Dynamics of droplet rebound from a weakly deformable gas-liquid interface

A droplet of radius a moves with kinetic energy 2 pi rho U-d(c)'(2)a(3)/3 in an incompressible, continuum ambient gas and rebounds from an initially planar, weakly deformable interface bounding a half-space of liquid. We study the rebound process in the limit We(d)equivalent to rho U-d(c)'(2)a/sigma much less than1, where sigma is the surface tension of the two liquid-gas interfaces and rho (d) is the density of the fluid comprising the drop and the planar half-space. When viscous dissipation in both the ambient gas and in the drop is negligible, the flow inside the drop is inviscid and driven by the deformation of the near contact dimple region. The dimple region is approximated as a section of a sphere of radius 2a. Analysis of the motion induced in the liquid phase, coupled with a physically appropriate description of the interfaces, provides a theoretical description of the deformation and flow modes that ensue. Analytical predictions based on a singular perturbation analysis valid in the limit ln(We(d)(-1/4))much greater than1 indicate that the time taken by the drop to complete a bounce is a We(d)(1/2)U(c)'(-1)pi (4/3)(1/2) ln(1/2)(We(d)(-1/4)) and the angular extent of the near contact region which undergoes strong deformation is (4We(d)ln(-1)(We(d)(-1/4))/3)(1/4). The asymptotes are compared to numerical solutions to the full governing equations. (C) 2001 American Institute of Physics.