Question

Using the diffusivity of the dye, calculate the time required for the dye to diffuse in water for both the laminar and the turbulent regimes. Comment on the difference between the two calculated diffusion times.

Answer 1

See explanation

Step-by-step explanation:

Let the dye and gel be denoted by species A and B respectively.

Express the dimensionless concentration change with respect to the initial concentration of species A, when diffusion coefficient is constant.

…… (1)

Here, surface concentration of species A is , initial concentration of species A is , diffusion coefficient of species A in species B is , depth is z, error function is , time is t, and concentration of species A with respect to depth and time is .

Substitute 0 for and re-arrange Equation (1).