# DSMC investigation of rarefied gas flow through diverging micro- and nanochannels

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## Abstract

Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging micro- and nanochannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0° and 17° are described at different pressure ratios (1.5 ≤ Π ≤ 2.5) and Knudsen numbers (0.03 ≤ Kn ≤ 12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent micro- and nanochannels and are compared with those of a micro- and nanochannel with a uniform cross section. The variations of the flow field properties in divergent micro- and nanochannels which are influenced by the area change, the channel pressure ratio, and the rarefication are discussed. The results show no flow separation in divergent micro- and nanochannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through micro- and nanochannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro- and nanochannels with non-uniform cross sections.

## Keywords

Divergent micro/nanochannel Rarefied gas flow DSMC Simplified Bernoulli trials Knudsen minimum## List of symbols

*a*Constant [kg s

^{−1}]- DOF
_{rot} Rotational degree of freedom

*d*_{p}Molecular diameter [m]

- DSMC
Direct simulation Monte Carlo

*H*Channel height [m]

- Kn
Knudsen number

*L*Channel length [m]

- Ma
Mach number

- \(\dot{M}\)
Mass flow rate [kg s

^{−1}]*m*_{p}Molecular mass [kg]

*n*Number density [m

^{−3}]- NTC
No time counter

*P*Pressure [Pa]

- PPC
Particle per cell

*R*Specific gas constant [J kg

^{−1}K^{−1}]- RMSE
Root mean squared error

- SBT
Simplified Bernoulli trials

*T*Temperature [K]

- VHS
Variable hard sphere

*w*Channel depth [m]

*x*,*y*Cartesian coordinates

## Greek symbols

*β*Divergence angle

*κ*_{b}Boltzmann constant [m

^{2}kg s^{−2}K^{−1}]- λ
Molecular mean free path [m]

- Π
Inlet-to-outlet pressure ratio

- ρ
Density [kg m

^{−3}]- ω
Viscosity index

## Subscripts

- in
Inlet

- m
Mean

- n
Normalised

- out
Outlet

- slip
Slip

- straight
Straight

## Notes

### Acknowledgements

The authors would like to thank Prof. Ali Beskok from the Southern Methodist University, the USA, and Prof. Yevgeny A. Bondar from the Novosibirsk State University, Russia, for the fruitful discussions concerning the results presented in this paper.

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