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
SN - 0021-9606
VL - 133
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 11
M1 - 114702
ER -