Numerical study of thermal creep flow between two ratchet surfaces

Abstract

Several designs of Knudsen pumps, the principle of which is based on a thermally driven flow generated along a microchannel, have been proposed in the literature. The fabrication of efficient prototypes, however, is generally limited by the difficulty to control the temperature distribution along the walls. An alternative possibility, which only requires isothermal hot or cold walls, is investigated. The pumping element consists of two facing isothermal ratchet surfaces with different temperatures. The asymmetric saw-tooth like surfaces lead to a rectified Knudsen flow along the walls. This flow is numerically simulated in the slip flow regime with Navier–Stokes equations and appropriate first-order velocity slip, including thermal creep and wall curvature effects, as well as temperature jump, boundary conditions. The influence of the geometrical parameters is investigated, among which the ratchet angle and the alignment of the ratchet pattern. The influence of the Knudsen number and of the temperature difference is analyzed as well and guidelines are drawn for designing a prototype.