Slip due to surface roughness for a Newtonian liquid in a viscous microscale disk pump

Abstract

In the present study, hydrophobic roughness is used to induce near-wall slip in a single rotating-disk micropump operating with Newtonian water. The amount of induced slip is altered by employing different sizes of surface roughness on the rotating disk. The magnitudes of slip length and slip velocities increase as the average size of the surface roughness becomes larger. In the present study, increased slip magnitudes from roughness are then associated with reduced pressure rise through the pump and lower radial-line-averaged shear stress magnitudes (determined within slip planes). Such shear stress and pressure rise variations are similar to those which would be present if the slip is induced by the intermolecular interactions which are associated with near-wall microscale effects. The present slip-roughness effects are quantified experimentally over rotational speeds from 50 to 1200 rpm, pressure increases from 0 to 312 kPa, net flow rates of 0–100 μl/min, and fluid chamber heights from 6.85 to 29.2 μm. Verification is provided by comparisons with analytic results determined from the rotating Couette flow forms of the Navier–Stokes equations, with different disk rotational speeds, disk roughness levels, and fluid chamber heights. These data show that slip length magnitudes show significant dependence on radial-line-averaged shear stress for average disk roughness heights of 404 and 770 nm. These slip length data additionally show a high degree of organization when normalized using by either the average roughness height or the fluid chamber height. For the latter case, such behavior provides evidence that the flow over a significant portion of the passage height is affected by the roughness, and near-wall slip velocities, especially when the average roughness height amounts to 11% of the h=6.86 μm passage height of the channel. Such scaling of the disk slip length bdisk with fluid chamber height h is consistent with d-type roughness scaling in macroscale flows.