6.1. Rate of Adsorption and Diffusion

So what we are doing? We do this normally in all box models kind of scenarios. We write again the mass balance in the sediment volume. This is delta x, delta y, delta z is the differential volume of the system. Now, here I can write other terms if I want to, yeah, I can write many things. Same as box model, I can write whatever is happening inside the system.

In sediment studies, we utilize mass balance equations to ensure all material entering and leaving a system is accounted for. This is similar to what we do in box models, where a defined volume (delta x, delta y, delta z) represents the system's boundaries. The mass balance allows us to analyze changes over time and understand how various components (like pollutants) interact in the sediment.

Think of a swimming pool – the water that enters and leaves the pool is akin to the mass in our sediment. Just like you have to account for water added from the hose and water removed by draining, we need to account for substances in sediments to understand their behavior over time.

So, the diffusion area is this, this is going into the system here, yeah, nothing wrong, so here this term here is diffusion. The overall accumulation is happening on the entire system, it is happening both in the fluid as well as the solid phase, that is not solid phase, C is only the fluid phase.

Here, we differentiate between two phases: the fluid phase (water) and the solid phase (sediments). The process of diffusion describes how materials move from areas of high concentration to low concentration. In our sediment model, we must account for how substances dissolve in water and also how they interact with solid particles, as this exchange dictates the concentration in the fluid phase.

Imagine making a cup of tea. When you add a tea bag to hot water, the tea particles diffuse into the water, creating a more flavorful liquid over time. This process parallels how pollutants diffuse into sediments and water in a natural system.

If you look at the case of soil, if you have unsaturated soil, some part of the pore space is filled with water and some of it is filled with air. So, this assumes that the diffusion is reduced because now for two reasons.

The effective diffusivity refers to how much a substance can diffuse through a porous medium — like soil — which contains both water and air. Since diffusion can be obstructed by solid particles, the effective diffusion rate is often lower than in a non-porous medium. This is due to both physical obstructions and the tortuosity of the pathways through which the molecules must move.

Consider trying to walk through a dense crowd vs. an empty hallway. In a crowded space (like soil packed with particles), your movement (similar to diffusion) is slower and more complicated than in a wide-open area, where you can move freely.

this we will invoke what is called as a local equilibrium assumption. These are all simplifications for what could be the real scenario what is happening in the system. Local equilibrium assumption assumes that when a solid is near a fluid, there are these chemicals that are sitting here and there is chemical here, the rate at which the diffusion is occurring is almost the same order of magnitude at which this adsorption is happening.

The local equilibrium assumption simplifies our models by suggesting that adsorption (the process where pollutants stick to surfaces) and diffusion (movement of pollutants) occur at comparable rates. This means that at any given point in the system, chemical interactions between the solid and fluid are balanced. In reality, this is a simplification but helps in creating functional models.

Think of a sponge submerged in water. If you hold it still for a moment, the water quickly diffuses into the sponge and the same time the water in the sponge can be absorbed or released back into the surrounding water. Here, the rates of absorption and diffusion reach a balance, just like in our local equilibrium assumption.

So, this term in the denominator is known as a retardation factor. If the chemical is highly adsorbing, the term becomes very big, which means it reduces the magnitude of diffusion, it retards diffusion.

The retardation factor is an important concept in understanding how pollutants behave in environments with solid materials. It reflects the relationship between adsorption and diffusion — when a material is adsorbed strongly to the solid, it lessens the speed at which it can diffuse away from that solid into the surrounding fluid. This means that highly adsorbing solids can slow down the spread of pollutants in environmental systems.

Imagine trying to run while carrying a heavy backpack. The weight of the backpack makes you slower, just like a high retardation factor slows the movement of pollutants. If the backpack were lighter (less adsorption), you could run faster (diffuse quicker).

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