Sinking of small sphere at low Reynolds number through interface
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 res...
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Published in | Physics of fluids (1994) Vol. 23; no. 7; pp. 072104 - 072104-9 |
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American Institute of Physics
01.07.2011
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Abstract | 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. |
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AbstractList | 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. |
Author | Kim, Ho-Young Lee, Duck-Gyu |
Author_xml | – sequence: 1 givenname: Duck-Gyu surname: Lee fullname: Lee, Duck-Gyu organization: School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, South Korea – sequence: 2 givenname: Ho-Young surname: Kim fullname: Kim, Ho-Young email: hyk@snu.ac.kr. Tel.: 82-2-880-9286. Fax: 82-2-880-9287. organization: School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, South Korea |
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Cites_doi | 10.1126/science.265.5169.219 10.1038/nphys545 10.1017/S0022112073002375 10.1063/1.3309454 10.1017/S0022112094000480 10.1103/RevModPhys.69.865 10.1016/0377-0257(92)80069-A 10.1017/S0022112097007234 10.1002/aic.v17:1 10.1063/1.869820 10.1017/S0022112008004382 10.1021/la702437c 10.1021/la0533260 10.1371/journal.pone.0001185.g001 10.1146/annurev.fluid.38.050304.092157 10.1017/S002211200900593X 10.1063/1.3427241 10.1016/0079-6816(93)90034-S 10.1021/la060606m 10.1017/S0022112008002784 10.1063/1.869044 10.1017/S0022112010004611 10.1016/0301-7516(77)90005-9 10.1021/la800245k 10.1016/0079-6816(93)90034-S |
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Keywords | Gas liquid interface Low Reynolds number Theoretical study Hydrodynamics Immersion Spheres Experimental study Viscous fluids |
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Title | Sinking of small sphere at low Reynolds number through interface |
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