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

Abstract

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.

Nonlinear oscillatory fully-developed rarefied gas flow in plane geometry

“…Simulations have been based on linearized 24,25 and nonlinear 26,[30][31][32]34,35,37 kinetic models, as well as on the Direct Simulation Monte Carlo (DSMC) method. [21][22][23][27][28][29]33,36 It is also noted that steady-state force driven Poiseuille type flows have been investigated [38][39][40][41][42][43] based on kinetic theory and modeling, clarifying certain phenomena and paradox appearing near the continuum regime that cannot be described by the typical hydrodynamic approach. Such phenomena include the nonconstant pressure profile across the channel, the bimodal shape of the temperature profile with a slight shallow at the channel center and the presence of axial heat flow.…”

“…Such phenomena include the nonconstant pressure profile across the channel, the bimodal shape of the temperature profile with a slight shallow at the channel center and the presence of axial heat flow. The analysis has been based on asymptotic methods, [38][39][40] kinetic model equations 40,42 and the DSMC method 38,41,43 and is extended in a wide range of the Knudsen number. [39][40][41][42][43] Considering all above and taking into consideration that in Refs.…”

“…The analysis has been based on asymptotic methods, [38][39][40] kinetic model equations 40,42 and the DSMC method 38,41,43 and is extended in a wide range of the Knudsen number. [39][40][41][42][43] Considering all above and taking into consideration that in Refs. 18 and 19, the results are formally limited to small amplitudes of the oscillating pressure gradient, in the present work, the nonlinear time-dependent fully developed rarefied gas flow between parallel plates, driven by an oscillating external force with arbitrary magnitude, is considered.…”

Crossover of ballistic, hydrodynamic, and diffusive phonon transport in suspended graphene

“…We solve the PBE with an ab initio full scattering matrix using a deviational Monte Carlo (MC) method [15], [21]. An advantage of MC simulation is that we can sample distribution functions for scattered and unscattered particles separately [22]. By doing so, we can quantitatively show the contributions of thermal conductivity and momentum destruction rate from the three regimes.…”

Ballistic and Collisional Flow Contributions to Anti-Fourier Heat Transfer in Rarefied Cavity Flow

“…A similar approach was used previously for the explanation of self-diffusion in long capillary tubes 12 and rarefied gas short tube propulsion efficiency 13 . These decomposed forms (ballistic and collision parts) for the macroscopic flow properties were presented in 11 , 14 , 15 . Considering ballistic and collision parts of the heat flux and temperature by using a new indicator of cold-to-hot heat transfer reveals new understandings of the behavior of cold-to-hot heat transfer in rarefied gas flows in the cavity geometry.…”