×

An analysis of single and double generator thermodynamic formalisms for the macroscopic description of complex fluids. (English) Zbl 0932.76007

Several seemingly distinct formalisms have been developed recently as an alternative to the modern conventional approach (based on balance equations) for describing the mechanics and thermodynamics of complex fluids under dynamical conditions. Two of these approaches for isolated thermodynamic systems are the single generator bracket formalism and the more recent GENERIC formalism incorporating a second generating functional. The interrelationships between these two alternate approaches are examined on an abstract level, and direct connections are determined for some specific examples of fluid systems: a compressible, nonisothermal, isotropic fluid, an arbitrary fluid with an unspecified internal variable, and a chemically reactive fluid system.

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
80A17 Thermodynamics of continua
82D15 Statistical mechanics of liquids
80A32 Chemically reacting flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lhuillier D., J. Mec. 19 pp 1– (1980)
[2] DOI: 10.1016/0020-7225(83)90056-3 · Zbl 0513.73002 · doi:10.1016/0020-7225(83)90056-3
[3] DOI: 10.1088/0034-4885/53/1/001 · doi:10.1088/0034-4885/53/1/001
[4] DOI: 10.1007/3-540-53996-4_41 · doi:10.1007/3-540-53996-4_41
[5] DOI: 10.1122/1.550592 · doi:10.1122/1.550592
[6] DOI: 10.1016/0375-9601(84)90297-4 · doi:10.1016/0375-9601(84)90297-4
[7] DOI: 10.1016/0375-9601(88)90243-5 · doi:10.1016/0375-9601(88)90243-5
[8] DOI: 10.1088/0305-4470/24/11/014 · Zbl 0735.73011 · doi:10.1088/0305-4470/24/11/014
[9] DOI: 10.1103/PhysRevE.56.6620 · doi:10.1103/PhysRevE.56.6620
[10] DOI: 10.1103/PhysRevE.56.6620 · doi:10.1103/PhysRevE.56.6620
[11] DOI: 10.1103/PhysRevE.57.1416 · doi:10.1103/PhysRevE.57.1416
[12] DOI: 10.1515/jnet.1996.21.2.175 · Zbl 0877.73004 · doi:10.1515/jnet.1996.21.2.175
[13] DOI: 10.1016/S0378-4371(96)00249-X · doi:10.1016/S0378-4371(96)00249-X
[14] Liu I. S., Arch. Rat. Mech. Anal. 46 pp 131– (1972)
[15] DOI: 10.1515/jnet.1997.22.4.356 · Zbl 0910.76003 · doi:10.1515/jnet.1997.22.4.356
[16] DOI: 10.1016/0375-9601(84)90634-0 · doi:10.1016/0375-9601(84)90634-0
[17] DOI: 10.1016/0375-9601(84)90635-2 · doi:10.1016/0375-9601(84)90635-2
[18] DOI: 10.1016/0167-2789(86)90209-5 · Zbl 0661.70025 · doi:10.1016/0167-2789(86)90209-5
[19] DOI: 10.1088/0305-4470/22/20/015 · Zbl 0706.76007 · doi:10.1088/0305-4470/22/20/015
[20] DOI: 10.1016/0375-9601(85)90797-2 · doi:10.1016/0375-9601(85)90797-2
[21] DOI: 10.1016/0167-2789(86)90001-1 · Zbl 0615.76093 · doi:10.1016/0167-2789(86)90001-1
[22] Edwards B. J., Phys. Rev.K 56 pp 4097– (1997)
[23] DOI: 10.2307/1999527 · Zbl 0529.58011 · doi:10.2307/1999527
[24] DOI: 10.1063/1.866987 · Zbl 0656.76002 · doi:10.1063/1.866987
[25] DOI: 10.1088/0305-4470/23/14/030 · doi:10.1088/0305-4470/23/14/030
[26] DOI: 10.1021/ie00053a009 · doi:10.1021/ie00053a009
[27] Rivlin R. S., J. Acoust. Soc.Am. 40 pp 1213– (1966)
[28] DOI: 10.1017/S0022112096001310 · Zbl 0857.76034 · doi:10.1017/S0022112096001310
[29] DOI: 10.1063/1.872210 · doi:10.1063/1.872210
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.