Predicting the Knudsen paradox in long capillaries by decomposing the flow into ballistic and collision parts.

The well-known Knudsen paradox observed in pressure driven rarefied gas flows through long capillaries is quantitatively explored by decomposing the particle distribution function into its ballistic and collision parts. The classical channel, tube, and duct Poiseuille flows are considered. The solution is obtained by a typical direct simulation Monte Carlo algorithm supplemented by a suitable particle decomposition indexation process. It is computationally confirmed that in the free-molecular and early transition regimes the reduction rate of the ballistic flow is larger than the increase rate of the collision flow deducing the Knudsen minimum of the overall flow. This description interprets in a precise, quantitative manner the appearance of the Knudsen minimum and verifies previously reported qualitative physical arguments.

Role of surface shape on boundary slip and velocity defect.

Although many gas-phase microfluidic devices contain curved surfaces, relatively little research has been conducted on the degree of slip over nonplanar surfaces. The present study demonstrates the influence of the surface shape (i.e., convex/concave) on the velocity slip and formation of the Knudsen layer. In addition, the study reveals that there is a simple relationship between the shear stress exerted on the surface and the velocity defect in the Knudsen layer.