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Keywords:

  • reactive mixing;
  • Damkohler number;
  • batch reactor;
  • fragmentation;
  • coalescence

Abstract

Reactive mixing in liquids can be quantitatively described by combining chemical kinetics and hydrodynamics so that dispersed reactants interact at evolving fluid–element interfaces. For the batch reactor we postulate that the dispersed fluid elements are fragmented in a cascade of increasingly smaller sizes and larger interfacial area. The reversible fragmentation–coalescence is described by a population dynamics equation that has an exact self-similar solution for the size distribution as a function of time. Two types of competitive reaction kinetics incorporating a diffusion-limited fast reaction satisfy nonlinear differential equations, written in terms of moments of the time-dependent dispersed-fluid size distribution. Applying a compressed time variable to transform to a simple system of differential equations readily solves the nonlinear equations. The straightforward solutions display realistic effects of dispersed fluid volume fraction, rate parameters, and initial concentrations. Final fractional conversions, occurring when the limiting reactant is depleted, are functions of a Damkohler number, volume fraction of dispersed reactant, and scaled initial conditions. © 2004 American Institute of Chemical Engineers AIChE J, 50: 835–847, 2004