Low Reynold’s number interactions of droplets of different viscosities

This project is concerned with the gravity-induced interaction/coalescence of a droplet of viscosity μ1 with another droplet of viscosity μ2 in a bulk fluid of viscosity μ3 with the motivating application being the flotation of oil droplets suspended in water by attachment to microbubbles. The specific questions which are to be investigated are:

Q1: What are the modes of interaction for the gravity-induced coalescence of two droplets of differing physical properties, and how do the various coalescence regimes depend on the relevant governing parameters. This question is specifically concerned with identifying regimes where the two coalescing droplets can be modelled as interacting spheres, and regimes where deformation strongly influences the coalescence process.

Q2: What is the coalescence time for the gravity-induced coalescence of two droplets of differing physical properties, and how does this depend on the relevant governing parameters. This question will examine how interparticle forces (Van der Waals forces and electrostatic forces) compete with hydrodynamic forces in order to determine the time required to drain away the external fluid between two coalescing droplets.

Q3: How can an understanding of the gravity-induced coalescence of two droplets of differing physical properties lead to an improvement in the efficiency of the flotation of oil droplets. Answers to questions Q1 and Q2 will provide valuable insight in to how flotation of oil droplets can be improved. Can flotation be enhanced by controlling the sizes of the bubbles and or droplets? Can flotation be improved by controlling the turbulence levels in the flotation tank? How can flotation be improved by changing the chemical properties of the system and the resulting interparticle forces.