Wave model for longitudinal dispersion: Application to the laminar‐flow tubular reactor
The wave model for longitudinal dispersion, published elsewhere as an alternative to the commonly used dispersed plug-flow model, is applied to the classic case of the laminar-flow tubular reactor. The results are compared in a wide range of situations to predictions by the dispersed plug-flow model as well as to exact numerical calculations with the 2-D model of the reactor and to other available methods. In many practical cases, the solutions of the wave model agree closely with the exact data. The wave model has a much wider region of validity than the dispersed plug-flow model, has a distinct physical background, and is easier to use for reactor calculations. This provides additional support to the theory developed elsewhere. The properties and the applicability of the wave model to situations with rapidly changing concentration fields are discussed. Constraints to be satisfied are established to use the new theory with confidence for arbitrary initial and boundary conditions.
Wave Concept in the Theory of Hydrodynamical Dispersion—a Maxwellian Type Approach
A new approach to the modelling of chemical reactors and contactors is discussed. This approach argues that the dispersion should, under most circumstances, be based on Maxwell's, rather than Fick's diffusion law. As a pair of first-order partial differential equations of the hyperbolic type and requiring only inlet conditions, the wave model is more realistic physically, has a much wider range of validity and in many practical cases is simpler mathematically. Only mass transfer problems are considered, but the results apply equally well to the hydrodynamic dispersion of heat. It is explained why the standard dispersion model fails in many practical applications and why the new wave model gives much better results.
Diffusion, convection and chemical reaction in a channel
Abstract For laminar flow between a flat conduit exact solutions of the problem of steady-state diffusion and convection are presented for constant wall concentration, constant flux across the wall and a heterogeneous chemical reaction of the first order. The initial conditions were considered to be arbitrary functions of the coordinate across the channel. The same was performed for the cases of simultaneous diffusion, convection and homogeneous chemical reaction for constant wall concentration and heterogeneous chemical reaction. The eigenvalues are presented in tables and the eigenfunctions are presented in analytical form, which contains the confluent hypergeometric function.