Abstract
Flow pumping in viscous fluids is of prime importance in micro-fluidic applications. Here we show that a single colloidal particle in front of a soft wall, manipulated by external means like an optical tweezer, can pump the ambient viscous fluid. The particle, moving back and forth parallel to the soft wall, can produce an averaged net flow in a direction perpendicular to the wall. Using a perturbative scheme, we present the results. Analysis show that this flow in terms of capillary number, scales as {text {Ca}}^2.
Highlights
Flow pumping in viscous fluids is of prime importance in micro-fluidic applications
A colloidal particle trapped by an optical tweezer which has enforced the particle to move in a periodic orbit, is not able to produce net flow
An alternative way is to use a single colloidal particle moving near a soft wall
Summary
To investigate the dynamics of this system, we denote by u(x) and p(x) , velocity and pressure fields in the fluid medium. Denoting the dimensionless Reynolds number by Re = ρUpa/η , we will assume that Re ≪ 1 This will restrict the dynamics of the fluid to the viscosity dominated regime. Regarding the detail structure of this equation, three different forces namely, viscous, tension and gravity, compete in force balance Relative strength of these forces can be given in terms of two dimensionless numbers: α gravitational force ga[2] ρ , viscous force ηUp β = surface tension = γ ,. We note that in the laboratory frame and as a result of no-slip boundary condition on the wall, the trajectory of a particular point of the interface should follow exactly the path of the fluid particles that are locally√in contact with points on the wall. The set of boundary Eqs. (4), (5) and (7), will allow us to find complete information about the shape of interface and the velocity fields on both sides of the interface
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