Binary Fluid Model Research Articles

SIMULATIONS OF GAS–GAS MIXING LAYERS WITH A LATTICE BOLTZMANN BINARY FLUID MODEL

Gas–gas mixing layers are important in many practical applications including transport of pollutants in smoke plumes and air–fuel mixing in combustion. In this paper, mixing layers are studied by conducting direct numerical simulations using a lattice Boltzmann model for binary fluids. The binary fluid model can simulate gases with different molecular weights. In this work, nitrogen–helium and nitrogen–nitrogen mixing layers are studied with different velocities. The computed results are compared with published experimental results and there is agreement between them within 7% for most cases.

Computation of multiphase systems with phase field models

Phase field models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near-critical interfacial phenomena, phase separation under shear, and microstructure evolution during solidification. However, because interfaces are replaced by thin transition regions (diffuse interfaces), phase field simulations require resolution of very thin layers to capture the physics of the problems studied. This demands robust numerical methods that can efficiently achieve high resolution and accuracy, especially in three dimensions. We present here an accurate and efficient numerical method to solve the coupled Cahn–Hilliard/Navier–Stokes system, known as Model H, that constitutes a phase field model for density-matched binary fluids with variable mobility and viscosity. The numerical method is a time-split scheme that combines a novel semi-implicit discretization for the convective Cahn–Hilliard equation with an innovative application of high-resolution schemes employed for direct numerical simulations of turbulence. This new semi-implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the Cahn–Hilliard equation at the same cost as that of an explicit scheme. It is derived from a discretization used for diffusive problems that we further enhance to efficiently solve flow problems with variable mobility and viscosity. Moreover, we solve the Navier–Stokes equations with a robust time-discretization of the projection method that guarantees better stability properties than those for Crank–Nicolson-based projection methods. For channel geometries, the method uses a spectral discretization in the streamwise and spanwise directions and a combination of spectral and high order compact finite difference discretizations in the wall normal direction. The capabilities of the method are demonstrated with several examples including phase separation with, and without, shear in two and three dimensions. The method effectively resolves interfacial layers of as few as three mesh points. The numerical examples show agreement with analytical solutions and scaling laws, where available, and the 3D simulations, in the presence of shear, reveal rich and complex structures, including strings.

LATTICE BOLTZMANN SIMULATION OF INTERFACIAL DEFORMATION

This study describes the numerical simulations of two-phase interfacial deformations using the binary fluid (BF) model in the lattice Boltzmann method (LBM), where a macroscopic fluid involves mesoscopic particles repeating collisions and propagations and an interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. Schemes for the BF model are proposed to simulate motions of immiscible two phases with different mass densities. For higher Reynolds number, the finite difference-based lattice Boltzmann scheme is applied to the kinetic equations of particles, which include convection terms to reduce the diffusivity of each phase volume. In addition, two parameters are introduced into the BF model to adjust surface tension and interfacial thickness independently. The numerical results of three-dimensional bubble motion under gravity and two-dimensional droplet deformation under shear stress indicate that the lattice-Boltzmann BF model with the proposed schemes would be applicable to simulating interfacial dynamics of immiscible two-phase fluids.

Lattice Boltzmann simulations of binary fluid flow through porous media

The lattice Boltzmann equation is often advocated as a simulation tool that is particularly effective for complex fluids such as multiphase and multicomponent flows through porous media. We construct a three-dimensional 19 velocity lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio based on the model proposed by Gunstensen. The model is tested for the following binary fluid flow problems: a stationary planar interface among two fluids; channel flow of immiscible binary fluids; the Laplace problem; and a rising bubble. The results agree well with semi-analytic results in a range of the Eötvös, Morton and Reynolds number. We also present preliminary simulation results for two large-scale realistic applications: the flow of an air-water mixture in a waste-water batch reactor and the saturation hysteresis effect in soil flow. We discuss some limitations of the lattice Boltzmann method in the simulation of realistic and difficult multiphase problems.

Simulation of Bubble Motion under Gravity by Lattice Boltzmann Method

We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method(LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single- and two-bubble motions, setting flow conditions according to the Eötvös and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two- bubble interaction of their approach and coalescence in circular tube. These results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity.

Simulation of Bubble Motion under Gravity by Lattice Boltzmann Method.

We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method(LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single- and two-bubble motions, setting flow conditions according to the Eötvös and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two- bubble interaction of their approach and coalescence in circular tube. These results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity.

Turbulent binary fluids: A shell model study

We introduce a shell (“GOY”) model for turbulent binary fluids. The variation in the concentration between the two fluids acts as an active scalar leading to a redefined conservation law for the energy, which is incorporated into the model together with a conservation law for the scalar. The model is studied numerically at very high values of the Prandtl and Reynolds numbers and we investigate the properties close to the critical point of the miscibility gap where the diffusivity vanishes. A peak develops in the spectrum of the scalar, showing that a strongly turbulent flow leads to an increase in the mixing time. The peak is, however, not very pronounced. The mixing time diverges with the Prandtl number as a power law with an exponent ∼ 0.9. The continuum limit of the shell equations leads to a set of equations which can be solved by a scaling ansatz, consistent with an exact scaling of the Navier-Stokes equations in the inertial range. In this case a weak peak also persists for a certain time in the spectrum of the scalar. Exact analytic solutions of the continuous shell equations are derived in the inertial range. Starting with fluids at rest, from an initial variation of the concentration difference, one can provoke a “spontaneous” generation of a velocity field, analogous to MHD in the early universe.

Criticality in Gaussian-molecule mixtures

A continuum binary fluid model consisting of Gaussian molecules with interactions specified by the Mayer f-functions f ab(r) = −exp(-r 2/r 2 0), f aa = f bb = 0, exhibits phase separation and criti...

Effect of an electric field on an interfacial profile

We consider the interface between two dielectric liquids in an electric field which is parallel to the interface. Using the Ginsburg-Landau model for binary fluids we add a term for the electric field energy and show that near the critical point the effect of the electric field is to change both the interface width and the critical temperature.