Lubrication analysis of the viscous micro/nano pump with slip

Abstract

A viscous pump is a device such that a cylindrical rotor is eccentrically placed in a channel, so that the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are small compared to the radius of the rotor, the hydrodynamic theory of lubrication may be utilized to study the viscous pump. Here lubrication theory is used to obtain an analytical solution which relates the flowrate, rotation rate, pressure drop and applied torque as functions of two geometric parameters for a viscous pump. This analysis differs from a previous similar study in two ways. Firstly, certain integrals are evaluated explicitly, and secondly the standard no-slip boundary condition of fluid mechanics has been replaced with the Navier boundary condition which allows a degree of tangential velocity slip on all solid boundaries. Comparison with the prior known solution shows that the solution obtained in this study predicts a slightly improved pump performance for the case of no-slip. For the case of slip, our results demonstrate that the performance of the pump is significantly improved.

Asymptotic analysis of the viscous micro/nano pump at low Reynolds number

“…We can view this another way: for nonzero values of and a fixed value of the torque L, the magnitude of the rotation rate is increased. This agrees well with the findings of Matthews and Hill [6], where the lubrication solution demonstrates that the performance of the viscous pump is greatly improved by the inclusion of slip. This, of course, is to be expected since the reason the viscous pump works is because it operates at a scale where slip effects are important.…”

“…Before we continue with a discussion concerning the effects of slip, comparisons with previous work with no-slip will be made. We compare our results to that of Day and Stone [5] and Matthews and Hill [6] who both employ a [3] who perform a complete Navier-Stokes simulation. For zero torque Day and Stone [5] and Matthews and Hill [6] demonstrate that for a cylinder placed closer to the bottom wall that the rotation direction is clockwise, which in this analysis implies α < 0 and y c > 0 and this agrees well with Eq.…”

“…Several numerical investigations appear in the literature, in particular those of Abdelgawad et al [2] and Sharatchandra et al [3,4]. The only analytical investigations to date apply the hydrodynamic theory of lubrication, as in [5] and more recently by Matthews and Hill [6]. Lubrication theory assumes that the distance of the rotating cylinder from the channel walls is much smaller than the diameter of the cylinder.…”

Computational Strategies for Micro‐ and Nanofluid Dynamics

“…Other application areas include nanosensors, 14,60 nanofilters and nanovalves, 61,62 nanoparticle collisions and flows, 63 and lubrication. [64][65][66][67][68][69] .…”

“…The setupis shown in Figure 4 Within the (x, y) plane, the CNTs are placed at (68,27) and (68,55). The rest of the simulation domain was filled with Argon atoms at a bulk density of 1.344 g cm À3 .…”