Gas flow near a smooth plate

Abstract

We examine gas flow adjacent to a molecularly smooth, solid, muscovite mica. The fluctuations in force acting on a glass sphere as a function of proximity to a mica plate were measured in air and were used to obtain the damping. The damping was interpreted as a lubrication force. The measured damping as a function of separation in the slip-flow regime corresponds to a slip length of 480 ± 70 nm, which is equivalent to highly specular gas molecule collisions. A slip-flow model fits the data for separations as small as one mean free path.

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path

“…The double-dip shape of the latter can be explained directly from the systematic errors of our setup mentioned above as a reason for the limitation in distances for the fit. As has been pointed out by other authors, 30 for surfaces with dissimilar properties (such as roughness), it is indeed possible to distinguish the different slip lengths of the plate and the sphere surface (or, λ s and k). However, we find that the corresponding fit residuals over the two-parameter space generally show very shallow minima, resulting in relatively large uncertainties in the obtained slip lengths and derived quantities (see Table II).…”

“…Thanks to its simplicity, the model (5) finds broad application in the literature 6,10,12,26,[28][29][30][46][47][48] to extract the slip length λ s from experimental data. However, it is mostly employed in the limit k → 0, corresponding to equal slip lengths on both surfaces.…”

“…The second line of research utilizes technologies such as the surface force apparatus (SFA) 3,4,26 or atomic force microscopes (AFM) 12,[27][28][29][30][31] to directly measure slip forces between rather microscopic surface areas. Although results obtained with AFM or SFA seem to show even larger spread…”

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

“…Honig et al (2010) and Bowles & Ducker (2011) used a thermal driven oscillation of a sphere glued to an AFM cantilever to measure the damping force versus gas film gap between the sphere and the substrate and compared the force obtained to the theoretical force obtained for a specific slip boundary condition; reported values of slip length ranged from 100nm to 600nm. Pan et al (2013) used a similar device where the sphere was forced to oscillate periodically with a prescribed amplitude where the aim was to demonstrate the slip length was independent of the oscillation amplitude of the cantilever, i.e. constant slip length.…”

“…The motion of the cantilever is described by spring mass damper equation with the driving force given by the lubrication approximation of the flow around a sphere with a slip boundary condition. The equation is mathematically equivalent to the rotor displacement equation (2.16), see for example equation (2) in Pan et al (2013), where in (2.16) the force F can be rewritten as the fluid, spring and damper components. However, in the cantilever problem the substrate is kept fixed while in the present case the stator is allowed to react to the motion of the rotor.…”