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One and two component weakly nonlocal fluids Peter Ván BUTE, Department of Chemical Physics –Nonequilibrium thermodynamics - weakly nonlocal theories.

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Presentation on theme: "One and two component weakly nonlocal fluids Peter Ván BUTE, Department of Chemical Physics –Nonequilibrium thermodynamics - weakly nonlocal theories."— Presentation transcript:

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2 One and two component weakly nonlocal fluids Peter Ván BUTE, Department of Chemical Physics –Nonequilibrium thermodynamics - weakly nonlocal theories –One component fluid mechanics - quantum (?) fluids –Two component fluid mechanics - granular material –Conclusions

3 –Thermodynamics = macrodynamics –Weakly nonlocal = there are more gradients –Examples: Guyer-Krumhans Ginzburg-Landau Cahn-Hilliard (- Frank) other phase field.

4 Classical Irreversible Thermodynamics Local equilibrium (~ there is no microstructure) Beyond local equilibrium (nonlocality): in time (memory effects) in space (structure effects) dynamic variables ?

5 Nonlocalities: Restrictions from the Second Law.

6 Nonequilibrium thermodynamics basic balances – basic state: – constitutive state: – constitutive functions: weakly nonlocal Second law: Constitutive theory Method: Liu procedure, Lagrange-Farkas multipliers Special: irreversible thermodynamics (universality)

7 Example 1 : One component weakly nonlocal fluid Liu procedure (Farkas’s lemma): constitutive state constitutive functions basic state

8 Schrödinger-Madelung fluid (Fisher entropy)

9 Potential form: Bernoulli equation Euler-Lagrange form Schrödinger equation Remark: Not only quantum mechanics - more nonlocal fluids - structures (cosmic) - stability (strange) Oscillator

10 Example 2: Two component weakly nonlocal fluid density of the solid component volume distribution function constitutive functions basic state constitutive state

11 Constraints: isotropic, second order Liu equations

12 Solution: Simplification:

13 PrPr Coulomb-Mohr isotropy: Navier-Stokes like +... Entropy inequality:

14 Properties 1 Other models: a) Goodman-Cowin configurational force balance b) Navier-Stokes type:somewhere

15 N S t s unstable stable 2 Coulomb-Mohr

16 3 solid-fluid(gas) transition relaxation (1D) 4 internal spin: no corrections

17 Conclusions -- Phenomenological background - for any statistical-kinetic theory - Kaniadakis (kinetic), Plastino (maxent) -- Nontrivial material (in)stability - not a Ginzburg-Landau - phase ‘loss’

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