On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field

Abstract

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.

Analytical Results of the Motion of Oscillating Dumbbell in a Viscous Fluid

“…For making further progress analytically, we introduce a few convenient notation. We assume that any dimensionless functions f (s, τ ) (which could be scalar, vectorial, or tensorial one) [2], has the following properties:…”

“…The study of particle motion in a viscous fluid is a key to understanding the physical processes associated with particle suspensions at low Reynolds number. It has been of interest to scientists for many years and is still an active area of research [2,3,7,8,24,25,27]. The interactions between particles in the viscous fluid plays important roles in many applications in medicine and technology, such as minimizing surgical invasion and controlling drug delivery [13,14,16,18,20].…”

Reconstructing the neutrally-buoyant particle flow near a singular corner

“…To date, several modeling approaches have been proposed *Corresponding author. E-mail address: francesco.romano@ensam.eu (Francesco Romanò) Executive Editor: Cristian Marchioli for particles in unbounded flows [13][14][15] and complementary exact [16,17], numerical [18,19], asymptotic [20][21][22][23],…”