# 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

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