Motion of a particle with stick-slip boundary conditions towards a hard wall or free surface is investigated in the range of Reynolds numbers much smaller than unity, based on the multipole expansion of the Stokes equations. The slip parameter can be interpreted as a measure of a solid particle roughness or as the effect of a surfactant on the motion of a small spherical non-deformable bubble. The particle friction coefficient is evaluated as a function of the distance from its center to the wall, based on the inverse power series expansion, and the results are used to derive explicit lubrication expressions for the friction coefficient, in a wide range of the slip parameters. It is pointed out that for a very small thickness of the fluid film, the lubrication expressions are more accurate than the series expansion. The drainage time is calculated and analyzed, and estimated in terms of explicit lubrication expressions.
REFERENCES(17)
1.
BATCHELOR, G.K., 2000. An Introduction to Fluid Dynamics. Cambridge University Press.
CICHOCKI, B., EKIEL-JEŻEWSKA, M.L., WAJNRYB, E., 2014. Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary. J. Chem. Phys., 140, 164902.
CICHOCKI, B., FELDERHOF, B.U., HINSEN, K., WAJNRYB, E., BŁAWZDZIEWICZ, J., 1994. Friction and mobility of many spheres in Stokes flow. J. Chem. Phys., 100, 3780-3790.
CICHOCKI, B., EKIEL-JEŻEWSKA, M.L., WAJNRYB, E., 1999. Lubrication corrections for three-particle contribution to short-time self-diffusion coefficients in colloidal dispersions. J. Chem. Phys., 111, 3265-3273.
FELDERHOF, B.U., 1976. Force density induced on a sphere in linear hydrodynamics: II. Moving sphere, mixed boundary conditions. Physica A, 84, 569-576.
JEFFREY, D.J., ONISHI, Y., 1984. Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech., 139, 261-290.
LECOQ, N., ANTHORE, R., CICHOCKI, B., SZYMCZAK, P., FEUILLEBOIS, F., 2004. Drag force on a sphere moving towards a corrugated wall. J. Fluid Mech., 513, 247-264.
MALYSA, K., KRASOWSKA, M., KRZAN, M., 2005. Influence of Surface Active Substances on Bubble Motion and Collision with Various Interfaces. Adv. Colloid Interface Sci., 114-115, 205-225.
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.