메뉴 건너뛰기




Volumn 388, Issue 17, 2009, Pages 3391-3398

Bi-velocity hydrodynamics

Author keywords

Burnett equations; Irreversible thermodynamics; Multicomponent diffusion; Navier Stokes equations; Onsager reciprocity

Indexed keywords

BOLTZMANN EQUATION; DIFFUSION IN LIQUIDS; FLUID MECHANICS; INTEGRAL EQUATIONS; KINETIC THEORY OF GASES; TRANSPORT PROPERTIES; VELOCITY; VISCOUS FLOW;

EID: 67349278753     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.04.029     Document Type: Article
Times cited : (53)

References (50)
  • 5
    • 33748707170 scopus 로고    scopus 로고
    • On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids
    • Bedeaux D., Kjelstrup S., and Öttinger H.C. On a possible difference between the barycentric velocity and the velocity that gives translational momentum in fluids. Physica A 371 (2006) 177-187
    • (2006) Physica A , vol.371 , pp. 177-187
    • Bedeaux, D.1    Kjelstrup, S.2    Öttinger, H.C.3
  • 6
    • 41349102298 scopus 로고    scopus 로고
    • Is the tracer velocity of a fluid continuum equal to its mass velocity?
    • 061201-1 to 10
    • Brenner H. Is the tracer velocity of a fluid continuum equal to its mass velocity?. Phys. Rev. E 70 (2004) 061201-1 to 10
    • (2004) Phys. Rev. E , vol.70
    • Brenner, H.1
  • 7
    • 12344284937 scopus 로고    scopus 로고
    • Navier-Stokes revisited
    • Brenner H. Navier-Stokes revisited. Physica A 349 (2005) 60-132
    • (2005) Physica A , vol.349 , pp. 60-132
    • Brenner, H.1
  • 8
    • 33748624874 scopus 로고    scopus 로고
    • Fluid dynamics revisited
    • Brenner H. Fluid dynamics revisited. Physica A 370 (2006) 190-224
    • (2006) Physica A , vol.370 , pp. 190-224
    • Brenner, H.1
  • 9
    • 67349226992 scopus 로고    scopus 로고
    • note
    • In fact, rather than restricting attention solely to the single-component case, Bedeaux et al. investigated the more general multicomponent case.
  • 10
    • 40849135895 scopus 로고    scopus 로고
    • Comment on "Weakly and strongly consistent formulations of irreversible processes"
    • 098901-1
    • Liu M. Comment on "Weakly and strongly consistent formulations of irreversible processes". Phys. Rev. Lett. 100 (2008) 098901-1
    • (2008) Phys. Rev. Lett. , vol.100
    • Liu, M.1
  • 11
  • 12
    • 67349171698 scopus 로고    scopus 로고
    • On the impossibility of a dissipative contribution to the mass flux in hydrodynamics
    • submitted for publication
    • H.C. Öttinger, H. Struchtrup, M. Liu, On the impossibility of a dissipative contribution to the mass flux in hydrodynamics, Phys. Rev. E (2009) (submitted for publication)
    • (2009) Phys. Rev. E
    • Öttinger, H.C.1    Struchtrup, H.2    Liu, M.3
  • 13
    • 85108192922 scopus 로고    scopus 로고
    • note
    • m was criticized by Kostädt and Liu [13] as being incomplete.
  • 14
    • 4243315811 scopus 로고    scopus 로고
    • Three ignored densities, frame-independent thermodynamics, and broken Galilean symmetry
    • Kostädt P., and Liu M. Three ignored densities, frame-independent thermodynamics, and broken Galilean symmetry. Phys. Rev. E 58 (1998) 5535-5540
    • (1998) Phys. Rev. E , vol.58 , pp. 5535-5540
    • Kostädt, P.1    Liu, M.2
  • 15
    • 85108240446 scopus 로고    scopus 로고
    • note
    • v ≠ 0 or, equivalently, when the bi-velocity relation (9b) holds.
  • 16
    • 85108231055 scopus 로고    scopus 로고
    • note
    • v.
  • 19
    • 84926951060 scopus 로고
    • The distribution of velocities in a slightly non-uniform gas
    • Burnett D. The distribution of velocities in a slightly non-uniform gas. Proc. London Math. Soc. 39 (1935) 385-430
    • (1935) Proc. London Math. Soc. , vol.39 , pp. 385-430
    • Burnett, D.1
  • 20
    • 84960552756 scopus 로고
    • The distribution of molecular velocities and mean motion in a non-uniform gas
