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- Nika, Grigor
(författare)
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A gradient system for a higher-gradient generalization of Fourier’s law of heat conduction
- 2023
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Ingår i: Modern physics letters B. - : World Scientific. - 0217-9849 .- 1793-6640. ; 37:11, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- We derive a generalized heat conduction problem for a rarefied gas at slip regime from a gradient system where the driving functional is the entropy. Specifically, we construct an Onsager system (X,S,Kheat) such that the associated evolution of the system is given by ∂tu=+Kheat(u)DS(u), where the Onsager operator, Kheat(u), contains higher-gradients of the absolute temperature u. Moreover, through Legendre-Fenchel theory we write the Onsager system as a classical gradient system (X,S,G) with an induced gradient flow equation, ∂tu=∇GDS(u). We demonstrate the usefulness of the approach by modeling scale-size thermal effects in periodic media that have been recently observed experimentally.
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| 2. |
- Zhdanov, Vladimir, 1952
(författare)
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Unification: Viscosity, permittivity, and hydration forces near an interface
- 2023
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Ingår i: Modern Physics Letters B. - 0217-9849. ; 37
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Tidskriftsartikel (refereegranskat)abstract
- In water-based solutions near interfaces, the hydration forces, dielectric permittivity, and viscosity depend on the short-range order in the arrangement of water molecules. The former two quantities were earlier rationalized by employing the Ginzburg-Landau expression for the solution free energy. Driven by the spirit of unification, we show that the dependence of the viscosity coefficient on the coordinate perpendicular to the interface can be rationalized in this framework as well by using in addition a linear Evans-Polanyi correlation between the activation energy determining viscosity and the solution free energy. In the conventional hydrodynamics, this effect is often formally described by introducing the partial-slip boundary conditions or a stagnant layer near interfaces. We show how the corresponding slip or stagnant-layer length can be explained and quantified.
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