Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient

Abstract

Cylindrical Couette gas flow in the noncontinuum regime has been investigated using the boundary treatment derived from Maxwell's slip-flow model. It is shown that the tangential momentum accommodation coefficient plays an important role in determining the predicted velocity profile. The present analysis is in close agreement with previous analytical studies and shows good qualitative agreement with available direct simulation Monte Carlo data. The results predict the presence of an inverted velocity profile for the case where the inner cylinder rotates and the outer cylinder is stationary. However, our analysis further shows that the phenomenon of velocity inversion is only dependent on the accommodation coefficient of the outer cylinder. From the analysis, we derive specific criteria for the accommodation coefficient of the outer cylinder under which ͑i͒ no velocity inversion will take place, ͑ii͒ a partially inverted velocity profile will be observed, and ͑iii͒ a fully inverted velocity profile will be present. In contrast, when the outer cylinder rotates and the inner cylinder is stationary, it is shown that velocity inversion does not occur.

Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime

“…It is clear that at Kn= 0.5, the analytical slip-flow solution cannot be relied upon and this discrepancy clearly grows with increasing oscillatory frequency. Although it is recognized that this is well beyond the accepted limit of the slip-flow regime, the results presented indicate a significant difference to the steady-state case ͑␤ → 0͒ where several authors 25,28 have shown good agreement between analytical solutions and DSMC data for Kn= 0.5 and Mach numbers up to 0.5.…”

“…However, the shear stress associated with the outer cylinder increases away from the oscillating wall at low frequencies, as indicated for the case of ␤ = 1 and for the limiting case of ␤ = 0, which is equivalent to the steady rotating Couette problem. 28 At first glance this may appear unusual, but it is due to the requirement that the torque on each cylinder must balance. It is straightforward to show that in the limit of ␤ → 0, the shear stress on the inner cylinder will approach ͑r 2 / r 1 ͒ 2 , which, for this particular case, results in a shear stress that is four times higher on the inner cylinder.…”

“…In its simplest form, this reduces to an oscillating cylindrical Couette flow. Although cylindrical Couette flow has been studied by many authors using a variety of approaches, e.g., Tibbs et al, 24 Aoki et al, [25][26][27] Yuhong et al, 28 and Myong et al, 29 there has been no attempt to understand the oscillatory motion of such devices. The present investigation is therefore concerned with understanding the nature of the oscillatory motion of cylindrical Couette flow throughout the entire Knudsen number regime.…”

Velocity inversion in nanochannel flow

“…The fluid particles and the wall particles at a distance r interact through a LennardJones(LJ) potential, V ij (r) = 4ǫ[(r/σ) −12 − A ij (r/σ) −6 ], where ǫ and σ represent the energy and length scales, and A ij = A ji is a dimensionless parameter that controls the attractive part of the potential for the fluid-fluid and the fluid-wall particles. As mentioned previously, this parameter is similar to the accommodation coefficient in continuum descriptions [1,2,3,4,5,6]. The potential is truncated at r c = 2.5σ.…”

On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

“…Reliable tools exist for the prediction of gas damping in the first two regimes (see e.g. [7][8][9][10][11][12][13]46]) but the situation is less defined at lower pressures. Even though numerical techniques of deterministic and statistical nature have been developed in the transition regime (see e.g.…”