Gaseous flow in microtubes at arbitrary Knudsen numbers

Abstract

New models that describe gas flow behaviour in microtubes are presented. To avoid time-consuming calculations in solving the integral equation which is obtained from the microscopic point of view, the high-order slip-flow boundary condition is utilized to correct the gas flow in such a micron or submicron spacing. The proposed model can be applied to arbitrary Knudsen number conditions under the assumption that the bulk flow velocity is negligible compared with the sonic velocity of the gas. The analytical solution of the pressure distribution for the first-order slip-flow model is obtained. The results show that the first-order slip-flow model is in good agreement with this model. The nonlinear pressure distribution is due to gas compressibility. The dominant mechanism influencing the nonlinear pressure distribution comes from the rarefaction of gas and the inlet pressure. The rarefaction effect increases the pressure drop at the inlet region of the channel and decreases the pressure drop at the exit region of the channel. The decrease of inverse Knudsen number changes the pressure distribution from concave to almost linear and increases the mass flow.

Low Mach number slip flow through diverging microchannel

“…It is important to understand the gas flow behavior through such geometry in terms of pressure drop, velocity distribution and flow structure. Most of the earlier work however focused on uniform cross-section microchannels with liquid or gas flow [1][2][3][4][5][6][7][8][9][10][11][12] and flow through other cross-section area microchannels have been inadequately studied. The low pressure gas flows through conventional tubes are governed by the same set of non-dimensional parameters as that of gas microflow; Sreekanth [13] and Demsis et al [14,15].…”

Slip and accommodation coefficients from rarefaction and roughness in rotating microscale disk flows

“…Reviews of these investigations are given by several sources. [1][2][3][4][5][6] One significant source of uncertainty in the data given from these sources is associated with the measurement of the channel depth or inner diameter D of the microchannel or capillary tube. Another source of uncertainty is associated with measurement of flow rate.…”

Curved Boundary Treatment of the Lattice Boltzmann Method for Slip Flow Simulations

“…Finally, Fig. 11 compares the velocity profiles from the present LB method with the analytical solutions of Weng et al [13] for various Kn. The tube radius is fixed as R=20x ,and Kn=0.025, 0.05, and 0.1 are considered.…”

“…In contrast to the case of channel flow, there is a lack of precise experimental data and appropriate slip model in the microtube flow. Weng et al [13] presented following slip model for the microtube flow, In principle, moving the origin must not influence the velocity profile, and it does not seem to affect the results when the present boundary condition is used. However, noticeable deviation can be captured in the figure for the case of Lee and Lin's boundary condition.…”