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.

UR - http://www.scopus.com/inward/record.url?scp=85120886420&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85120886420&partnerID=8YFLogxK

U2 - 10.1155/2021/9211272

DO - 10.1155/2021/9211272

M3 - Article

AN - SCOPUS:85120886420

VL - 2021

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 9211272

ER -