Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions

Abstract

Deformation due to hydrodynamic interactions between two deformable buoyant drops may result in the alignment and coalescence of horizontally offset drops. Three-dimensional boundary integral calculations are presented for systems containing two, three or four drops and it is argued that the interactions which occur between three drops or four drops may be characterized qualitatively by the two-drop interactions. In a dilute monodisperse suspension, the rate of coalescence of deformable drops is calculated using far-field analytical results and is found to be proportional to the Bond number. The rate of coalescence in a dilute polydisperse suspension of bubbles in corn syrup is determined by performing a large number of laboratory experiments for Bond numbers based on the larger bubble radius 15 < [Bscr ] < 120. The rate of coalescence is enhanced (by a factor of 10 for [Bscr ] = 10), owing to the effects of deformation, compared to the predictions of models which include hydrodynamic interactions and van der Waals forces among spherical bubbles. The rate of coalescence is greater than the rate predicted by the Smoluchowski model which ignores all hydrodynamic interactions. The experimental results are used to calculate the evolution of the bubble size distribution in suspensions using a standard one-dimensional population dynamics model; deformation affects the size distribution in suspensions, resulting in a wider range of bubble sizes.