PROPERTIES OF EXACT AND APPROXIMATE TRAVELING-WAVE SOLUTIONS FOR TRANSPORT WITH NONLINEAR AND NONEQUILIBRIUM SORPTION

Nonlinear sorption leads to the existence of moving concentration fron ts of substances transported in porous media that do not change shape. The cause for the existence of such traveling wave fronts is a balanc e between the self-sharpening effect of nonlinear sorption and the spr eading effects of dispersion and sorption kinetics. While analytical s olutions for the transport of nonlinearly sorbing substances are usual ly not available, the asymptotic front speed and the shape of travelin g waves can in some situations be determined analytically. This is don e by deriving a traveling wave equation in a moving coordinate system. In the case of simultaneous linear equilibrium and nonlinear nonequil ibrium sorption, this traveling wave equation is a second-order differ ential equation. Because this equation cannot be solved analytically f or typical nonlinear sorption isotherms, the second-order term is usua lly neglected. In this paper the significance of the second-order term is discussed for a simple piecewise linear sorption isotherm that all ows the analytical solution of both the full and the simplified differ ential equations. These analytical solutions make it possible to calcu late the approximation error as a function of how and isotherm paramet ers and thus to localize domains where the error may be significant. I n addition, the analytical solutions are used to discuss the identifia bility of model parameters from asymptotic front shape data.