Interface dynamics of immiscible two-phase lattice-gas cellular automata: A model with random dynamic scatterers and quenched disorder in two dimensions

TL;DR

This paper models interface dynamics in two-phase immiscible fluids using lattice gas cellular automata with disorder, capturing phenomena like Saffman-Taylor instability and interface roughening, relevant to Hele-Shaw cell experiments.

Contribution

Introduces a lattice gas cellular automata model incorporating random scatterers and quenched disorder to simulate interface dynamics in two-phase flows, reproducing key experimental phenomena.

Findings

Saffman-Taylor instability observed in the model matches real fluid behavior.

Interface roughening exponents align with the universality class of the random deposition model.

Development of viscous fingers and bubbles in unstable interface cases.

Abstract

We use a lattice gas cellular automata model in the presence of random dynamic scattering sites and quenched disorder in the two-phase immiscible model with the aim of producing an interface dynamics similar to that observed in Hele-Shaw cells. The dynamics of the interface is studied as one fluid displaces the other in a clean lattice and in a lattice with quenched disorder. For the clean system, if the fluid with a lower viscosity displaces the other, we show that the model exhibits the Saffman-Taylor instability phenomenon, whose features are in very good agreement with those observed in real (viscous) fluids. In the system with quenched disorder, we obtain estimates for the growth and roughening exponents of the interface width in two cases: viscosity-matched fluids and the case of unstable interface. The first case is shown to be in the same universality class of the random deposition model with surface relaxation. Moreover, while the early-time dynamics of the interface behaves similarly, viscous fingers develop in the second case with the subsequent production of bubbles in the context of a complex dynamics. We also identify the Hurst exponent of the subdiffusive fractional Brownian motion associated with the interface, from which we derive its fractal dimension and the universality classes related to a percolation process.