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Kinetics and reactive mixing: Fragmentation and coalescence in turbulent fluids
Author(s) -
Madras Giridhar,
McCoy Benjamin J.
Publication year - 2004
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.10098
Subject(s) - damköhler numbers , coalescence (physics) , volume fraction , turbulence , thermodynamics , chemistry , nonlinear system , cascade , reaction rate , mixing (physics) , mechanics , statistical physics , physics , chromatography , biochemistry , quantum mechanics , astrobiology , catalysis
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