Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.
We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35<Ca(c)<0.4 for the viscosity ratio of unity, consistent with previous numerical simulations and experiments. Droplet breakup can also be promoted by increasing the Reynolds number. Finally, we numerically investigate a single bubble rising under buoyancy force in viscous fluids for a wide range of Eötvös and Morton numbers. Numerical results are compared with theoretical predictions and experimental results, and satisfactory agreement is shown.
A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media
In the present paper we study the immiscible two-phase flow in porous media using the lattice Boltzmann model proposed by He et al. [X. He, R. Zhang, S. Chen, G.D. Doolen, Phys. Fluids 11 (1999) 1143–1152]. By considering a set of appropriate boundary conditions for the density distribution function defined in that model, we account for the effect of wettability at solid–fluid interfaces and capillarity in the pores where the fluid–fluid interfaces reside. Different contact angles of the fluid–fluid interface at solid walls can be realized by taking appropriate values for the density distribution function at the solid sites of the porous domain. It is shown that the steady state contact angle is a linear function of the density value assigned to the solid sites. The model is then applied to the study of viscous coupling effects in immiscible two-phase flow in irregular pore networks, with respect to the overall wetting saturation, the viscosity ratio and the wetting angle. Our results show that when the wetting fluid is less viscous than the non-wetting fluid then the apparent relative permeability of the non-wetting phase may take values greater than unity due to the “lubricating” effect of the wetting films that cover the solid walls. The proposed model is an ideal tool for modeling immiscible two-phase flow in porous media, due both to its ability to incorporate complicated boundary conditions at the pore walls and also capture the physical aspects of the flow in the bulk and the interfaces. Furthermore, the width of the fluid–fluid interfaces is kept less than 3–4 lattice units allowing for simulations in relatively low resolution porous lattices.
Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model
The lattice Boltzmann method is applied to the study of immiscible two-phase flows using a Rothman–Keller-type (RK) model. The focus is on the algorithm proposed by Latva-Kokko and Rothman, which has been modified and integrated into the Reis and Phillips model, which belongs to the RK family. A key element of the RK model is the recoloring step applied at the interface of two fluids, at which the fluids are separated and sent to their own region. When convection is weak, the interface in the Reis and Phillips model suffers from “lattice pinning”, which is a problem that may prevent the interface from moving. While the recoloring algorithm proposed by Latva-Kokko and Rothman diminishes this problem, it was not used in the work of Reis and Phillips. This is the framework in which the present study has been conducted. Its scope is twofold: first, to integrate and adapt the Latva-Kokko and Rothman recoloring algorithms for reducing the lattice pinning problem found in the Reis and Phillips model; and second, to conduct a set of numerical tests to show that the combination of the two algorithms leads to an improvement in the quality of the results, along with a better convergence. The context of the work is two-dimensional, with the D2Q9 lattice used as the basic computational element.
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