Visualising Multi-Phase Lattice Gas Fluid Layering Simulations

Complex fluids that exhibit phenomena such as layering and separation of multiple phases are computationally expensive to model using conventional numerical integration of partial differential equations. Lattice gas approaches are significantly cheaper to simulate and can still reveal good insights into the essential behaviours. We describe simulations of multi-phase layering in a lattice gas based on the Kawasaki exchange model and introduce a gravitational potential parameter to complement the temperature coupling. We identify the existence of some phase transitional behaviours in the number of phases as well as shifts in the critical temperature arising from the gravitational layering. We illustrate the model with graphical renderings in both two and three dimensions.

[1]  H. Eyring,et al.  An Elementary Theory of Condensation , 1939 .

[2]  Meakin,et al.  Invasion percolation in a destabilizing gradient. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[3]  K. Binder.  Applications of the Monte Carlo Method in Statistical Physics , 1984 .

[4]  K. Kawasaki.  Diffusion Constants near the Critical Point for Time-Dependent Ising Models. I , 1966 .

[5]  F. Ebrahimi.  The shape of invasion percolation clusters in random and correlated media , 2007, 0712.1287.

[6]  T. D. Lee,et al.  Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .

[7]  Jean-Pierre Rivet,et al.  Lattice Gas Hydrodynamics , 1987 .

[8]  K. Binder,et al.  Dynamic properties of the Monte Carlo method in statistical mechanics , 1973 .

[9]  P. Arratia.  Complex fluids at work , 2011 .

[10]  K. Kawasaki,et al.  Dynamics of fluctuations in Ostwald ripening: a new equation of motion for the structure function , 1987 .

[11]  Oliver Penrose,et al.  Kinetics of nucleation in a lattice gas model: Microscopic theory and simulation compared , 1983 .

[12]  R. Lenormand.  Liquids in porous media , 1990 .

[13]  M. Masihi,et al.  Invasion Percolation in Presence of Gravity , 2010 .

[14]  L. Yarrington,et al.  Gravity‐destabilized nonwetting phase invasion in macroheterogeneous porous media: Near‐pore‐scale macro modified invasion percolation simulation of experiments , 2001 .

[15]  G. Mahan,et al.  Ising model with magnetic field and the lattice gas , 1977 .

[16]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[17]  F. Y. Wu.  The Potts model , 1982 .

[18]  W. Bragg,et al.  The effect of thermal agitation on atomic arrangement in alloys , 1935 .

[19]  鈴木 増雄.  Time-Dependent Statistics of the Ising Model , 1965 .

[20]  Kenneth A. Hawick,et al.  Data-Parallelism and GPUs for Lattice Gas Fluid Simulations , 2010, PDPTA.