## DIMACS TR: 2000-31

## Binary Fluids with Long Range Segregating Interaction I:

Derivation of Kinetic and Hydrodynamic Equations

### Authors: S. Bastea, R. Esposito, J. L. Lebowitz and R. Marra

**
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 Vlasov-Navier-Stokes equations.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-31.ps.gz

DIMACS Home Page