BUOYANCY-DRIVEN INTERACTIONS BETWEEN 2 DEFORMABLE VISCOUS DROPS

Time-dependent interactions between two buoyancy-driven deformable dro ps are studied in the low Reynolds number flow limit for sufficiently large Bond numbers that the drops become significantly deformed. The f irst part of this paper considers the interaction and deformation of d rops in axisymmetric configurations. Boundary integral calculations ar e presented for Bond numbers B = DELTArhoga2/sigma in the range 0.25 l ess-than-or-equal-to B < infinity and viscosity ratios lambda in the r ange 0.2 less-than-or-equal-to lambda less-than-or-equal-to 20. Specif ically, the case of a large drop following a smaller drop is considere d, which typically leads to the smaller drop coating the larger drop f or B much greater than 1. Three distinct drainage modes of the thin fi lm of fluid between the drops characterize axisymmetric two-drop inter actions: (i) rapid drainage for which the thinnest region of the film is on the axis of symmetry, (ii) uniform drainage for which the film h as a nearly constant thickness, and (iii) dimple formation. The initia l mode of film drainage is always rapid drainage. As the separation di stance decreases, film flow may change to uniform drainage and eventua lly to dimpled drainage. Moderate Bond numbers, typically B = O(10) fo r lambda = O(1), enhance dimple formation compared to either much larg er or smaller Bond numbers. The numerical calculations also illustrate the extent to which lubrication theory and analytical solutions in bi polar coordinates (which assume spherical drop shapes) are applicable to deformable drops.The second part of this investigation considers th e 'stability' of axisymmetric drop configurations. Laboratory experime nts and two-dimensional boundary integral simulations are used to stud y the interactions between two horizontally offset drops. For sufficie ntly deformable drops, alignment occurs so that the small drop may sti ll coat the large drop, whereas for large enough drop viscosities or h igh enough interfacial tension, the small drop will be swept around th e larger drop. If the large drop is sufficiently deformable, the small drop may then be 'sucked' into the larger drop as it is being swept a round the larger drop. In order to explain the alignment process, the shape and translation velocities of widely separated, nearly spherical drops are calculated using the method of reflections and a perturbati on analysis for the deformed shapes. The perturbation analysis demonst rates explicitly that drops will tend to be aligned for B > O(d/a) whe re d is the separation distance between the drops.