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Pore water fluxes and mass balance Solute transport: Fick’s first law of diffusion: Einstein equation (diffusive depth/time scale) x 2 = 2Dt Pore water profiles: Reaction Advection  Changing porosity, diffusivity. Diffusion only case diffusive flux ( = J ) = - D dC/dz - PowerPoint PPT Presentation

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  • Pore water fluxes and mass balanceSolute transport:Ficks first law of diffusion:

    Einstein equation (diffusive depth/time scale)x2 = 2Dt

    Pore water profiles:ReactionAdvectionChanging porosity, diffusivity

  • 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. SoJ = - D(bulk) dC/dzIn 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.

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