Formulation of electro-chemico-osmotic processes in soils

Electrokinetic techniques have been used for various purposes including consolidation of soils, dewatering of sludges, and hazardous waste remediation among others. Estimating the feasibility of employing electro-osmosis in a particular operation depends on the ability to predict the outcome under a variety of conditions. Predictions of this type are frequently facilitated by the use of a mathematical model designed to represent the physical system under consideration in a rigorous fashion. First, a review of fundamental aspects of electro-chemico-osmotic flow in soils is presented. Following a brief outline of previous studies, identification and quantification of the significant processes, and the construction of mathematical representations are given. This is achieved using an approach based on the macroscopic conservation of mass equations and the principle of a continuum, in contrast to an approach based on the irreversible thermodynamics of coupled flows. Special emphasis is given to coupling effects on transport processes. A complete model and associated boundary conditions are then obtained for electrokinetic processes in a compressible porous medium. The proposed model takes into consideration the migration of a contaminant plume in a flow field generated by an applied electric potential.Symbols a_v soil compressibility - A an entity - C_w mass fraction of water component in the water phase - C_s mass fraction of chemical component in the water phase - C^* capacitance of the porous medium per unit volume of porous volume - D mechanical dispersion coefficient - D_fw^ps hydrodynamic diffusion tensor for the chemical component in the water phase - D_fw^pw hydrodynamic dispersion coefficient for the water component in the water phase - D_f( )/Dt material derivative with respect to an observer moving at the water phase velocity V_f - D_s( )/Dt material derivative with respect to moving solids - e void ratio - f a function - F = 0 equation of a moving boundary - g gravitational acceleration - k permeability tensor of the porous medium - k_e coefficient of electro-osmotic permeability - k_ec coefficient of migration potential - k_hc chemico-osmotic coupling coefficient - m_i number of moles of the ith component - m_i0 number of moles of the ith component at a reference level - n porosity - p pore pressure - p_oi pore pressure at a reverence level - q specific discharge of water phase - q_e current density - q_fe^p0 constant current density applied at a boundary - q₀ constant flow rate - q_r specific discharge of the water phase relative to the moving solid matrix - R net mass transfer rate of the chemical component in the water phase - t time - u velocity of a moving surface - _i partial molar density of ith component - V_f velocity of the water phase - V_s velocity of the solid (rate of deformation) - x vertical coordinate - coefficient of matrix compressibility - _p compressibility of water phase in motion - total (overburden) stress tensor - effective stress tensor - _h streaming current conductivity - _e electrical conductivity - electrical potential - _f viscosity of the water phase - _hf density of the water phase