Axisymmetric boundary integral simulations of film drainage between two viscous drops

Abstract

Film drainage between two drops with viscosity equal to that of the matrix fluid is studied using a numerical method that can capture both the external problem of two touching drops and the inner problem of pressure-driven local film drainage, without assumptions about the dimensions of the film or the use of lubrication approximations. We use a non-singular boundary integral method that has sufficient stability and accuracy to simulate film thicknesses down to and smaller than $10^{-4}$ times the undeformed drop radius. After validation of the method we investigate the validity of various results obtained from simple film-drainage models and asymptotic theories. Our results for buoyancy-driven collisions are in agreement with a recently developed asymptotic theory. External-flow-driven collisions are different from buoyancy-driven collisions, which means that the internal circulation inside the drop plays a significant role in film drainage, even for small capillary numbers, as has been recently shown (Nemer et al ., Phys. Rev. Lett ., vol. 92, 2004, 114501). Despite that, we find excellent correspondence with simple drainage models when considering the drainage time only.