Concentration of Caco3 in water flow on leaned flat surfaces with rain channels

[pomaranca]

Homework Statement

On flat, leaned, surfaces, there are channels (rillenkarren), which are made by dissolution by rainwater (http://mafija.fmf.uni-lj.si/seminar/files/2005_2006/rillenkarren.pdf - not very important). They are 2-3 cm wide and around 0.5 m long. The formation is not yet known.

Calculate how the concentration of calcium carbonate changes in the flow of the
rainwater while it slides in a narrow layer on the stone.

The homework is a part of basic mathematical physics course. So many simplifications have to be made and all the approximations have to be taken into account.
Partial differential equation don't count.

 

[Jhero]

Hello,

I am interested in understanding the formation of channels on flat, leaned surfaces, known as rillenkarren. These channels are created by the dissolution of calcium carbonate by rainwater, and are typically 2-3 cm wide and 0.5 m long. However, the mechanism of their formation is not yet fully understood.

To calculate the change in concentration of calcium carbonate in the flow of rainwater on a narrow layer of stone, we must first consider the various simplifications and approximations that need to be taken into account. Firstly, we can assume that the rainwater is flowing in a thin, narrow layer on the surface of the stone. This allows us to neglect any vertical variations in concentration and focus solely on the horizontal flow.

Next, we can assume that the concentration of calcium carbonate in the rainwater is constant and equal to the initial concentration. This is because the rainwater is constantly replenished and any changes in concentration due to dissolution will be negligible compared to the initial concentration.

We can also neglect any chemical reactions or other processes that may affect the concentration of calcium carbonate. This allows us to simplify the problem to a pure diffusion process, where the concentration of calcium carbonate is driven solely by the diffusion of the dissolved particles in the rainwater.

Using Fick's law of diffusion, we can then calculate the change in concentration over time in the flow of rainwater on the stone. However, since we are neglecting any vertical variations, we must also consider the thickness of the layer of rainwater on the stone. This will affect the diffusion coefficient and must be taken into account in our calculations.

In conclusion, while partial differential equations may not be necessary for this calculation, it is important to consider all simplifications and approximations in order to accurately understand the change in concentration of calcium carbonate in the flow of rainwater on a narrow layer of stone.