Sinking of small sphere at low Reynolds number through interface

• Published in: Physics of fluids (1994) Vol. 23; no. 7; pp. 072104 - 072104-9
• Main Authors: Lee, Duck-Gyu, Kim, Ho-Young
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.07.2011
• Subjects: Applied fluid mechanics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamics, hydraulics, hydrostatics; Physics; Gas liquid interface; Low Reynolds number; Theoretical study; Hydrodynamics; Immersion; Spheres; Experimental study; Viscous fluids
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3614536

A dense solid sphere gently released on an air-liquid interface slowly sinks into liquid due to gravity, while the motion is resisted by viscous and capillary forces. Here, we predict the sinking velocity of the interface-straddling sphere by a simplified model and experimentally corroborate the results. The viscous drag on the sphere is determined by integrating the surface stress, which is the solution of the Stokes equation, over the wetted area that changes with time. To compute the interfacial tension force that depends on the meniscus profile, we solve the dynamic boundary condition for the normal and tangential stresses at the air-liquid interface. The predicted sinking velocity, a function of the sphere density and radius, liquid density, viscosity and surface tension, and the dynamic contact angle, is in good agreement with the experimental measurements except for the late stages when meniscus snapping occurs. We also construct a scaling law for the steady velocity of a sinking sphere, which gives the characteristic sinking time.