    • Burnett D. The distribution of molecular velocities and mean motion in a non-uniform gas. Proc. London Math. Soc. 40 (1936) 382-435
    • (1936) Proc. London Math. Soc. , vol.40 , pp. 382-435
    • Burnett, D.1
  • 22
    • 85108188035 scopus 로고    scopus 로고
    • note
    • 22 obtained in this purely theoretical manner is no different from that which would be obtained by actually performing low Reynolds number flow experiments.
  • 23
    • 0000637543 scopus 로고
    • Method of moments of Grad
    • Reinecke S., and Kremer G.M. Method of moments of Grad. Phys. Rev. A 42 (1990) 815-820
    • (1990) Phys. Rev. A , vol.42 , pp. 815-820
    • Reinecke, S.1    Kremer, G.M.2
  • 24
    • 67349184644 scopus 로고    scopus 로고
    • note
    • Our description of these efforts as being ad hoc stems from the fact that the constitutive relations used by these authors for the entropy production rate σ does not derive from use of Gibbs' relation (5) jointly with that for the diffuse entropy flux, Eq. (13). The net effect of this is that whereas in LIT each diffuse flux is uniquely and rationally assigned a single conjugate force in the entropy production-rate formulation, this is not true of either EIT or GNT; that is, constitutive expressions such as (15), involving two "forces" rather than one, essentially spring full-blown from those theories rather than possessing a wholly rational basis.
  • 25
    • 84980081651 scopus 로고
    • On the kinetic theory of rarefied gases
    • Grad H. On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2 (1949) 331-407
    • (1949) Comm. Pure Appl. Math. , vol.2 , pp. 331-407
    • Grad, H.1
  • 26
    • 0001294845 scopus 로고
    • Principles of the kinetic theory of gases
    • Flügge S. (Ed), Springer, Berlin
    • Grad H. Principles of the kinetic theory of gases. In: Flügge S. (Ed). Handbuch der Physik XII: Thermodynamik der Gase (1958), Springer, Berlin 205-294
    • (1958) Handbuch der Physik XII: Thermodynamik der Gase , pp. 205-294
    • Grad, H.1
  • 27
    • 0001351025 scopus 로고
    • Asympototic theory of the Boltzmann equation
    • Grad H. Asympototic theory of the Boltzmann equation. Phys. Fluids 6 (1963) 147-181
    • (1963) Phys. Fluids , vol.6 , pp. 147-181
    • Grad, H.1
  • 29
    • 48749121763 scopus 로고    scopus 로고
    • Beyond the Navier-Stokes equations: Burnett hydrodynamics
    • Garcia-Colin L.S., Velasco R.M., and Uribe F.J. Beyond the Navier-Stokes equations: Burnett hydrodynamics. Phys. Rep. 465 (2008) 149-189
    • (2008) Phys. Rep. , vol.465 , pp. 149-189
    • Garcia-Colin, L.S.1    Velasco, R.M.2    Uribe, F.J.3
  • 30
    • 22044451285 scopus 로고    scopus 로고
    • The method of moments and the nonequilibrium thermodynamics of rarefied gases
    • Zhdanov V.M., and Roldugin V.I. The method of moments and the nonequilibrium thermodynamics of rarefied gases. J. Exp. Theor. Phys. 86 (1998) 1141-1148
    • (1998) J. Exp. Theor. Phys. , vol.86 , pp. 1141-1148
    • Zhdanov, V.M.1    Roldugin, V.I.2
  • 31
    • 54649083292 scopus 로고    scopus 로고
    • Non-equilibrium thermodynamics and kinetic theory of rarefied gases
    • Zhdanov V.M., and Roldughin V.I. Non-equilibrium thermodynamics and kinetic theory of rarefied gases. Physics-Uspekhi 41 (1998) 349-378
    • (1998) Physics-Uspekhi , vol.41 , pp. 349-378
    • Zhdanov, V.M.1    Roldughin, V.I.2
  • 34
    • 34250403722 scopus 로고
    • (Shohavaliev), Transport phenomena in the Burnett approximation for multicomponent gas mixtures
    • Shavaliyev M.Sh. (Shohavaliev), Transport phenomena in the Burnett approximation for multicomponent gas mixtures. Fluid Dyn. 9 (1974) 96-104
    • (1974) Fluid Dyn. , vol.9 , pp. 96-104
    • Shavaliyev, M.Sh.1
  • 35
    • 85108223733 scopus 로고    scopus 로고
    • note
    • T = 0.
  • 36
    • 34548469703 scopus 로고
