Nonlinear oscillatory fully-developed rarefied gas flow in plane geometry

Abstract

Note: This paper is part of the special issue on Direct Simulation Monte Carlo-The Legacy of Graeme A. Bird.

Gaseous transport phenomena in rarefied conditions via deterministic and stochastic methods with applications in vacuum and fusion engineering

“…Then, as δ is further increased G A (δ, θ) tends to a maximum at some δ (depending on θ) and it is then again decreased. It is noted that, the above behavior described for the Poiseuille coefficient amplitude is in agreement with the one reported in [117,118,130].…”

“…In addition, for a specific θ, the phase angle is very close to zero at the free-molecular limit and is increased as δ is increased, tending to the maximum phase angle difference of π/2 at the viscous limit. It is noted that similar to the Poiseuille coefficient amplitude, the above remarks for the phase angle are in accordance with the ones made in [117,118,130].…”

“…In the aforementioned cases, the flow consists of the inviscid piston flow in the channel center dominated by inertia forces and the frictional Stokes wall layer dominated by viscous forces. This flow description, including the velocity overshoot inside the Stokes layer, is known as the "Richardson effect" and has been observed in the viscous limit [128,131,132], as well as, under rarefied conditions [117,118,130].…”

Rarefied oscillatory and pulsatile gas flows in capillaries and enclosures with applications in vacuum technology and microfluidics

“…Obviously, the pumping power has two peaks within each oscillatory cycle because it consists of the product of the oscillatory flow times the oscillatory pressure gradient and its integral over one cycle is not zero in order to drive the mixture flow, although the oscillatory net flow is zero. The dependency of the mixture pumping power on the flow parameters is similar to the one observed in oscillatory single gas flow [164,128]. In general, as θ is decreased its amplitude is decreased and its phase angle lag is increased and this behavior becomes more dominant as δ is increased.…”

“…Also, it has been shown that as the velocity amplitude of the oscillating wall is increased, the macroscopic quantities may contain several harmonics [161][162][163]. The corresponding nonlinear force driven flow has been recently examined with the DSMC method [164] and it is presented in Chapter 5 along with the deterministic formulation.…”