact how materials, like pollutants or heat, disperse in the atmosphere.

Based on this, we define a bunch of other things. So we add a correction factor called as B, which is now dependent on the stability as well and this when we have a bunch of equations where we calculate B for different values of, in the equation previous slide, this number is dependent on z by Lm, z is any height, at any height it is the comparison of that height with the Lm.

As thermal forces are factored in, additional correction factors for the equations used to calculate mass flux are introduced. This correction factor (B) varies based on height and the Monin-Obukhov length scale, indicating how different atmospheric conditions influence measurements. By incorporating these corrections, researchers can obtain a more accurate representation of flux in environments influenced by thermal variations.

Imagine trying to measure how quickly smoke disperses from a chimney on a windy day. If it is calm, the smoke spreads evenly upwards, but if there is wind, it may be blown sideways or upwards rapidly. To get a true measure of how quickly the smoke disperses, you would need to adjust your calculations based on the conditions that day—just like how scientists adjust their equations based on the stability of air and thermal conditions.

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