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Feb 2013

Volume 54, Issue 2, Articles (02xxxx)

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J. Math. Phys. 54, 021506 (2013); http://dx.doi.org/10.1063/1.4790887 (24 pages)

Gui-Qiang Chen, Vaibhav Kukreja, and Hairong Yuan
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back to top Fluids

Extended thermodynamics of charged gases with many moments

M. C. Carrisi and S. Pennisi

J. Math. Phys. 54, 023101 (2013); http://dx.doi.org/10.1063/1.4789544 (18 pages)

Online Publication Date: 1 February 2013

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Recently a model with many moments for the description of relativistic gases has been studied and an exact closure has been found, depending on an arbitrary set of single variable functions. In the case of a charged gas and when the electromagnetic field acts as an external force, the exploitation of the entropy principle produces an additional condition. A closure compatible with this further condition has been found, when the highest order moment has an even number of free indexes. It amounts in restrictions on the arbitrary single variable functions appearing in the general case. They are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants. When the highest order moment has an odd number M of free indexes the further condition is different from that appearing in the case M even and alternative techniques must be used to find a closure compatible with it. In this paper we take into account this last model and we find a closure compatible with the further condition. As well as in the case M even, also in the case M odd we find that the arbitrary single variable functions of the general theory are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants.
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05.70.Ce Thermodynamic functions and equations of state
02.10.Ab Logic and set theory
02.10.De Algebraic structures and number theory

Effects of Marangoni numbers on thermocapillary drop migration: Constant for quasi-steady state?

Zuo-Bing Wu and Wen-Rui Hu

J. Math. Phys. 54, 023102 (2013); http://dx.doi.org/10.1063/1.4792476 (10 pages)

Online Publication Date: 22 February 2013

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The overall steady-state energy balance with two phases in a flow domain requires that the change in energy of the domain is equal to the difference between the total energy entering the domain and that leaving the domain. From the condition, the integral thermal flux across the surface is studied for a steady thermocapillary drop migration in a flow field with uniform temperature gradient at small and large Marangoni (Reynolds) numbers. The drop is assumed to have only a slight axisymmetric deformation from a sphere. It is identified that a conservative/nonconservative integral thermal flux across the surface in the steady thermocapillary drop migration at small/large Marangoni (Reynolds) numbers. The conservative flux confirms the assumption of quasi-steady state in the thermocapillary drop migration at small Marangoni (Reynolds) numbers. The nonconservative flux may well result from the invalid assumption of quasi-steady state, which indicates that the thermocapillary drop migration at large Marangoni (Reynolds) numbers cannot reach steady state and is thus a unsteady process.
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47.55.dm Thermocapillary effects
47.55.nb Capillary and thermocapillary flows
68.03.Cd Surface tension and related phenomena
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