Population Balance Modeling of Turbulent Mixing for Miscible Fluids

Blending one fluid into another by turbulent mixing is a fundamental operation in fluids engineering. Here we propose that population balance modeling of fragmentation-coalescence simulates the size distribution of dispersed fluid elements in turbulent mixing. The interfacial area between dispersed and bulk fluids controls the transfer of a scalar molecular property, for example, mass or heat, from the dispersed fluid elements. This interfacial area/volume ratio is proportional to a negative moment of the time-dependent size distribution. The mass transfer coefficient, in the form of a Damkohler number, is the single geometry- and state-dependent parameter that allows comparison with experimental data. The model results, easily realized by simple computations, are evaluated for batch and flow vessels.