Modelling viscous segregation in immiscible fluids using lattice-gas automata

Abstract

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.