mass transport of solutes

MASS TRANSPORT OF SOLUTES

I. Basic Processes

A. Diffusion

B. Advection

II. The Finer Details

A. Diffusion

F = -D dc

dx

Fick’s Law

II. The Finer DetailsA. Diffusion

F = -D dc dx

F = mass flux of solute per unit area per unit timeD = diffusion coefficient (area per time) dc = concentration gradient (mass/volume/ dx distance)

Fick’s Law

II. The Finer Details

A. Diffusion

B. Advection

Vx = K dh

ne dl

II. The Finer Details

A. Diffusion

B. Advection

C. Mechanical Dispersion

Dm = aL vL

where aL = dynamic dispersivity

(a function of the aquifer’s physical properties, and controls the degree of ‘spread’ of the material)

II. The Finer Details

A. Diffusion

B. Advection

C. Mechanical Dispersion

1) Longitudinal

2) Transverse

Longitudinal

Transverse

II. The Finer DetailsA. DiffusionB. AdvectionC. Mechanical Dispersion

1) Longitudinal2) Transverse

D. Hydrodynamic Dispersion“hard to separate diffusion and mechanical dispersion”

D. Hydrodynamic Dispersion“hard to separate diffusion and mechanical dispersion”

DL = aL vL+ D*

where

DL = hydrodynamic dispersion

aL = dynamic dispersivity

vL = average linear velocity

D*= molecular diffusionwhere D* = (D x n) / (tortuosity)2

II. Action !!!

dC = DL d2C - vx dC

dt dx2 dx

Dispersion and Diffusion

“Pure”Advection

Continuous source…..

(one time source) “A slug”

Continuous source…..

II. The Finer DetailsA. DiffusionB. AdvectionC. Mechanical Dispersion

1) Longitudinal2) Transverse

D. Hydrodynamic DispersionE. Retardation