Eruptive flow response in a multi-component driven system by an interacting lattice gas simulation

Abstract

An interacting lattice gas model is used to study flow of immiscible components A and B (molecular weights M A and M B , M A < M B ) by Monte Carlo simulations. Concentration gradients and hydrostatic pressure bias ( H) drive these constituents from their source at the bottom against gravitational sedimentation in an effective medium. Response of their flux densities ( j A , j B ) to the hydrostatic bias H are examined. If both constituents are released with equal probabilities (a non-interacting source), their flux densities respond linearly to bias with j A > j B except at the extreme bias H → 1 where j A → j B . Flow response becomes complex if the constituents from their source are released according to their current lattice concentrations (an interacting source): a crossover occurs from j A > j B at low bias ( H ≤ 0.4 ) to j B > j A at higher bias ( H > 0.4 ) . Constituent with the lower molecular weight ( A) responds linearly on increasing the bias except at very high bias ( H ≥ 0.8 ) where the response becomes negative. The heavier component ( B) responds non-linearly: a high response at low values of H is followed by a linear response before the onset of eruptive response at high range of H. The volatility parameter diverges as eruption occurs at H → 1 .