Boundary-driven nonequilibrium gas flow in a grooved channel via kinetic theory

Abstract

The nonequilibrium flow of a gas in a two-dimensional grooved channel, due to the motion of the wall of the channel, is investigated based on kinetic theory. The presence of the rectangular grooves that are placed periodically on the stationary wall results in a two-dimensional flow pattern. The problem is modeled by the linearized Bhatnagar-Gross-Krook ͑BGK͒ and S-model kinetic equations, which are solved for the corresponding perturbed distribution functions by the discrete velocity method. Maxwell diffuse type reflecting boundary conditions are used to model the gas-surface interaction, while periodic boundary conditions are imposed at the inlet and outlet of the channel. The computed macroscopic quantities of practical interest include velocity profiles, contours of pressure, density, and temperature, as well as the flow rate and the heat flux through the channel and the drag coefficient along the moving boundary. The results are valid in the whole range of the Knudsen number, from the free molecular regime through the transition and slip regimes up to the hydrodynamic limit, for various values of the depth and the width of the groove and the periodic length of the channel. A comparison between the BGK and S-model results is performed. Several interesting flow patterns and characteristics are examined in terms of the geometrical parameters of the flow configuration, including an unexpected behavior of the velocity profile across the channel at large Knudsen numbers.

Mesoscopic simulation of fluid flow in periodically grooved microchannels

“…Cao et al [8] investigated the effect of surface roughness on slip flow of gaseous argon in submicron platinum microchannels by nonequilibrium molecular dynamics and found that the roughness geometry produces significant effects on the boundary conditions and the channel friction characteristics. Naris and Valougeorgis [9] using kinetic theory studied nonequillibrium flows of a gas in a two-dimensional grooved channel, due to the motion of the channel wall and they quantified the effects of groove width and depth on drag force and flow rate. Lin [10] investigated a micromixer composed of a channel with patterned grooves on the bottom of the channel and found that the micromixer enhances mixing by initiating helical streamlines with transverse rotations.…”

A dissipative particle dynamics study of flow in periodically grooved nanochannels

“…They found that, as the substrate wavelength approaches length scales comparable with the liquid molecular diameter, the continuum solutions overestimate the degree of slip. Naris and Valougeorgis investigated non‐equilibrium flow of a gas in a two‐dimensional grooved channel, due to the motion of the channel wall. On the basis of kinetic theory, they quantified the effect of groove width and depth on drag force and flow rate.…”

A fast iterative model for discrete velocity calculations on triangular grids

“…(7), are defined in a compact form. These quantities can be defined by using the vector b i = [c 1 , c 1 + c 3 , p,p + c 1 , p + c 1 + c 3 , 2p] and the sine theorem for the geometry given in Fig 1. It is seen that the six angle elements of b i are the upper bounds of the six polar angle sectors of h r .…”

“…In spite of this, the discrete velocity (DV) method is considered as an efficient approach for solving problems in rarefied gas dynamics [5]. Even more, in certain physical systems where, due to the flow conditions and parameters, linearization of the governing kinetic equations and reduction of the number of spatial and velocity coordinates are permitted, the DV method has shown to be probably the most powerful computational scheme for providing reliable results in the whole range of the Knudsen number [6,7]. Such problems commonly appear in several technological fields including the emerging field of nano and microfluidics [8].…”