Simulation of Rising Bubbles Dynamics Using the Lattice Boltzmann Method

Abstract

DEDICATIONThis thesis is dedicated to my lovely wife Jacqueline Yhamen for being so supportive and understanding. I have not been able to spend time with you during this long and quite difficult moment you have been through. I hope you find here the love I was unable to share when needed.

Lattice Boltzmann Simulation of Deformation and Breakup of a Droplet under Gravity Force Using Interparticle Potential Model

“…aeö aeö -=-ç÷ ç÷ èø èø (10) In Equation (10), ρ 0 was set equal to 1. While component 2 is assumed to be ideal gas so that G 22 =0 and () yrr = [24][25][26], the interaction between the two components and the immiscibility of the mixture are described by G 12 . In the multicomponent model proposed by Martys and Chen [ 27], the macroscopic velocity ( (11) where, ¢ u is a velocity common to the various components defined as Given the form of potential in Equation 8, the rate of net momentum change induced at each site due to the interaction is simply given as in [ 16]: (14) In case of the fluid-solid wall interaction, separate forces should be calculated for each phase to account for the fluid-solid forces.…”

“…In order to consider the buoyant effect associated with density difference between two fluids, an effective buoyant force, ( , e s F ) was introduced. It is defined by [ 26] , e applied ss r =Fg (18) In fact, because of the density difference between the phases, the buoyancy and gravity Consequence is defined as: (19) Equating Equations (18) and (19) yields to: where, ρ H is the heavier fluid density and ρ L is the lighter fluid density, and ρ σ=H is the density of the droplet as actually used in the simulation. The g applied represents the gravitational acceleration actually used in the simulation and applied to component sonly.…”