LATTICE BOLTZMANN SIMULATION OF RISING BUBBLES USING AN EFFECTIVE BUOYANCY APPROACH

Simulations of rising bubbles – particularly for conditions comparable to air rising in water under Earth gravity -- have proven challenging. Recently, Lattice Boltzmann methods appear to be the one of the most popular and promising approaches for rising bubble simulation, but attaining air-water-like conditions has been hindered by difficulties achieving adequately high liquid/gas density ratios in these models.

We propose and test a method for incorporating an effective buoyant force into a body force applied only to the gas component of a multicomponent, multiphase, Shan-and-Chen-type Lattice Boltzmann method. The buoyant force g(ρ_liquid-ρ_gas) is replaced by an equivalent body force g_{applied in simulation} ρ_{gas in simulation}. Gas and liquid densities and viscosities can be identical in the simulations, but the bubble experiences a buoyant force consistent with the desired density difference.

This is an approximation because, in its simplest form, it neglects viscosity differences between the gas and liquid phases. Nevertheless, comparison of simulations with well-established observations show that expected bubble shapes are well-reproduced over a broad range of the relevant dimensionless Morton, Eötvös, and Reynolds numbers, suggesting that the viscosity difference is of secondary importance in the ranges considered so far.

The proposed method should permit simulation of conditions much closer to real air bubbles rising in water than previously possible. Future applications include study of methane release from saturated peat soils in boreal and low-latitude peatlands such as the Florida Everglades.