2.2. Bulk Flow

The flux of any species A generally is the combination of velocity and the concentration.

So if you are looking at the concentration, we call it as j, so, i is 1, 2 for air or water okay plus j.

A

j = v * c + j_A

where j_A is the molecular diffusion term. The term v * c represents bulk flow, meaning there is a velocity that is carrying concentration from one point to another.

Flux refers to the rate at which a substance crosses a unit area. In this context, it arises from two key components: velocity (v) and concentration (c). The combination of velocity carrying a specific concentration and the molecular diffusion leads to the overall flux of a species. The molecular diffusion term (j_A) addresses the movement of particles from areas of high concentration to areas of low concentration, while the bulk flow term reflects the effect of movement due to velocity.

Imagine a river carrying leaves down its current. The leaves represent a species, and their movement downstream is a result of the river's velocity, similar to how bulk flow operates. Meanwhile, if you drop a few leaves on still water (where there is no bulk flow), their movement might occur slowly through diffusion as they spread out.

Bulk flow essentially means there is a velocity that is carrying the concentration wherever it is from one point to another point.

The velocity bulk flow is also called advection. Sometimes, people use advection also as a representation of bulk flow, which means there is a flow and the main mechanism of mass transfer is flow, material being carried by flow.

Bulk flow is characterized by the velocity at which a substance is transported, which plays a significant role in mass transfer. This flow is often referred to as advection, indicating that the main means of transporting material is through a flowing medium, like water or air. In many environmental scenarios, advection is the dominant mechanism when a significant flow exists, overshadowing the effects of molecular diffusion.

Consider how a strong wind can carry pollen from one area to another. The movement of pollen through the air is akin to advection, where the wind acts as the flowing medium, transporting the pollen quickly compared to how it would spread if left to diffuse on its own.

There are certain scenarios where the bulk flow is negligible or advection is negligible, which implies that the flux is primarily due to molecular diffusion.

a) v * c ≈ 0 ⇒ j = j_A, bulk flow or advection is negligible.

b) v * c >> j_A ⇒ j = v * c, molecular diffusion is negligible.

In certain environmental circumstances, the influence of bulk flow may be minimal, leading to a situation where the movement of substances is primarily due to molecular diffusion alone. In the first case, where v * c approaches zero, the only movement is from diffusion, while in the opposite scenario, where bulk flow is significantly larger than diffusion, the latter can be ignored. These two scenarios help in understanding when to consider advection versus diffusion in various environmental systems.

Picture a calm pond where leaves float on the surface without any significant current. Here, the way leaves disperse is driven entirely by diffusion, as opposed to a river where a strong current would carry leaves downstream, illustrating scenarios of negligible bulk flow versus significant advection.

In systems like rivers where there is a flow, the assumption that bulk flow is greater than diffusion is most often true. Conversely, in lakes or undisturbed bodies of water, especially in deeper areas, diffusion may play a more significant role due to minimal flow and varying mixing conditions.

Different environmental systems exhibit varying dynamics of bulk flow and molecular diffusion. In flowing systems like rivers, bulk flow typically dominates because the current facilitates rapid transportation of materials. In contrast, lakes, particularly in deeper regions, might experience limited flow, allowing diffusion to act as the primary mechanism for mass transfer, especially when it comes to the mixing of chemicals or pollutants.

Think of a lake with a deep, still section versus a flowing river. In the river, you can see leaves and debris carried swiftly downstream – that’s bulk flow at work. However, in the quiet, deep part of a lake, pollutants or chemicals released into the water might take much longer to diffuse through the still water, demonstrating how diffusion can dominate in such environments.

--