The Taylor and hyperbolic models of unsteady longitudinal dispersion of a passive impurity in convection-diffusion processes (Q2761328)

The paper deals with nonstationary convection-diffusion equation for concentration of a passive admixture~\(c(R,t),\) \(\frac{\partial c}{\partial t} + (V\cdot\nabla)c = (\nabla\cdot D\cdot\nabla)c,\) where \(V\) is the velocity vector of the carrying medium, \(R\) is the radius vector of a point in space, and \(D\) is the tensor of diffusion coefficients. By means of an asymptotic method similar to Chapman-Enskog technique of kinetic gas theory or averaging Krylov-Bogolyubov technique of nonlinear mechanics, the author derives a nonstationary diffusion equation for impurity concentration averaged over the tube cross-section, obtained earlier by \textit{G. Taylor} from physical considerations [Proc. Roy. Soc. Lond. Ser. A, 219, No.~1137, 186-203 (1993)]. In the framework of asymptotic method, a recurrent system of equations is obtained for expansion terms of arbitrary order. The estimations are given for applicability of Taylor model for longitudinal dispersion, which refine the estimates established by Taylor.