    • Stress induced diffusion in monatomic gases and gas suspensions
    • Annis B.K. Stress induced diffusion in monatomic gases and gas suspensions. Phys. Fluids 14 (1971) 269-277
    • (1971) Phys. Fluids , vol.14 , pp. 269-277
    • Annis, B.K.1
  • 37
    • 85108221442 scopus 로고    scopus 로고
    • note
    • 1.
  • 40
    • 0009300460 scopus 로고
    • Thermal conductivity of multicomponent gas mixtures
    • Muckenfuss C., and Curtiss C.F. Thermal conductivity of multicomponent gas mixtures. J. Chem. Phys. 29 (1958) 1273-1277
    • (1958) J. Chem. Phys. , vol.29 , pp. 1273-1277
    • Muckenfuss, C.1    Curtiss, C.F.2
  • 41
    • 0002494926 scopus 로고
    • Higher order approximation to the thermal conductivity of monatomic gas mixtures
    • see also
    • see also. Assael M.J., Wakeham W.A., and Kestin J. Higher order approximation to the thermal conductivity of monatomic gas mixtures. Int. J. Thermophys. 1 (1980) 7-32
    • (1980) Int. J. Thermophys. , vol.1 , pp. 7-32
    • Assael, M.J.1    Wakeham, W.A.2    Kestin, J.3
  • 42
    • 0001046665 scopus 로고
    • Effect of viscous transfer of momentum on diffusion in a gas mixture
    • Zhdanov V., Kagan Yu., and Sazykin A. Effect of viscous transfer of momentum on diffusion in a gas mixture. Sov. Phys. JETP 15 (1962) 596-602
    • (1962) Sov. Phys. JETP , vol.15 , pp. 596-602
    • Zhdanov, V.1    Kagan, Yu.2    Sazykin, A.3
  • 43
    • 33747375927 scopus 로고    scopus 로고
    • On a kinetic justification of the generalized nonequilibrium thermodynamics of multicomponent systems
    • Zhdanov V.M., and Roldugin V.I. On a kinetic justification of the generalized nonequilibrium thermodynamics of multicomponent systems. J. Exp. Theor. Phys. 95 (2002) 682-696
    • (2002) J. Exp. Theor. Phys. , vol.95 , pp. 682-696
    • Zhdanov, V.M.1    Roldugin, V.I.2
  • 44
    • 0037054371 scopus 로고    scopus 로고
    • Nonequilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces
    • (see esp. pp. 132-138)
    • Roldughin V.I., and Zhdanov V.M. Nonequilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces. Adv. Colloid Interface Sci. 98 (2002) 121-215 (see esp. pp. 132-138)
    • (2002) Adv. Colloid Interface Sci. , vol.98 , pp. 121-215
    • Roldughin, V.I.1    Zhdanov, V.M.2
  • 45
    • 33746761784 scopus 로고    scopus 로고
    • Multicomponent diffusion revisited
    • 07301-1 to 6
    • Lam S.H. Multicomponent diffusion revisited. Phys. Fluids 18 (2008) 07301-1 to 6
    • (2008) Phys. Fluids , vol.18
    • Lam, S.H.1
  • 46
    • 21744447597 scopus 로고    scopus 로고
    • A continuum theory of phoretic phenomena: Thermophoresis
    • Brenner H., and Bielenberg J.R. A continuum theory of phoretic phenomena: Thermophoresis. Physica A 355 (2005) 251-273
    • (2005) Physica A , vol.355 , pp. 251-273
    • Brenner, H.1    Bielenberg, J.R.2
  • 47
    • 34250807849 scopus 로고    scopus 로고
    • Measurements of thermophoretic velocities of aerosol particles in microgravity conditions in different carrier gases
    • Prodi F., Santachiara G., DiMatteo L., Vedernikov A., Beresnev S.A., and Chernyak V.G. Measurements of thermophoretic velocities of aerosol particles in microgravity conditions in different carrier gases. Aerosol Sci. 38 (2007) 645-655
    • (2007) Aerosol Sci. , vol.38 , pp. 645-655
    • Prodi, F.1    Santachiara, G.2    DiMatteo, L.3    Vedernikov, A.4    Beresnev, S.A.5    Chernyak, V.G.6
  • 50
    • 0015641928 scopus 로고
    • Theory of diffusiophoresis of spherical aerosol particles and of drag in a gas mixture
    • Annis B.K., Malinauskas A.P., and Mason E.A. Theory of diffusiophoresis of spherical aerosol particles and of drag in a gas mixture. Aerosol Sci. 4 (1973) 271-281
    • (1973) Aerosol Sci. , vol.4 , pp. 271-281
    • Annis, B.K.1    Malinauskas, A.P.2    Mason, E.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.