메뉴 건너뛰기




Volumn 389, Issue 7, 2010, Pages 1297-1316

Bi-velocity transport processes. Single-component liquid and gaseous continua

Author keywords

Burnett equations; Hydrodynamics; Irreversible thermodynamics; Onsager reciprocity; Transport processes

Indexed keywords

BINARY MIXTURES; BOLTZMANN EQUATION; CONSTITUTIVE EQUATIONS; GASES; HYDRODYNAMICS; INTEGRAL EQUATIONS; KINETIC THEORY OF GASES; LIQUIDS; THERMAL EXPANSION; THERMODYNAMICS; VELOCITY;

EID: 73449145941     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.12.022     Document Type: Article
Times cited : (19)

References (63)
  • 1
    • 67349278753 scopus 로고    scopus 로고
    • Bi-velocity hydrodynamics
    • Brenner H. Bi-velocity hydrodynamics. Physica A 388 (2009) 3391-3398
    • (2009) Physica A , vol.388 , pp. 3391-3398
    • Brenner, H.1
  • 2
    • 67649487937 scopus 로고    scopus 로고
    • Bi-velocity hydrodynamics: Single-component fluids
    • Brenner H. Bi-velocity hydrodynamics: Single-component fluids. Internat. J. Eng. Sci. 47 (2009) 930-958
    • (2009) Internat. J. Eng. Sci. , vol.47 , pp. 930-958
    • Brenner, H.1
  • 3
    • 67649470371 scopus 로고    scopus 로고
    • Bi-velocity hydrodynamics. Multicomponent fluids
    • Brenner H. Bi-velocity hydrodynamics. Multicomponent fluids. Internat. J. Eng. Sci. 47 (2009) 902-929
    • (2009) Internat. J. Eng. Sci. , vol.47 , pp. 902-929
    • Brenner, H.1
  • 7
    • 12344295474 scopus 로고    scopus 로고
    • Kinematics of volume transport
    • Brenner H. Kinematics of volume transport. Physica A 349 (2005) 10-59
    • (2005) Physica A , vol.349 , pp. 10-59
    • Brenner, H.1
  • 8
    • 73449106892 scopus 로고    scopus 로고
    • It is pointed out in footnote (10) of Ref. [2] that the choice of the symbol and name for this velocity is arbitrary in the absence of additional physical information
    • It is pointed out in footnote (10) of Ref. [2] that the choice of the symbol and name for this velocity is arbitrary in the absence of additional physical information
  • 11
    • 36149006492 scopus 로고
    • Reciprocal relations in irreversible processes
    • Onsager L. Reciprocal relations in irreversible processes. I, Phys. Rev. 37 (1931) 405-426
    • (1931) I, Phys. Rev. , vol.37 , pp. 405-426
    • Onsager, L.1
  • 12
    • 36149006040 scopus 로고
    • Reciprocal relations in irreversible processes. II
    • Onsager L. Reciprocal relations in irreversible processes. II. Phys. Rev. 38 (1931) 2265-2279
    • (1931) Phys. Rev. , vol.38 , pp. 2265-2279
    • Onsager, L.1
  • 13
    • 36149003004 scopus 로고
    • On Onsager's principle of microscopic reversibility
    • Casimir H.B.G. On Onsager's principle of microscopic reversibility. Rev. Modern Phys. 17 (1945) 343-350
    • (1945) Rev. Modern Phys. , vol.17 , pp. 343-350
    • Casimir, H.B.G.1
  • 16
    • 0004080557 scopus 로고    scopus 로고
    • Princeton Univ. Press, Princeton, New Jersey
    • Debenedetti P.G. Metastable Liquids (1996), Princeton Univ. Press, Princeton, New Jersey
    • (1996) Metastable Liquids
    • Debenedetti, P.G.1
  • 17
    • 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
  • 18
    • 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
  • 20
    • 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
  • 22
    • 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
  • 23
    • 67149110240 scopus 로고    scopus 로고
    • A nonmolecular derivation of Maxwell's thermal-creep boundary condition for gases and liquids via application of the LeChatelier-Braun principle to Maxwell's thermal stress
    • 053602-10
    • Brenner H. A nonmolecular derivation of Maxwell's thermal-creep boundary condition for gases and liquids via application of the LeChatelier-Braun principle to Maxwell's thermal stress. Phys. Fluids 21 (2009) 053602-10
    • (2009) Phys. Fluids , vol.21
    • Brenner, H.1
  • 24
    • 33745659657 scopus 로고    scopus 로고
    • Thermophoretic motion of a slightly deformed sphere through a viscous fluid
