Oscillatory Couette flow at arbitrary oscillation frequency over the whole range of the Knudsen number
Tóm tắt
The oscillatory Couette flow is important for further advancement of microengineering. In practice the size of the microfluidics can be so small that it can be compared with the molecular mean free path. Moreover, the oscillation frequency can be close to that of the intermolecular collisions. Under such conditions the problem must be solved on the kinetic level. In the present work, the oscillatory Couette flow is considered on the basis of the non-stationary kinetic equation. The solution to the problem is determined by two parameters: the Knudsen number and the ratio of collision frequency to oscillation frequency. The kinetic equation is solved by the discrete velocity method over the wide range of both parameters.
Tài liệu tham khảo
Abramowitz M, Stegun IA (eds) (1972) Handbook of mathematical functions with formulas, graphs and mathematical tables, 9 edn. Dover, New York
Bhatnagar PL, Gross EP, Krook MA (1954) A model for collision processes in gases. Phys Rev 94:511–525
Cercignani C, Pagani CD (1966) Variational approach to boundary value problems in kinetic theory. Phys Fluids 9(6):1167–1173
Gross EP, Ziering S (1958) Kinetic theory of linear shear flow. Phys Fluids 1(3):215–224
Hadjiconstantinou NG (2005) Oscillatory shear-driven gas flows in the transition and free-molecular flow regimes. Phys Fluids 17(100):611–619
Landau LD, Lifshitz EM (1989) Fluid mechanics. Pergamon, New York
Loyalka SK, Petrellis N, Storvik TS (1979) Some exact numerical results for the BGK model: Couette, Poiseuille and thermal creep flow between parallel plates. Z Angew Math Phys (ZAMP) 30:514–521
Marques Jr W, Kremer GM, Sharipov FM (2000) Couette flow with slip and jump boundary conditions. Continuum Mech Thermodyn 16(6):379–386
Naris S, Valougeorgis D (2005) The driven cavity flow over the whole range of the Knudsen number. Phys Fluids 17(9):097–106
Park JH, Bahukudumbi P, Beskok A (2004) Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime. Phys Fluids 16(2):317–330
Sharipov F (2003) Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. II. Slip and jump coefficients. Eur J Mech B Fluids 22:133–143
Sharipov F, Kalempa D (2003) Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient. Phys Fluids 15(6):1800–1806
Sharipov F, Kalempa D (2007) Gas flow near a plate oscillating longitudinally with an arbitrary frequency. Phys Fluids 19(1):017–110
Sharipov F, Seleznev V (1998) Data on internal rarefied gas flows. J Phys Chem Ref Data 27(3):657–706
Sharipov F, Marques Jr W, Kremer GM (2002) Free molecular sound propagation. J Acoust Soc Am 112(2):395–401
Sharipov F, Cumin LMG, Kalempa D (2004) Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number. Eur J Mech B Fluids 23:899–906
Siewert CE (2002) Poiseuille, thermal creep and Couette flow: results based on the CES model for the linearized Boltzmann equation. Eur J Mech B Fluids 21:579–597
Siewert CE, Sharipov F (2002) Model equations in rarefied gas dynamics: viscous-slip and thermal-slip coefficients. Phys Fluids 14(12):4123–4129
Sone Y, Takata S, Ohwada T (1990) Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules. Eur J Mech B Fluids 9(3):273–288
Valougeorgis D, Naris S (2003) Acceleration schemes of the discrete velocity method: gaseous flows in rectangular microchannels. SIAM J Sci Comp 25(2):534–552
Willis DR (1962) Comparison of kinetic theory analyses of linearized Coutte flow. Phys Fluids 5:127–135