Boundary-integral method for drop deformation between parallel plates

A new boundary-integral method is proposed to study the deformation of drops between two parallel walls. The free-space Green's functions are extended to obey the no-slip condition at the walls. The current formulation is limited to drops with viscosity equal to the matrix fluid, but can be extended to study the effect of non-unit viscosity ratio systems. With this method the influence of the capillary number and the degree of confinement on drop deformation is investigated. Results for small capillary are compared with small-deformation theory and large capillary results with recent experiments. In both cases an excellent match is observed. Drops undergoing shear flow deform stronger and align themselves more in the flow direction as the distance between the walls becomes smaller relatively to the drop size. Furthermore, the shapes of the drops start to divert significantly from the normal ellipsoidal shapes found, as they show more pointed tips closer to the walls.The transient deformation behavior for more confined systems shows that the drops stretch out to a maximum value, and the slowly retract again to a steady situation. For larger capillary numbers even damped, oscillatory behavior is observed. Investigating the critical capillary number reveals that a minimum is found at a mediocre degree of confinement, after which the critical capillary number increases again to values even larger than the unconfined system. The breakup mode also makes a significant change as it goes from binary to ternary breakup, where the breakup occurs as the drop is retracting