    • Mohan A., and Brenner H. Thermophoretic motion of a slightly deformed sphere through a viscous fluid. SIAM J. Appl. Math. 66 (2006) 787-801
    • (2006) SIAM J. Appl. Math. , vol.66 , pp. 787-801
    • Mohan, A.1    Brenner, H.2
  • 25
    • 0001722720 scopus 로고
    • Note on the conditions at the surface of contact of a fluid with a solid body
    • Clarendon Press, Oxford
    • Goldstein S. Note on the conditions at the surface of contact of a fluid with a solid body. Modern Developments in Fluid Dynamics vol. II (1938), Clarendon Press, Oxford 676-680
    • (1938) Modern Developments in Fluid Dynamics , vol.II , pp. 676-680
    • Goldstein, S.1
  • 26
    • 0010213518 scopus 로고
    • Fluid mechanics in the first half of this century
    • Goldstein S. Fluid mechanics in the first half of this century. Ann. Rev. Fluid Mech. 1 (1969) 1-28
    • (1969) Ann. Rev. Fluid Mech. , vol.1 , pp. 1-28
    • Goldstein, S.1
  • 27
    • 84976128750 scopus 로고
    • On the no-slip boundary condition
    • Richardson S. On the no-slip boundary condition. J. Fluid Mech. 59 (1973) 707-719
    • (1973) J. Fluid Mech. , vol.59 , pp. 707-719
    • Richardson, S.1
  • 28
    • 0023738371 scopus 로고
    • Determination of the macroscopic (partial) slip boundary condition over a randomly rough surface with a perfect slip microscopic boundary condition
    • Jansons K.M. Determination of the macroscopic (partial) slip boundary condition over a randomly rough surface with a perfect slip microscopic boundary condition. Phys. Fluids 31 (1988) 15-17
    • (1988) Phys. Fluids , vol.31 , pp. 15-17
    • Jansons, K.M.1
  • 29
    • 0030153046 scopus 로고    scopus 로고
    • Effective boundary conditions for Stokes flow over a rough surface
    • Sarkar K., and Prosperetti A. Effective boundary conditions for Stokes flow over a rough surface. J. Fluid. Mech. 316 (1996) 223-240
    • (1996) J. Fluid. Mech. , vol.316 , pp. 223-240
    • Sarkar, K.1    Prosperetti, A.2
  • 30
    • 0034206383 scopus 로고    scopus 로고
    • Molecular wall effects: Are conditions at a boundary boundary conditions?
    • Brenner H., and Ganesan V. Molecular wall effects: Are conditions at a boundary boundary conditions?. Phys. Rev. E 61 (2000) 6879-6897
    • (2000) Phys. Rev. E , vol.61 , pp. 6879-6897
    • Brenner, H.1    Ganesan, V.2
  • 31
    • 28544445269 scopus 로고    scopus 로고
    • Microfluidics: The no-slip boundary condition
    • Foss J., Tropea. C., and Yarin A. (Eds), Springer, New York (Chapter 15)
    • Lauga E., Brenner M.P., and Stone H.A. Microfluidics: The no-slip boundary condition. In: Foss J., Tropea. C., and Yarin A. (Eds). Handbook of Experimental Fluid Dynamics (2005), Springer, New York (Chapter 15)
    • (2005) Handbook of Experimental Fluid Dynamics
    • Lauga, E.1    Brenner, M.P.2    Stone, H.A.3
  • 33
    • 0000911805 scopus 로고
    • On stresses in rarified [sic] gases resulting from inequalities of temperature
    • Maxwell J.C. On stresses in rarified [sic] gases resulting from inequalities of temperature. Philos. Trans. R. Soc. Lond. A 170 (1879) 231-262
    • (1879) Philos. Trans. R. Soc. Lond. A , vol.170 , pp. 231-262
    • Maxwell, J.C.1
  • 35
    • 0032347474 scopus 로고    scopus 로고
    • Maxwell's thermal creep in two space dimensions
    • To quote these authors: "Only a rough explanation of thermal creep was available to Maxwell. Our present understanding is not much better, and remains only semiquantitative"
    • Shida K., and Hoover W.G. Maxwell's thermal creep in two space dimensions. J. Phys. Soc. Japan 67 (1998) 2277-2280 To quote these authors: "Only a rough explanation of thermal creep was available to Maxwell. Our present understanding is not much better, and remains only semiquantitative"
    • (1998) J. Phys. Soc. Japan , vol.67 , pp. 2277-2280
    • Shida, K.1    Hoover, W.G.2
  • 36
    • 0000614811 scopus 로고
    • Thermal creep in rarefied gas
