MIXING WITH DIFFUSION AND FAST CHEMICAL REACTION IN SIMPLE SHEAR FLOW: A COMPARISON OF STRETCH MODEL TO TWO-DIMENSIONAL DIFFUSION WITH PERIODIC BOUNDARY CONDITIONS

Abstract

The lamellar stretch model for describing mixing with simultaneous diffusion and fast chemical reaction is evaluated for simple shear flow between two parallel plates by comparing the predicted concentration profiles to those computed from the governing partial differential equation. A direct algorithm is devised to solve the sparse matrix originating from the discretization of the PDE. Under conditions where initial striation thickness equals the characteristic dimension of the flow geometry, the lamellar stretch model turns out to be quite accurate for k ≥ 106 or k ≤ 1, where k is the product of the Reynolds number and the Schmidt number. In the intermediate range of k values, where mechanical and diffusional mixing are of comparable importance, the model is less accurate