Boundary layers and images in dispersed flow reactors: A green's function approach

Modelling of a dispersed flow reactor is formulated in terms of a Green's function in such a way that appropriate boundary conditions are incorporated from the outset. A method based on the method of images is used to determine this Green's function, and hence the distribution of substrate concentration within a reactor with any number of segments, for both stationary and evolutionary states. Using the new formulation, a quantitative explanation in terms of boundary layers is proposed for recent experimental observations of surprising discontinuities of steady concentration at internal boundaries between reactor segments with large diffusion coefficients. The same considerations account for the absence of backmixing at such interfaces. Detailed predictions of corresponding time-dependent phenomena are then given, so that future experiments can be brought to bear on current questions as to the validity of commonly used boundary conditions and of the governing equations themselves. The calculations leading to these predictions also serve to illustrate the computational advantages of the new method, as compared with methods using Laplace and related transformations.