Terminal shape and velocity of a rising bubble by phase-field-based incompressible Lattice Boltzmann model

Abstract

This article describes the simulation of three-dimensional buoyancy-driven bubble rise using a phase-field-based incompressible Lattice Boltzmann model. The effect of the Cahn-Hilliard mobility parameter, which is the rate of diffusion relaxation from non-equilibrium toward equilibrium state of chemical potential, is evaluated in detail. In contrast with previous work that pursues a high density ratio of binary fluids in the hydrodynamic equation, we apply a large dynamic viscosity ratio, together with a matched density pair and a separate compensating gas phase buoyant force, and the numerical results fit previous experimental results well. Through analysis, it is noted that for cases with moderate Reynolds number, a large value of mobility keeps a relatively sharp interface, while smaller values of mobility would result in diffusive interfacial regions. Moreover, for cases with large Reynolds number, small bubbles at the tail tend to separate more easily when the value of mobility is larger. This article offers some potentially useful details for performing phase-field-based simulations.

The mechanics of shallow magma reservoir outgassing

“…The Reynolds number of our pore‐scale calculation is small for both early stages (i.e., while bubbles interacts to form channels Re < 1) and MVP transport through channels (Re ∼ 1). In our pore‐scale simulations, various values for the Bond number are set by varying the magnitude of the buoyancy force acting on the vapor phase [ Ngachin et al ., ; Parmigiani et al ., ; Ren et al ., ].…”

A brief review of the phase-field-based lattice Boltzmann method for multiphase flows

“…Using another improved phase-field-based LB model, Ren et al (2016b) numerically studied a three-dimensional buoyancydriven bubble rising with a small density ratio. Recently, based on the Allen-Cahn phase-field-based theory, Su et al 2018proposed an advanced LB multiphase model for simulating multiphase flows with high density ratios and adopted it to investigate the single bubble rising dynamics at a large density ratio of 1000.…”

“…Due to its wide applications, the Rayleigh-Taylor instability has been extensively studied using experimental, theoretical, and as well as numerical approaches (Zhou, 2017a;Zhou, 2017b). Several researchers have also used the phase-field-based LBM to study the Raylegh-Taylor instability (He et al, 1999a;He et al, 1999b;Zu and He, 2013;Liang et al, 2014;Shao et al, 2014;Ren et al, 2016b), while the most of these work are only to validate the codes of the developed LB models. Two important physical quantities characterizing the Rayleigh-Taylor instability are the dimensionless Reynolds number and the Atwood number, which can be defined respectively as,…”

Implementation of Dynamic Neutron Radiography and Integrated X-Ray and Neutron Tomography in Porous Carbonate Reservoir Rocks

“…Direct flow simulations are ordinarily used to investigate single phase flow and transport in complex porous media (e.g., Blunt et al, 2013;Bultreys et al, 2016, and references therein). As an alternative to classical computational fluid dynamics approaches (finite difference, finite element method, finite volume method), the lattice-Boltzmann method (LBM) is well-established for modeling flow in complex geometries without need of any simplification (e.g., De Rosis, 2014; Ren et al, 2016;Yang et al, 2016;Benioug et al, 2017;Xie et al, 2017). The LBM describes the flow of a large number of particles interacting with the medium and among themselves following the Navier-Stokes equation at the macroscopic scale (Ladd, 1994).…”