Pore water fluxes and mass balance 

Solute transport:Fick’s first law of diffusion:

 

 Einstein equation (diffusive depth/time scale)

 x2 = 2Dt

Pore water profiles:Reaction

Advection Changing porosity, diffusivity

 

CF Dx

Diffusion only case

 

diffusive flux ( = J ) = - D dC/dz

 

"Fick's first law of diffusion"

 

Solutes diffuse from high concentration to low concentration (high and low activity), and the flux is proportional to the concentration gradient.

 

Diffusion only case

For diffusion in a porous medium (i.e., in pore water) the area occupied by sediment grains must be taken into account by factoring in the sediment porosity (), and by using a "bulk" diffusivity rather than the molecular diffusivity. So

J = - D(bulk) dC/dz

 

In pure water D (molecular) varies with solute chemistry, and with temperature.

For pore water, D (bulk) also takes into account the effects of electrical effects (electroneutrality), and sediment tortuosity ().

Porosity = total connected water volume (as fraction of bulk sediment volume)

Tortuosity a measure of diffusive path length relative to bulk length.

 The tortuosity effect is given by: 

D(bulk) = D(molec) / 2

Tortuosity can be detemirned empirically, by measuring the electrical resistivity of bulk sediment and sea water:

  2 = * F

where F is the "formation factor", the ratio of bulk sediment resistivity to pore water resistivity.

 Often, tortuosity is estimated using only porosity data, with an empirical relationship of the form:

  2 = ()(-n)

 where n is typically 1.5 or 2.

ConcentrationDe

pth (c

m)

0

5

10