MODELING VISCOUS SEGREGATION IN IMMISCIBLE FLUIDS USING LATTICE-GAS AUTOMATA

WHEN immiscible liquids with different viscosities are forced to flow through a channel, the more viscous liquid tends to concentrate in the centre. This process influences the flow of oil-water mixtures in pipelines1,2, the extrusion of polymers3, the flow of blood in small arteries4 and of magmas approaching the Earth's surface during a volcanic eruption5. Segregation occurs because it minimizes the pressure required to maintain a given flow rate6,7; there is still scant information, however, on the timescales and fluid configurations involved in the approach to the equilibrium state. Explicit solutions of the time-dependent Navier-Stokes equation using numerical (for example, finite-element3) methods are possible only for simple interface shapes. Here we use an alternative approach to the study of viscous segregation, involving immiscible lattice-gas automata. Two-dimensional calculations exhibit the expected segregation for a variety of starting configurations, and for an initially homogeneous emulsion the fluid must flow 50-100 times the channel width before most of the more viscous fluid reaches the channel centre. For constant flow rates, segregation occurs so as to progressively decrease the pressure. © 1990 Nature Publishing Group.