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Rarefaction and compressibility effects on steady and transient gas flows in microchannels

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Abstract

The main theoretical and experimental results from the literature about steady pressure-driven gas microflows are summarized. Among the different gas flow regimes in microchannels, the slip flow regime is the most frequently encountered. For this reason, the slip flow regime is particularly detailed and the question of appropriate choice of boundary conditions is discussed. It is shown that using second-order boundary conditions allows us to extend the applicability of the slip flow regime to higher Knudsen numbers that are usually relevant to the transition regime.

The review of pulsed flows is also presented, as this kind of flow is frequently encountered in micropumps. The influence of slip on the frequency behavior (pressure gain and phase) of microchannels is illustrated. When subjected to sinusoidal pressure fluctuations, microdiffusers reveal a diode effect which depends on the frequency. This diode effect may be reversed when the depth is shrunk from a few hundred to a few μm.

Thermally driven flows in microchannels are also described. They are particularly interesting for vacuum generation using microsystems without moving parts.

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Abbreviations

a :

Aspect ratio, h/b (dimensionless)

a i :

Widths of microdiffusers (m)

A i :

Coefficients for second-order slip flow models (dimensionless)

b :

Width (m)

c :

Mean-square molecular speed (m s−1)

d :

Molecular diameter (m)

E :

Diode efficiency (dimensionless)

Eck :

Eckert number (dimensionless)

h :

Microchannel depth (m)

k :

Boltzmann constant (J K−1)

Kn :

Knudsen number, λ/2h (dimensionless)

L :

Characteristic length of the studied volume (m)

L i :

Lengths of diffusers parts (m)

l :

Microchannel length (m)

l SV :

Characteristic length of a sampling volume (m)

m :

Mass of a molecule (kg)

Ma :

Mach number (dimensionless)

n :

Number density (m−3)

\(\ifmmode\expandafter\dot\else\expandafter\.\fi{N} \) :

Molecular flux (s−1)

P :

Pressure (Pa)

p :

Fluctuating pressure (Pa)

P* :

Pressure gain (dimensionless)

p* :

Fluctuating pressure gain (dimensionless)

Pra :

Prandtl number (dimensionless)

q :

Mass flow rate (kg s-1)

q* :

Reduced mass flow rate, q/q NS0 (dimensionless)

r :

Specific gas constant (J mol−1 K−1)

Re :

Reynolds number (dimensionless)

Sc :

Schmidt number (dimensionless)

T :

Temperature (K)

U :

Tangential velocity (m s−1)

Π:

Inlet over outlet pressure ratio, P i/P o (dimensionless)

α :

Diffuser angle (rad)

δ :

Mean molecular spacing (m)

ϕ :

Phase (rad)

γ :

Ratio of specific heats (dimensionless)

λ :

Mean free path (m)

ρ :

Density (m3s−1)

σ :

Tangential momentum accommodation coefficient (dimensionless)

σ T :

Thermal accommodation coefficient (dimensionless)

τ :

Characteristic time of intermolecular collisions (s)

i:

Inlet

n:

Normal direction

NS0:

Navier-Stokes model with no-slip boundary conditions

NS1:

Navier-Stokes model with first-order slip flow boundary conditions

NS2 :

Navier-Stokes model with second order slip flow boundary conditions

QHD1:

Quasihydrodynamic model with first-order slip flow boundary conditions

o:

Outlet

t:

Tangential direction

w:

Wall

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  1. LGMT—Institut National des Sciences Appliquées, 31077, Toulouse Cedex 4, France

    Stéphane Colin

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Colin, S. Rarefaction and compressibility effects on steady and transient gas flows in microchannels. Microfluid Nanofluid 1, 268–279 (2005). https://doi.org/10.1007/s10404-004-0002-y

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