Abstract
A general solution of the unsteady Stokes equation in spherical coordinates is derived for flow in the exterior of a sphere, and then applied to study the arbitrary unsteady motion of a rigid sphere in an unbounded single fluid domain which is undergoing a time-dependent mean flow. Calculation of the hydrodynamic force and torque on the sphere leads to a generalization of the Faxen’s law to time-dependent flow fields which satisfy the unsteady Stokes equation. For illustrative purposes, we consider the relative motion of gas bubbles which undergo very rapid oscillations so that the generalized Faxen’s law derived for a solid sphere can be applied. We also demonstrate that our results reduce to those of Faxen for the steady flow limit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brenner, H.:Chem. Eng. Sci.,18, 1 (1963).
Faxen, H.: Dissertation, Uppsala University, Sweden (1921).
Stokes, G. G.:Trans. Camb. Phil. Soc.,9, 29 (1851).
Basset, A. B.: “A Treatise on Hydrodynamics”, Vol. II, Dover, New York (1888).
Lamb, H.: “Hydrodynamics”, Dover, New York (1932).
Hauge, E. H. and Martiri-Löf, A.:J. Stat. Phys.,7, 259 (1973).
Happel, J. and Brenner, H.: “Low Reynolds Number Hydrodynamics”, Martinus Nijhoff Publisher, Netherland (1983).
Batchelor, G. K.: “An Introduction to Fluid Dynamics”, Cambridge University Press, U. K. (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yang, SM. Motions of a sphere in a time-dependent stokes flow: A generalization of Faxen’s law. Korean J. Chem. Eng. 4, 15–22 (1987). https://doi.org/10.1007/BF02698094
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02698094