Technical Report CSTN-132 Visualising Multi-Phase Lattice Gas Fluid Layering Simulations K.A. Hawick Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand email: k.a.hawick@massey.ac.nz Tel: +64 9 414 0800 Fax: +64 9 441 8181 April 2011 ABSTRACT Complex fluids that exhibit phenomena such as lay- ering and separation of multiple phases are computa- tionally expensive to model using conventional numer- ical integration of partial differential equations. Lat- tice gas approaches are significantly cheaper to simu- late 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 ex- change 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 ren- derings in both two and three dimensions. KEY WORDS multi-phase fluid; Kawasaki model; lattice gas; gravi- tational bias; diffusion. 1 Introduction Complex fluids such as multi-phase systems of sand, mud, oil and so forth[1] have attracted considerable re- cent interest in the literature due to recent oil industry events. Simulating and visualising such systems is at- tractive – particularly on a semi-interactive manner so that the effect of thermal and other parameters can be experienced. Simulating a lattice gas mode[2] is considerably cheaper computationally than simulating a full numer- ical time integration of the corresponding partial differ- ential equations. Full symmetry lattice gas models[3] are based on a correct momentum and energy treat- Figure 1: A Q = 7 species system run for 16384 steps on a 128 3 model with p v =0.5. ment of microscopic particle constituents. These mod- els have been shown to handle the microscopic details of single phase fluids well, but it is non trivial to add multiple particle species. Complex fluid model such as invasion percolation[4] can be based on straightforward assumptions about fluid flow in porous media [5] – essentially basing the flow model on a definite substrate model. Work has been reported in the literature[6] on the effect of desta- bilizing gravitational gradients[7] and viscous gravita- tional forces[8]. 1