    • Sone Y. Thermal creep in rarefied gas. J. Phys. Soc. Japan 21 (1966) 1836-1837
    • (1966) J. Phys. Soc. Japan , vol.21 , pp. 1836-1837
    • Sone, Y.1
  • 37
    • 31344465939 scopus 로고    scopus 로고
    • A continuum model of thermal transpiration
    • Bielenberg J.R., and Brenner H. A continuum model of thermal transpiration. J. Fluid Mech. 546 (2006) 1-23
    • (2006) J. Fluid Mech. , vol.546 , pp. 1-23
    • Bielenberg, J.R.1    Brenner, H.2
  • 38
    • 73449116812 scopus 로고    scopus 로고
    • Earlier empirical demonstrations [18,29] that the no-slip condition boundary condition applied generally to vv rather than to vm did not, at the time, recognize the existence of the pressure gradient contribution to the diffuse flux of appearing in Eq, 3.20, That is, as opposed to the present bi-velocity arguments, those earlier monovelocity arguments did not recognize the necessity for the ∇ p term in (3.20, However, it is shown in Appendix B that the ∇ p contribution to jv is negligible compared with that of ∇ T when interpreting both the thermophoretic and thermal transpiration experiments used in establishing the viability of 5.4, As such, those earlier experimental demonstrations of the validity of of the no-slip velocity boundary condition continue to remain valid in our current bi-velocity re-interpretation of these data
    • v is negligible compared with that of ∇ T when interpreting both the thermophoretic and thermal transpiration experiments used in establishing the viability of (5.4). As such, those earlier experimental demonstrations of the validity of of the no-slip volume velocity boundary condition continue to remain valid in our current bi-velocity re-interpretation of these data
  • 40
    • 34250807849 scopus 로고    scopus 로고
    • Measurements of thermophoretic velocities of aerosol particles in microgravity conditions in different carrier gases
    • Prodi F., Santachiara G., Di Matteo 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    Di Matteo, L.3    Vedernikov, A.4    Beresnev, S.A.5    Chernyak, V.G.6
  • 42
    • 0001904431 scopus 로고
    • Fisher S.S. (Ed), AIAA, New York
    • Talbot L. In: Fisher S.S. (Ed). Rarefied Gas Dynamics. Prog. Astronaut & Aeronaut. vol. 74, part 1 (1981), AIAA, New York 467-xxx
    • (1981) Prog. Astronaut & Aeronaut. , vol.74 PART 1
    • Talbot, L.1
  • 44
    • 0036027965 scopus 로고    scopus 로고
    • Measurements of diffusiophoretic velocities of aerosol particles in the transition region
    • Prodi F., Santachiara G., and Cornetti C. Measurements of diffusiophoretic velocities of aerosol particles in the transition region. J. Aerosol Sci. 33 (2002) 181-188
    • (2002) J. Aerosol Sci. , vol.33 , pp. 181-188
    • Prodi, F.1    Santachiara, G.2    Cornetti, C.3
  • 45
    • 0038595314 scopus 로고
    • The theory of thermophoresis and diffusiophoresis of aerosol particles and their experimental testing
    • Hidy G.M., and Brock J.R. (Eds), Pergamon Press, Oxford
    • Derjaguin B., and Yalamov Y. The theory of thermophoresis and diffusiophoresis of aerosol particles and their experimental testing. In: Hidy G.M., and Brock J.R. (Eds). Topics in Current Aerosol Research, vol. 3, part 2 (1972), Pergamon Press, Oxford 1-200
    • (1972) Topics in Current Aerosol Research, vol. 3, part 2 , pp. 1-200
    • Derjaguin, B.1    Yalamov, Y.2
  • 46
    • 33748924841 scopus 로고    scopus 로고
    • Elementary kinematical model of thermal diffusion in liquids and gases
    • 036306-1-20
    • Brenner H. Elementary kinematical model of thermal diffusion in liquids and gases. Phys. Rev. E 74 (2006) 036306-1-20
    • (2006) Phys. Rev. E , vol.74
    • Brenner, H.1
  • 47
    • 67349178095 scopus 로고    scopus 로고
    • Pressure-driven diffusive gas flows in micro-channels: From the Knudsen to the continuum regime
    • Dongari N., Sharma A., and Durst F. Pressure-driven diffusive gas flows in micro-channels: From the Knudsen to the continuum regime. Microfluidics Nanofluidics (2009) 679-692
