- 01-133 S. Bastea, R.Esposito, J. L. Lebowitz, R. Marra
- Binary Fluids with Long Range Segregating Interaction I:
Derivation of Kinetic and Hydrodynamic Equations.
(110K, TeX, 50 pages)
Apr 3, 01
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Abstract. We study the evolution of a two component fluid consisting of ``blue''
and ``red'' particles which interact via strong short range (hard core)
and weak long range pair potentials. At low temperatures the equilibrium
state of the system is one in which there are two coexisting phases.
Under suitable choices of space-time scalings and system parameters we
first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation
for the one particle position and velocity distribution functions,
appropriate for a description of the phase segregation kinetics in
this system. Further scalings then yield Vlasov-Euler and
incompressible Vlasov-Navier-Stokes equations. We also obtain, via the
usual truncation of the Chapman-Enskog expansion, compressible