Editing Library of analytic solutions (under construction)
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Governing equation for single aqueous solute, with sorption: | Governing equation for single aqueous solute, with sorption: | ||
− | <math>\frac{ \partial \ | + | <math>\frac{ \partial \thetaC}{\partial t}=-v(\mathbf{x})\theta\nabla C+\nabla \cdot (\mathbf{\theta D(\mathbf{x})} \nabla C) - R(C) -\frac{\rho_b}{\theta}\frac{\partial q}{\partial t}</math> |
Where <math>C</math> and <math>q</math> are the aqueous and sorbed concentrations of the solute, respectively, <math>v(\mathbf{x})</math> is the velocity vector, <math>\mathbf{D(\mathbf{x})}</math> is the dispersion tensor, <math>R(C)</math> is a general reaction term, <math>\rho_b</math> is the bulk dry density of the porous media, and <math>\theta</math> is the porosity of the media. | Where <math>C</math> and <math>q</math> are the aqueous and sorbed concentrations of the solute, respectively, <math>v(\mathbf{x})</math> is the velocity vector, <math>\mathbf{D(\mathbf{x})}</math> is the dispersion tensor, <math>R(C)</math> is a general reaction term, <math>\rho_b</math> is the bulk dry density of the porous media, and <math>\theta</math> is the porosity of the media. | ||
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Where <math>\lambda </math> is the first-order decay constant and <math>\gamma</math> is a zeroth-order growth term. This equation is linear with constant coefficients, and thus amenable to analytical solution using a wide variety of methods. | Where <math>\lambda </math> is the first-order decay constant and <math>\gamma</math> is a zeroth-order growth term. This equation is linear with constant coefficients, and thus amenable to analytical solution using a wide variety of methods. | ||
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= Density flow (interface)= | = Density flow (interface)= |