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

  • Amin Ebrahimi
  • Ehsan Roohi
Research Paper


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.


Divergent micro/nanochannel Rarefied gas flow DSMC Simplified Bernoulli trials Knudsen minimum 

List of symbols


Constant [kg s−1]


Rotational degree of freedom


Molecular diameter [m]


Direct simulation Monte Carlo


Channel height [m]


Knudsen number


Channel length [m]


Mach number


Mass flow rate [kg s−1]


Molecular mass [kg]


Number density [m−3]


No time counter


Pressure [Pa]


Particle per cell


Specific gas constant [J kg−1 K−1]


Root mean squared error


Simplified Bernoulli trials


Temperature [K]


Variable hard sphere


Channel depth [m]

x, y

Cartesian coordinates

Greek symbols


Divergence angle


Boltzmann constant [m2 kg s−2 K−1]


Molecular mean free path [m]


Inlet-to-outlet pressure ratio


Density [kg m−3]


Viscosity index
















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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.High-Performance Computing (HPC) Laboratory, Department of Mechanical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Materials Science and EngineeringDelft University of TechnologyDelftThe Netherlands

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