Finite Reynolds number effects in fluid mixtures : an investigation using numerical simulation methods

• Main Author: Kendon, Vivien Mary
• Published: University of Edinburgh 1999
• Subjects: 530.44
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.653291

The scaling theory of the spinodal decomposition of a symmetric binary fluid mixture in the inertial region has been reviewed, and extended by considering energy balance, as well as the momentum balance described by the Navier-Stokes equation (NSE). The prediction for the asymptotic growth rate of the size of the separating fluid domains is ~<I>t<SUP>2/3</SUP></I>, as in simple scaling theory, but the ratio of the nonlinear to viscous terms in the NSE (the Reynolds number) is predicted to remain finite. This is due to the viscous term remaining important to the system dynamics, in contrast to simple scaling theory where the viscous term is assumed to be negligible. Spinodal decomposition in binary fluid mixtures has been successfully simulated using a lattice Boltzmann method. The simulation results were combined using a characteristic length and time obtained from the physical parameters (density, viscosity, interfacial tension) to scale the domain size, the resulting single scaling plot covers five decades of length and eight of time from the viscous hydrodynamic region (linear scaling) through a broad crossover region to the inertial region. This is a larger range than all previous results combined, and the first unambiguous simulation results for the inertial region. Both the order parameter and the fluid velocity in the spinodal system have been analysed in detail. The order parameter shows good scaling behaviour (collapse of the structure factor) while various velocity-related quantities, such as the dissipation rate, were found not to scale. A comparison of the relative magnitude of the terms in the NSE confirmed that the results include simulation of the inertial region where the inertial terms dominate the dynamics. Careful analysis of the growth rate due to diffusion also allowed this to be discounted from making a significant contribution to the hydrodynamic coarsening under observation in this study. The persistence behaviour of the spinodal system has been studied, although the order parameter data are not sufficient for a precise determination to be made of the value of the persistence exponent. It was possible to show that the persistence behaviour follows a power law decay (as opposed to exponential) and to show that there is some dependence on the domain growth exponent (linear/<I>f<SUP>2/3</SUP></I>).