TY - JOUR
T1 - Hydrodynamic interactions and collision efficiencies of spherical drops covered with an incompressible surfactant film
AU - Blawzdziewicz, J.
AU - Wajnryb, E.
AU - Loewenberg, Michael
PY - 1999/9/25
Y1 - 1999/9/25
N2 - A theory is developed for the hydrodynamic interactions of surfactant-covered spherical drops in creeping flows. The surfactant is insoluble, and flow-induced changes of surfactant concentration are small, i.e. the film of adsorbed surfactant is incompressible. For a single surfactant-covered drop in an arbitrary incident flow, the Stokes equations are solved using a decomposition of the flow into surface-solenoidal and surface-irrotational components on concentric spherical surfaces. The surface-solenoidal component is unaffected by surfactant; the surface-irrotational component satisfies a slip-stick boundary condition with slip proportional to the surfactant diffusivity. Pair hydrodynamic interactions of surfactant-covered bubbles are computed from the one-particle solution using a multiple-scattering expansion. Two terms in a lubrication expansion are derived for axisymmetric near-contact motion. The pair mobility functions are used to compute collision efficiencies for equal-size surfactant-covered bubbles in linear flows and in Brownian motion. An asymptotic analysis is presented for weak surfactant diffusion and weak van der Waals attraction. In the absence of surfactant diffusion, collision efficiencies for surfactant-covered bubbles are higher than for rigid spheres in straining flow and lower in shear flow. In shear flow, the collision efficiency vanishes for surfactant diffusivities below a critical value if van der Waals attraction is absent.
AB - A theory is developed for the hydrodynamic interactions of surfactant-covered spherical drops in creeping flows. The surfactant is insoluble, and flow-induced changes of surfactant concentration are small, i.e. the film of adsorbed surfactant is incompressible. For a single surfactant-covered drop in an arbitrary incident flow, the Stokes equations are solved using a decomposition of the flow into surface-solenoidal and surface-irrotational components on concentric spherical surfaces. The surface-solenoidal component is unaffected by surfactant; the surface-irrotational component satisfies a slip-stick boundary condition with slip proportional to the surfactant diffusivity. Pair hydrodynamic interactions of surfactant-covered bubbles are computed from the one-particle solution using a multiple-scattering expansion. Two terms in a lubrication expansion are derived for axisymmetric near-contact motion. The pair mobility functions are used to compute collision efficiencies for equal-size surfactant-covered bubbles in linear flows and in Brownian motion. An asymptotic analysis is presented for weak surfactant diffusion and weak van der Waals attraction. In the absence of surfactant diffusion, collision efficiencies for surfactant-covered bubbles are higher than for rigid spheres in straining flow and lower in shear flow. In shear flow, the collision efficiency vanishes for surfactant diffusivities below a critical value if van der Waals attraction is absent.
UR - http://www.scopus.com/inward/record.url?scp=0002101345&partnerID=8YFLogxK
U2 - 10.1017/S002211209900590X
DO - 10.1017/S002211209900590X
M3 - Article
AN - SCOPUS:0002101345
VL - 395
SP - 29
EP - 59
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -