Bed of polydisperse viscous spherical drops under thermocapillary effects

Viscous flow past an ensemble of polydisperse spherical drops is investigated under thermocapillary effects. We assume that the collection of spherical drops behaves as a porous media and estimates the hydrodynamic interactions analytically via the so- called cell model that is defined around a specific representative particle. In this method, the hydrodynamic interactions are assumed to be accounted by suitable boundary conditions on a fictitious fluid envelope surrounding the representative particle. The force calculated on this representative particle will then be extended to a bed of spherical drops visualized as a Darcy porous bed. Thus, the “effective bed permeability” of such a porous bed will be computed as a function of various parameters and then will be compared with Carman–Kozeny relation. We use cell model approach to a packed bed of spherical drops of uniform size (monodisperse spherical drops) and then extend the work for a packed bed of polydisperse spherical drops, for a specific parameters. Our results show a good agreement with the Carman–Kozeny relation for the case of monodisperse spherical drops. The prediction of overall bed permeability using our present model agrees well with the Carman–Kozeny relation when the packing size distribution is narrow, whereas a small deviation can be noted when the size distribution becomes broader.