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Access Type

WSU Access

Date of Award

January 2021

Degree Type


Degree Name



Mechanical Engineering

First Advisor

Leela Arava

Second Advisor

Hassan Farhat


The focus of this work is to investigate the morphology of rotating drops. These drops are subjected to shear flow through their viscous surrounding in the context of oil in water (O/W) or water in oil (W/O) single drop emulsions. To do that a color-gradient lattice Boltzmann method was used. This model is capable of simulating very high viscosity and moderate density ratios emulsions such as O/W subjected to simple shear flow with considerably high accuracy.It is accepted that the multi-relaxation collision model (MRT) is more accurate than the single relaxation time (SRT). However, this statement cannot be generalized to all flow conditions. Besides it is much easier to use the SRT for simulating complex flows. Hence, it was important to investigate the validity limit of the SRT in both single and multiphase flows. The multi-relaxation time (MRT) Lattice Boltzmann method (LBM) was developed to overcome several constraints, which are inherent to the more famous single relaxation time (SRT) Bhatnagar–Gross–Krook (LBGK) model. Constraints, such as fixed Prandtl number, fixed ratio between kinematic and bulk viscosity, and Reynolds number limitations undermine the SRT usefulness. Furthermore, the SRT method fails to accurately characterize high viscosity fluids’ behavior near the domain’s walls, an issue which can be circumvented with the MRT method. However, the MRT requires a careful selection of its relaxation parameters for achieving the desired outcome. The ad-hoc nature of this selection makes the method cumbersome, especially for three-dimensional (3D) domains. Additionally, it is known that the MRT solution requires about 10% - 15% more computational time than the SRT for the same domain size. Four widely used single-phase flow conditions were explored by using the SRT and the MRT methods. It is shown that the SRT has good accuracy when used for simulating low viscosity fluid cases; however, the SRT exhibits a non-physical velocity jump at the domain surface boundaries when used for simulating high viscosity fluid flows. This issue can be resolved by augmenting the SRT domain’s height, which in turn leads to an increase in the required computational time. The main advantages of the MRT are due to its capability in overcoming the velocity jump in most of the high viscosity fluid cases and in its ability to simulate flows with ultra-low viscosities, which was demonstrated in the characterization of the flow around S822 airfoil with Reynolds numberRe  40,000 . As for testing multiphase flows, It will be shown that the MRT offers very little advantages over the SRT for oil in water (O/W) and water in oil (W/O) emulsion systems, in which the suspended phase is a sandwiched film. These systems are characterized by dynamic viscosity ratio up to 1000 and subjected to simple shear flow. Contrary to that, the MRT excels in providing a smooth velocity transition at the interface of emulsions flown between two parallel plates, and can successfully attain the theoretical central velocity, while the SRT falls short of reaching such velocity. In addition, a method is proposed in this work to allow a system with high density ratio. This facilitates the simulation of buoyant bubbles in extremely high dynamic viscosity ratio systems (over 50000), where the MRT reveals its capabilities in matching an experimental bubble shape outside of the known Grace shape diagram. This is not feasible to do with the SRT method. Based on the fact that the SRT collision scheme has reasonable accuracy in single shear flows, a SRT color-gradient lattice Boltzmann method is used for investigating the morphology of rotating drops. The rheological behavior of these various systems is reported and the favorable conditions for drops rotation are revealed. The stability of rotating drops in viscous surrounding is explored and the deviation in behavior from that of the theoretical construct of drops rotating in vacuum is delineated. Furthermore, the distribution of contaminants in the form of non-ionic surfactants residing on the rotating drop interface is tracked and presented. Finally, it is shown that the angular speed of a rotating hot drop in cold surrounding, is directly related to the retention of a hot core for considerably longer time.

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