TY - JOUR

T1 - Motion of a spherical particle near a planar fluid-fluid interface

T2 - The effect of surface incompressibility

AU - Bławzdziewicz, J.

AU - Ekiel-Jeewska, M. L.

AU - Wajnryb, E.

N1 - Funding Information:
This work was supported by NSF Grant No. CBET-0931504. M.L., E.-J., and E.W. benefited from the Polish Ministry of Science and Higher Education Grant No. 45/N-COST/2007/0 and the COST P21 Action “Physics of droplets.”

PY - 2010/9/21

Y1 - 2010/9/21

N2 - Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluid interface under creeping-flow conditions is discussed. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particle-wall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesian-representation method.

AB - Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluid interface under creeping-flow conditions is discussed. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particle-wall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesian-representation method.

UR - http://www.scopus.com/inward/record.url?scp=77956968181&partnerID=8YFLogxK

U2 - 10.1063/1.3475197

DO - 10.1063/1.3475197

M3 - Article

C2 - 20866149

AN - SCOPUS:77956968181

VL - 133

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

SN - 0021-9606

IS - 11

M1 - 114702

ER -