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A Semianalytical Analysis of Compressible Electrophoretic Cake Formation
Author(s) -
Kambham Kiran K. R.,
Tuncay Kagan,
Corapcioglu M. Yavuz
Publication year - 1995
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/95wr00143
Subject(s) - settling , electrokinetic phenomena , consolidation (business) , mechanics , geotechnical engineering , void ratio , compressibility , suspension (topology) , geology , materials science , mathematics , thermodynamics , physics , accounting , homotopy , pure mathematics , business , nanotechnology
Leaks in geomembrane liners of waste landfills and liquid impoundments cause chemical contaminants to leak into the subsurface environment. A mathematical model is presented to simulate electrophoretic sealing of impoundment leaks. The model describes the formation of a compressible clay cake because of electrical and gravitational forces. The model includes mass balance equations for the solid particles and liquid phase, modified Darcy's law in an electrical field, and Terzaghi's definition of effective stress. The formulation is presented in the Eulerian coordinates. The resulting second‐order, nonlinear partial differential equation and the lower boundary condition are linearized to obtain an analytical solution for time‐dependent settlement. After discretizing in time the analytical solution is applied to simulate compression of an accreting sediment. In the simulation of an accreting sediment, solid fluxes on either side of suspension/sediment interface are coupled using a no‐jump condition. The velocity of a discrete particle in the suspension zone is assumed to be equal to the algebraic sum of electrophoretic and Stoke's settling velocities. An empirical relationship available in the literature is used to account for the effect of concentration on the velocity of solid particles in the suspension zone. The validity of the semianalytical approach is partially verified using an exact steady state solution for self‐weight consolidation. The simulation results obtained for a set of material parameters are presented graphically. It is noted that the electrokinetic consolidation of sediment continues even after the completion of electrophoretic settling of all clay particles. An analysis reveals that the electrophoretic cake formation process is quite sensitive to voltage gradient and the coefficient of compressibility.