Impingement-sheet mixing of liquids at unequal flow rates

Abstract

Mixing of liquids by the impingement of two, thin sheets at unequal flow rates was studied using competitive, consecutive azo couplings that provide quantitative information about the micromixing. Liquid flow rate ratios of 6.0 and 12.0 were investigated at total flow rates ranging from 13–45 l min −1. An expression for the energy dissipation rate in the impingement zone resulting from the inelastic collision was derived from the momentum balance and the geometry of the impinging sheets. For the experimental data, energy dissipation rates were calculated to lie in the range 6 900–97 500 W kg −1. The major parameters affecting the micromixing rate of unequal, impinging sheets are the energy dissipation rate in the impingement zone (ε i) and the volumetric flow rate ratio (α). Previously, the micromixing results for equal, impinging sheets were explained by a simple model assuming diffusion of the reactants within slabs of fixed thickness equal to the Kolmogorov microscale. Attempts to fit the experimental data for unequal, impinging sheets to a similar model, modified to account for volumetric flow rate ratio, resulted in a relatively poor correlation of the experimental results. However, a modification of the mixing modulus, to account for the effects of α on the diffusion length, yielded a reasonable correlation of the experimental data for unequal, impinging sheets to the model for equal, impinging sheets. Consequently, an expression was derived that relates the micromixing time for both equal and unequal, impinging sheets to α and ε i.