2.1. Fick’s Law of Diffusion

The term jA, we had discussed that this is defined by Fick’s law of diffusion.

jA = -D (∂C/∂z)

This is very well studied, but it has the same form as what we had discussed last classes, potential difference versus resistance.

Fick's law of diffusion describes how substances move from areas of higher concentration to areas of lower concentration. The formula jA = -D (∂C/∂z) indicates that the flux (jA) of a substance is proportional to the negative gradient of concentration (∂C/∂z), with D being the diffusion coefficient. The negative sign indicates that diffusion occurs in the direction opposite to the concentration gradient, meaning substances move from high to low concentration.

Imagine placing a drop of dye in a glass of water. Initially, the dye is highly concentrated in one spot (high concentration), but over time, it spreads throughout the water (low concentration), creating an even mixture. This process occurs due to diffusion as described by Fick's Law.

Now, the signage is like this. You see this is negative sign. The negative sign is an indicator of the direction of the flux, so this depends on how you are defining the frame of reference of this thing.

In Fick's law, the negative sign indicates the direction of the particle movement, showing that particles move from an area of higher concentration to an area of lower concentration. The definition of the reference frame is important; if you define movement in one direction (for example, from z to z + Δz), the flux will be negative if the concentration is higher at z than at z + Δz. This emphasizes how critical it is to clearly define the frame of reference when considering flux.

Think of a crowd of people in a room. If everyone is moving toward the exits (higher concentration at entry points, lower towards the exits), you can define that movement. If you take the exits as your reference point, the movement is considered towards a lower concentration of people, illustrating how the direction of flux changes based on your reference point.

As we discussed D is the diffusion coefficient is the proportionality constant. But now people have figured out what the DA diffusion coefficient is a function of?

The diffusion coefficient D is crucial for determining how quickly substances diffuse. It varies based on several factors, including the density of the medium, temperature, and the size of the molecules involved. Higher temperatures generally increase molecular motion, thus increasing diffusion rates, while larger molecules encounter more resistance, slowing down diffusion.

Consider the difference in how quickly a drop of food coloring disperses in hot water compared to cold water. In hot water (higher temperature), the diffusion coefficient is higher, and the color disperses rapidly. However, in cold water, the diffusion coefficient is lower, resulting in slower spreading of the dye. Similarly, a large lump of sugar dissolves more slowly than sugar granules due to the difference in molecular size.

In the case for environmental purposes, D is measured through air and water. These are the two fluids that we are interested in.

For environmental assessments, researchers often measure the diffusion coefficient D in two key mediums: air and water. Understanding how different substances move through these environments helps assess pollutant behaviors. There are also established correlations to predict D based on known diffusion coefficients of similar substances, taking into account factors like molecular weight.

Think of pollutants releasing into a river. Knowing the diffusion coefficients of similar contaminants in water helps researchers predict how fast a new one will spread. If a specific chemical has a known diffusion rate in water, scientists can estimate how quickly a similar pollutant will disperse based on its molecular weight and structure.

Flux is higher if resistance is low, and when considering convection versus diffusion, the flux increases with convection.

In the context of diffusion, 'resistance' refers to barriers that hinder the movement of particles. Lowering resistance, such as through increasing fluid motion (convection), enhances the diffusion flux, making mass transfer more efficient. Conversely, if only diffusion is present without any convection, the resistance is higher, and the flux is reduced.

Imagine mixing a salad dressing of oil and vinegar. If you shake the bottle (convection), the ingredients mix quickly and easily (lower resistance). However, if you just let them sit together, they separate and mix much more slowly (higher resistance). This illustrates how mixing enhances diffusion rates by reducing barriers.

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