Poiseuille Coefficient

To calculate the Poiseuille coefficient Gp in the slip flow regime (5 < 8 < 100) the Navier-Stokes equation is solved with the velocity slip boundary conditions (8). Then for the channel the flow rate reads... 

In the free-molecular regime (8 0) assuming the diffuse gas-smf ace interaction on the channel/ tube wall, the coefficients Gp and Gt can be calculated directly without numerical solution of the kinetic equation. In the case of the channel, the Poiseuille coefficient Gp is given by the following double integral ... 

In the case of a mbe, the expression of the Poiseuille coefficient Gp is quite simple ... 

Gas Flow in Nanochannels, Fig. 2 Poiseuille coefficient versus rarefaction parameter 5 solid lines, kinetic equation solution [11] pointed line, free-molecular value based on Eq. 12 dashed line, Navier-Stokes solution Eq. 16... 

To calculate the coefficients Gp and Gt in the transitional regime (5 1), the kinetic equation is applied. The coefficients Gp and for the channel flow obtained in [11] assuming the diffuse scattering are presented in Figs. 2 and 3, respectively. For all values of the aspect ratio bja, the Poiseuille coefficient Gp has the Knudsen minimum near the point 5 1. For... 

The coefficients Gp and Gt for the tube flow reported in [20] are presented in Figs. 4 and 5, respectively. Like for the channel, the Poiseuille coefficient Gp also has a small minimum in the transition regime (8 1). Its variation near the... 

Gas Flow in Nanochannels, Table 2 Poiseuille coefficient vems accommodation coefficients at and On [14]... 

Numerical results on the capillary flow of polyatomic gases can be found in [4]. Comparing these results with the data presented here, it is concluded that the Poiseuille coefficient Gp is slightly affected by the internal structure of molecules. The thermal creep coefficient Gp for polyatomic gases differs from that for monatomic gases. 

The Poiseuille coefficient Gp for the diffuse scattering is presented in Table 1. It tends to infinity in both limits h oo and 8 —> 0. In the transition regime, the coefficient Gp has the well-known Knudsen minimum. 

Micro- and Nanoscale Table 1 Poiseuille coefficient parameter 5, diffuse scattering... 

Micro- and Nanoscale Gas Dynamics, Table 2 Poiseuille coefficient Gp versus accommodation coefficients a, and (Reprinted with permission from [5]) ... 

Poiseuille coefficient deterniines a gas flow induced by a pressure gradient. 

To calculate the coefficients Gp and Gp in the transitional regime (5 1) the kinetic equation is applied. The coefficients Gp and G for the channel flow obtained in [11] assuming the diffuse scattering are presented in Figs. 2 and 3, respectively. For all values of the aspect ratio b/a the Poiseuille coefficient Gp has the Knudsen minimum near the point 5 1. For the square channel (fc/a= 1) the minimum is rather shallow. Since the variation of Gp near the free molecular regime is small its free molecular value can be used for practical calculations in the range 0 < 5 < 5. Then for i5 > 5 the hydrodynamic solution (16) with the slip boundary condition can be used. Such an approximation works with a precision of 10%. However,... 

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