Equivalent Diffusion in a Thin Film Flow with a Non-One-Dimensional Velocity Field and Anisotropic Diffusion Tensor

For describing the mass transfer processes in channels, Taylor's dispersion theory [1, 2] is widely used. This theory makes it possible, with asymptotic rigor, to replace the complete diffusion (heat conduction) equation with a convective term that depends on the coordinate transverse to the flow by an effective diffusion (dispersion) equation with constant coefficients, averaged over the channel cross-section. In numerous subsequent studies, Taylor's theory was generalized to include more complex situations, and novel algorithms for constructing the dispersion equations were proposed (see, for example, [3-8] where original methods of mass dispersion analysis were used). For thin film flows a theory similar to [1, 2] leads to a matrix of dispersion coefficients [9, 10]. In this study, Taylor's theory is extended to film flows with a non-one-dimensional velocity field and anisotropic diffusion tensor. These characteristics also depend to a considerable extent on the spatial coordinates and time. The dispersion equations obtained can be simplified in regions in which the effective diffusion coefficient tensor changes sharply.