2. Lecture 44 - Prof. Ravi Krishna

So, in the box model one of the things that we have we discussed is you know what will happen, the dispersion modeling was a slight departure from what we are doing in the box model. So, dispersion modeling is one subset of this, we are not exactly following the box model concept in its totality. We are using the box inside a plume and then we are integrating that, but here in box model we are using it as trying to calculate for the entire system here. So, one component of this is interface mass transfer, we will discuss that. We will discuss this exchange between interfaces. For this, we have to go and look at some fundamentals of mass transfer, okay.

In this introduction, Prof. Ravi Krishna explains two modeling approaches: box modeling and dispersion modeling. The box model is a simplified way to analyze an environmental system as a whole. On the other hand, dispersion modeling focuses on how substances spread within a specific region, like a plume. He mentions that while dispersion modeling is valuable, it does not completely follow the box model approach. Instead, they are using concepts from both to discuss interphase mass transfer, which involves the movement of substances across different phases (like air, water, and soil). Understanding the fundamentals of mass transfer is crucial for analyzing these phenomena.

Think of box modeling like looking at a whole pizza, where each slice represents a different aspect of the environmental system. Dispersion modeling is like observing how the toppings move when the pizza is disturbed or jostled. Even though each approach looks at things differently, they are both essential in understanding the overall effect, much like how both the whole pizza and the movement of toppings tell you something about the pizza itself.

So let’s talk about mass transfer concepts fundamentals. We will talk a little bit about fundamentals, then we will look at the application where we are okay. So what we are really interested in finding out here is again this. So, if you take the example of the dispersion model, if you need to calculate the term Q, Q is the rate of release of a chemical A from a surface which has some chemical okay. So the surface could be a water, could be soil, could be anything okay.

In this part of the lecture, Prof. Krishna focuses on mass transfer concepts that are essential for understanding environmental processes. The term 'Q' represents the rate at which a chemical (like a pollutant) is released from a surface (such as water or soil) into the surrounding environment. Understanding how chemicals release and disperse is crucial for calculating their impact on ecosystems and human health.

Imagine you have a sponge soaked in water. When you press the sponge, water starts to seep out, much like how chemical A is released from a surface. The faster you press the sponge, the more water is released. In the same way, the rate of release of a chemical depends on various factors including the type of surface and the conditions of the environment.

For example, simple examples of this say we have water, we have air, and here we have an oil spill let us say we have an oil spill, okay. If you assume that the oil has a density, which is less than that of water. The density of the oil is less than that of water, it will float on water okay. When it floats on water, depending on the composition of the oil, some components will evaporate and some components will dissolve.

Professor Krishna uses the example of an oil spill to illustrate the processes involved in interphase mass transfer. Since oil is less dense than water, it floats when spilled. Components within the oil can either evaporate into the air or dissolve into the water, impacting the surrounding environment. This example highlights the need to calculate how much of the chemical is evaporating or dissolving over time to understand the spill’s environmental impact.

Think about spilling a cup of oil on a puddle of water. The oil sits on top and can evaporate into the air, creating an unpleasant smell, or it may mix partially with the water underneath. Understanding how this process works helps scientists predict the long-term effects of spills on aquatic life and water quality.

Another example of this is, I have a boat that is carrying a lot of chemical, there is sediment which is under water, we had discussed this. The density of the chemical is greater than that of water, then it will not float, it will sink. It will sink down to the ground. So if you are in a river, it will sink and it will occupy a region at the bottom on the bed of the sediment.

Prof. Krishna explains how a chemical with a greater density than water behaves differently when spilled. Instead of floating, it sinks to the bottom of a river, where it can spread over time. The presentation explores how this contamination can eventually interact with the environment and may even release back into the water later. This emphasizes that not all chemicals behave the same way in water and that time is a crucial factor in measuring their environmental effects.

Imagine dropping a heavy stone in a pond. Instead of floating, the stone sinks straight to the bottom, much like how a dense chemical behaves. When you visit the pond later, the stone has settled but might influence the water if it starts leaching into it. Similarly, the chemical might stay buried but can still affect the water quality and aquatic life over time.

So normally what would you do if you want to mix sugar, you want to dissolve sugar into water? What is your normal thing is to stir it. Why do you stir it? Why do you stir it? What is the purpose of stirring?

This section discusses the concept of mixing and molecular diffusion. Stirring is a common method to facilitate the dissolution of sugar into water, which speeds up the process. The professor emphasizes that even without stirring, the sugar would still dissolve, albeit much slower due to molecular diffusion, which is the natural movement of molecules from an area of higher concentration to one of lower concentration.

Consider the process of adding a drop of food coloring to a glass of water. If you don’t stir the water, the color will eventually spread throughout due to diffusion, but it will take much longer compared to just stirring it. This illustrates how molecular diffusion works even when we don’t actively help it along.

So, if you take Ohm’s law, this is a rate, this is the potential difference, this is the resistance, this is a universal law. You take some other law for a Bernoulli equation or something or Darcy's law, any such thing, all of them are the same format, rate equals potential difference divided by resistance okay.

Prof. Krishna draws a parallel between chemical potential and laws of physics, such as Ohm’s law. The rate of movement (or mass transfer) is influenced by the difference in chemical potential and the resistance encountered by the molecules as they move. This principle lends itself to understanding how chemicals transfer across different media in nature.

Think about how electricity flows through wires. The rate of flow depends on the voltage difference (potential) and resistance in the wire. Similarly, in mass transfer, chemicals move from areas of high potential (high concentration) to low potential (low concentration) depending on how much resistance there is in the environment, such as through soil or water.

--