TY - JOUR
T1 - Axisymmetric boundary integral simulations of film drainage between two viscous drops
AU - Janssen, P.J.A.
AU - Anderson, P.D.
AU - Peters, G.W.M.
AU - Meijer, H.E.H.
PY - 2006
Y1 - 2006
N2 - Film drainage between two drops with viscosity equal to that of the matrix fluid is studiedusing a numerical method that can capture both the external problem of two touchingdrops as well as the inner problem of pressure-driven local film drainage, without assumptionsabout the dimensions of the film or the use of lubrication approximations.We use a non-singular boundary integral method that has sufficient stability and accuracyto simulate film thicknesses down to and smaller than 10−4 times the undeformeddrop radius. After validation of the method we investigate the validity of various resultsobtained from simple film-drainage models and asymptotic theories. Our results forbuoyancy-driven collisions are in agreement with a recently developed asymptotic theory.External-flow-driven collisions are different than buoyancy-driven collisions, which meansthat the internal circulation inside the drop plays a significant role in film drainage, evenfor small capillary numbers, as has been recently shown [Nemer et al, Phys. Review Letters,92, 114501, 2004]. Despite, we find excellent correspondence with simple drainagemodels when considering the drainage time only.
AB - Film drainage between two drops with viscosity equal to that of the matrix fluid is studiedusing a numerical method that can capture both the external problem of two touchingdrops as well as the inner problem of pressure-driven local film drainage, without assumptionsabout the dimensions of the film or the use of lubrication approximations.We use a non-singular boundary integral method that has sufficient stability and accuracyto simulate film thicknesses down to and smaller than 10−4 times the undeformeddrop radius. After validation of the method we investigate the validity of various resultsobtained from simple film-drainage models and asymptotic theories. Our results forbuoyancy-driven collisions are in agreement with a recently developed asymptotic theory.External-flow-driven collisions are different than buoyancy-driven collisions, which meansthat the internal circulation inside the drop plays a significant role in film drainage, evenfor small capillary numbers, as has been recently shown [Nemer et al, Phys. Review Letters,92, 114501, 2004]. Despite, we find excellent correspondence with simple drainagemodels when considering the drainage time only.
U2 - 10.1017/S0022112006002084
DO - 10.1017/S0022112006002084
M3 - Article
SN - 0022-1120
VL - 567
SP - 65
EP - 90
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -