TY - JOUR
T1 - On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field
AU - Al-Hatmi, Mohammed M.
AU - Purnama, Anton
N1 - Publisher Copyright:
© 2021 Mohammed M. Al-Hatmi and Anton Purnama.
PY - 2021
Y1 - 2021
N2 - Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.
AB - Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.
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U2 - 10.1155/2021/9211272
DO - 10.1155/2021/9211272
M3 - Article
AN - SCOPUS:85120886420
SN - 0161-1712
VL - 2021
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
M1 - 9211272
ER -