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A mathematical interpretation of diffusion processes with concentration-dependent diffusion coefficient

Authors:	K N Rai L Thakur

Institution:	(1) Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi, India

Abstract:	The integral balance method has been used to obtain an approximate analytical solution of a nonlinear boundary value problem which arises in the theory of diffusion with a concentration-dependent coefficient. It is the purpose of this paper to give an interpretation of the supposition of interface reactions which obey the law of kinetic mass action.Nomenclature C(Z,t) concentration - C ₀ concentration at initial time - D diffusivity - D ₀ diffusivity at initial time - F(t) a function of time - K ₀ half-order reaction rate constant - k ₁ first-order reaction rate constant - k ₂ second-order reaction rate constante - L characteristic length - n parameter - t time - Z space variable Dimensionless variables and similarity criteria $m_0 = \frac{{k_0 L^2 }}{{2D_0 \sqrt {C_0 } }}$ nondimensional half-order reaction rate constant - $m_1 = \frac{{k_1 L^2 }}{{D_0 }}$ nondimensional first-order reaction rate constant - $m_2 = \frac{{k_2 C_0 L^2 }}{{D_0 }}$ nondimensional second-order reaction rate constant - x=Z/L dimensionless space variable - F ₀=D ₀ t/L ² Fourier number - g(F ₀)=F(t)–C ₀]/C ₀ a function of generalized time - (x, F ₀)=C(x,t)–C ₀]/C ₀ dimensionless concentration - <(F ₀)> dimensionless average concentration

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