Dissertations and Theses

Date of Award


Document Type



Mechanical Engineering

First Advisor

Taehun Lee

Second Advisor

Andreas Carlson


LBM, Multiphase flow, CFD, Conservative phase field, Surface tension


In this thesis, we numerically investigated multi-phase fluid dynamics (2 and 3-phase flow) by solving the Navier-Stokes equations coupled with the conservative phase field (CPF) equations using the Lattice Boltzmann method (LBM). To effectively simulate the large-scale multi-phase physics, we developed an open-source software, IMEXLBM, which can be easily parallelized on both CPUs and GPUs without significant modifications to the code. We first validated various parts of this software and then used this method to study the interaction of rising bubbles with a static oil droplet as well as the engulfment of the water droplet on solids coated with a layer of oil.

The accuracy of the LBM implementation of IMEXLBM was validated with simulations on both CPUs and GPUs of the 3D flow around a sphere. The efficiency and structure of the software were studied using simulations of a 3D Taylor-Green vortex on GPUs: We validated our results against previous studies and then investigated both strong scaling, i.e., the decrease of the computational time for a given problem on an increasing number of processors, and weak scaling, i.e., the evolution of the computational time when increasing the number of processors at a fixed load on each processor.

We then moved on to the validation of the CPF implementation. We studied the effect of mobility, a non-physical numerical parameter, by simulating the deformation of a droplet in a simple shear flow. We proposed to use a non-standard variable for mobility in order to reduce the dependency of the results on this parameter. Then, we tested three different surface tension force

v formulations, namely (1) the continuum surface tension force formulation (CSF), (2) the stress form surface tension force formulation, and (3) the potential form surface tension force formulation. Simulations of static droplets led us to choose the CSF for the rest of the thesis. Finally, we validated the three-phase flow implementation by studying the evolution of two immiscible droplets initially in contact and with various spreading factors. We constructed a phase diagram of the final morphology as a function of the spreading factor and were able to obtain the three expected morphologies; separated, partially engulfed, and completely engulfed.

After having extensively validated our numerical implementation, we moved on to study two new ternary flow problems. First, we studied the interaction between a rising bubble and a stationary droplet. Our results indicated that the bubble-droplet aggregate with double emulsion morphology can minimize the distortion of the bubble-droplet aggregate and achieve a greater terminal velocity than the aggregate with partially engulfed morphology. Second, we investigated the engulfment of a droplet on solids coated by thin and thick fluid films. When an aqueous drop contacts an immiscible oil film, it displays complex interfacial dynamics. When the spreading factor is positive, upon contact the oil spreads onto the drop’s liquid-air interface, first forming a liquid bridge whose curvature drives an apparent drop spreading motion and later fully coating the drop. Inertially and viscously limited dynamics were explored using the Ohnesorge number Oh as a function of 𝐻/𝑅, the ratio between the initial drop radius R and the film height 𝐻. Both regimes showed that the radial growth of the liquid bridge π‘Ÿ is insensitive to the film height, and scales with time 𝑇 as π‘Ÿ ∼ 𝑇 0.5 for π‘‚β„Ž β‰ͺ 1 and π‘‚β„Ž ≫ 1 as π‘Ÿ ∼ 𝑇 0.4 . Contrary to the growth of the liquid bridge, however, we found that the late time engulfment dynamics and final interface profiles were significantly affected by 𝐻/𝑅



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