The Combined Effects of Gravitational and Thermocapillary Driving Forces on the Interactions of Slightly Deformable, Surfactant - Free Drops

By an asymptotic approach previously employed for gravitational or thermocapillary motion alone, collision efficiencies are calculated for slightly deformable drops in combined gravitational and thermocapillary motion with negligible inertia and thermal convection. The constant imposed temperature gradient may be aligned with gravity in either the same or opposite direction. In the dimensionless parameter space, deformation becomes important at a smaller drop size ratio when the temperature gradient and gravity are aligned in the same direction, because the driving force is larger and induces dimple formation earlier. For the same reason, in a physical system of ethyl salicylate (ES) drops in an unbounded matrix of diethylene glycol (DEG), deformation becomes important for smaller drops when the driving forces have a parallel, rather than anti-parallel, arrangement. In developing the population dynamics for slightly deformable drops, a new, simplified expression for the collision efficiency for spherical drops in the absence of van der Waals forces is presented, which successfully separates the contributions of the two driving forces. Two collision-forbidden regions can occur for opposed driving forces leading to a shark-fin shaped collision efficiency curve for two slightly deformable drops. As shown in population dynamics, if the drop distribution is broad enough, it is possible for drops to jump the first collision-forbidden region.