    • (2009) Microfluidics Nanofluidics , pp. 679-692
    • Dongari, N.1    Sharma, A.2    Durst, F.3
  • 51
    • 85108215622 scopus 로고    scopus 로고
    • s = 0 for an isentropic process, over(s, ̂) = const., as would be expected to hold in such circumstances
    • s = 0 for an isentropic process, over(s, ̂) = const., as would be expected to hold in such circumstances
  • 52
    • 85108206799 scopus 로고    scopus 로고
    • Analogous to the case for entropy [38, to the extent that the constitutive equation (7.5) is valid, it would follow from (7.7) that πv, 0 for an isochoric process, over(v, ̂) = const, as would be expected in such circumstances
    • v = 0 for an isochoric process, over(v, ̂) = const., as would be expected in such circumstances
  • 53
    • 0006886326 scopus 로고    scopus 로고
    • Fourier's law: A challenge to theorists
    • Imperial College Press, London
    • Bonetto F., Lebowitz J.L., and Rey-Bellet L. Fourier's law: A challenge to theorists. Mathematical Physics (2000), Imperial College Press, London 128-150
    • (2000) Mathematical Physics , pp. 128-150
    • Bonetto, F.1    Lebowitz, J.L.2    Rey-Bellet, L.3
  • 56
    • 0003107810 scopus 로고
    • On the reciprocal relations of Onsager
    • Coleman B.D., and Truesdell C. On the reciprocal relations of Onsager. J. Chem. Phys. 33 (1960) 28-31
    • (1960) J. Chem. Phys. , vol.33 , pp. 28-31
    • Coleman, B.D.1    Truesdell, C.2
  • 57
    • 73449140517 scopus 로고    scopus 로고
    • By unbiased we mean without constitutive commitment except for the fact that the specific momentum density appearing in the momentum equation is vm (see Ref, 45, that the velocity appearing in the kinetic-energy term of the energy equation is also vm, and that the constitutive equation for the diffuse entropy flux is given by Eq, 3.2) in which the constitutive equation for the symbol q is left open. The basis for these particular constitutive choices is discussed in Refs, 1,2
    • m, and that the constitutive equation for the diffuse entropy flux is given by Eq. (3.2) in which the constitutive equation for the symbol q is left open. The basis for these particular constitutive choices is discussed in Refs. [1,2]
  • 58
    • 67349171698 scopus 로고    scopus 로고
    • Inconsistency of a dissipative contribution to the mass flux in hydrodynamics
    • (8 pp.)
    • Öttinger H.C., Struchtrup H., and Liu M. Inconsistency of a dissipative contribution to the mass flux in hydrodynamics. Phys. Rev. E 80 (2009) 056303 (8 pp.)
    • (2009) Phys. Rev. E , vol.80 , pp. 056303
    • Öttinger, H.C.1    Struchtrup, H.2    Liu, M.3
  • 59
    • 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
  • 60
    • 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
  • 61
    • 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
  • 62
    • 73449139503 scopus 로고    scopus 로고
    • That the work of the Russian school has seemingly failed to impress Western-based LIT researchers (as judged by the paucity of citations thereto in the Western literature devoted to irreversible thermodynamics) presumably originates from the fact that this Russian work fails to cite data in support of its thesis
    • That the work of the Russian school has seemingly failed to impress Western-based LIT researchers (as judged by the paucity of citations thereto in the Western literature devoted to irreversible thermodynamics) presumably originates from the fact that this Russian work fails to cite data in support of its thesis
  • 63
    • 26344468007 scopus 로고
    • A model for collision processes in gases. 1. Small amplitude processes in charged and neutral one-component systems
    • Bhatnagar P.L., Gross E.P., and Krook M. A model for collision processes in gases. 1. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (1954) 511-525
    • (1954) Phys. Rev. , vol.94 , pp. 511-525
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.