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 Details A.Diffusion F = -D dc dx F = mass flux of solute per unit area per unit time D = diffusion coefficient (area per time) dc = concentration gradient (mass/volume/ dxdistance) Fick’s Law

II. The Finer Details A.Diffusion B.Advection V x = K dh n e dl

II. The Finer Details A.Diffusion B.Advection C.Mechanical Dispersion D m = a L v L where a L = 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 Details A.Diffusion B.Advection C.Mechanical Dispersion 1) Longitudinal 2) Transverse D. Hydrodynamic Dispersion “hard to separate diffusion and mechanical dispersion”

D. Hydrodynamic Dispersion “hard to separate diffusion and mechanical dispersion” D L = a L v L + D* where D L = hydrodynamic dispersion a L = dynamic dispersivity v L = average linear velocity D*= molecular diffusion where D* = (D x n) / (tortuosity) 2

II. Action !!! dC = D L d 2 C - v x dC dt dx 2 dx Dispersion and Diffusion “Pure” Advection

Continuous source…..

(one time source) “A slug” Continuous source…..

II. The Finer Details A.Diffusion B.Advection C.Mechanical Dispersion 1) Longitudinal 2) Transverse D. Hydrodynamic Dispersion E. Retardation