COMPUTATIONAL STUDY OF DROPLET AND CAPSULE FLOW IN CHANNELS WITH INERTIAL EFFECTS

The flow of droplets and capsules in channels is important for a variety of industrial and biological applications. Droplet flow is common in microfluidic devices and emulsion processing as well as oil recovery from porous materials. Capsules are used to encapsulate sensitive materials and can be used to study the mechanical properties of biological cells. A computational method was developed to study the two-phase flow of drops with and without surfactants, and capsules surrounded by a thin elastic membrane. This new computational method allowed for the inclusion of inertial effects on droplet and capsule flow which has not received much attention in the past. Results are presented for both the steady flow in straight cylindrical channels, and the transient flow in response to sudden expansions or contractions in the channel diameter. Increasing the Reynolds number was seen to cause non-monotonic trends in the capsule deformation and velocity. Parameters such as the drop viscosity and presence of surfactants were seen to have smaller effects when the Reynolds number became large. Capsules flowing in channels were seen to have limiting elastic capillary numbers above which no stable shape could be found. The transient deformation of drops and capsules moving through expansions depended strongly on the shape of the drop upstream of the expansion. The transient deformation increased with the capillary number up to a limiting value. The flow of droplets through channels was seen to produce large deformations that could break the drop apart at low viscosity ratios. The inclusion of inertial effects caused increases in the transient deformation as well as oscillations as the drops relaxed back into their steady shape

Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence

We perform direct numerical simulations of surfactant-laden droplets in homogeneous-isotropic turbulence with Taylor Reynolds number $Re_\lambda\approx180$. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, allowing us to extend the framework developed by Kolmogorov (1949) and Hinze (1955) for surfactant-free bubbles to surfactant-laden droplets. We find the Kolmogorov-Hinze scale ($d_H$) is indeed a pivotal length scale in the droplets' dynamics, separating the coalescence-dominated and the breakage-dominated regimes in the droplet size distribution. We see that droplets smaller than $d_H$ have spheroid-like shapes, whereas larger droplets have long convoluted filamentous shapes with diameters equal to $d_H$. As a result, droplets smaller than $d_H$ have areas that scale as $d^2$, while larger droplets have areas that scale as $d^3$, where $d$ is the droplet equivalent diameter. We further characterise the filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier phase enclosed by the dispersed phase) on each droplet. The number of handles per unit length of filament ($0.06d_H^{-1}$) scales inversely with surface tension, while the number of voids is independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely inside the droplets.Comment: 31 pages, 13 figure

Surfactants, Thermal And Surface Energy Effects On Emulsions’ Transport Properties: A Study Using Lattice Boltzmann Method

This work aims to provide an efficient Gunstensen LBM based CFD model, capable of solving complex problems related to droplets behavior in shear and parabolic flows. Thermal conditions determine the outcome of the physical and transport properties of emulsions during their various processing phases. A better understanding of the intricate relationship between thermal, surfactants and hydrodynamics can help in the optimization of these processes during the production of emulsions. To investigate the outcome of coupling thermal, surfactants and hydrodynamics on emulsions behavior, a robust quasi-steady thermal-surfactants numerical scheme is presented and used here. To validate the model, the rheological behavior of oil-in-water system was investigated. The numerical results matched well the experimental results of the similar oil-in-water system under steady-state thermal conditions. Furthermore, it is shown that the proposed numerical model can handle cases with transient thermal conditions while maintaining good accuracy. The model has been improved to study the combined effects of temperature, and contact angle on the movement of slugs and droplets of oil in water (O/W) system flowing between two parallel plates and in 3D confined flow study. This is found in the enhanced oil recovery technique which includes thermal, contact angle and surfactant effects for breaking up trapped crude oil. The model static contact angle due to the deposition of the O/W droplet on a flat surface with simulated hydrophilic characteristic at different fluid temperatures, matched very well the proposed theoretical calculation. Furthermore, the model was used to simulate the dynamic behavior of droplets and slugs deposited on the domain\u27s upper and lower surfaces, while subjected to parabolic flow conditions. The model accurately simulated the contact angle hysteresis for the dynamic droplets cases. It was also shown that at elevated temperatures the required power to transport the mixture diminished remarkably. The aim is to improve our understanding of the underlying physics associated with the secondary and tertiary extraction process of trapped crude oil in wells by injecting hot water. Finally, the model was utilized for the investigation of the flow behavior of O/W emulsions with the goal of delineating the best practices for transporting these emulsions in circular ducts. The effects of temperature, volume fraction, flow pressure gradient, and surfactants concentration are investigated in a Poiseuille flow setup. A dimensionless power number ratio was introduced and successfully used for guiding the selection of the most cost-efficient means for transporting O/W emulsion

Electro-deformation of a moving boundary: a drop interface and a lipid bilayer membrane

This dissertation focuses on the deformation of a viscous drop and a vesicle immersed in a (leaky) dielectric fluid under an electric field. A number of mathematical tools, both analytical and numerical, are developed for these investigations. The dissertation is divided into three parts. First, a large-deformation model is developed to capture the equilibrium deformation of a viscous spheroidal drop covered with non-diffusing insoluble surfactant under a uniform direct current (DC) electric field. The large- deformation model predicts the dependence of equilibrium spheroidal drop shape on the permittivity ratio, conductivity ratio, surfactant coverage, and the elasticity number. Results from the model are carefully compared against the small-deformation (quasispherical) analysis, experimental data and numerical simulation results in the literature. Moreover, surfactant effects, such as tip stretching and surface dilution effects, are greatly amplified at large surfactant coverage and high electric capillary number. These effects are well captured by the spheroidal model, but cannot be described in the second-order small-deformation theory. The large-deformation spheroidal model is then extended to study the equilibrium deformation of a giant unilamellar vesicle (GUV) under an alternating current (AC) electric field. The vesicle membrane is modeled as a thin capacitive spheroidal shell and the equilibrium vesicle shape is computed from balancing the mechanical forces between the fluid, the membrane and the imposed electric field. Detailed comparison against both experiments and small-deformation theory shows that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, electric field strength and frequency, and vesicle size. Asymptotic analysis is conducted to compute the crossover frequency where a prolate vesicle crosses over to an oblate shape, and comparisons show the spheroidal model gives better agreement with experimental observations. Finally, a numerical scheme based on immersed interface method for two-phase fluids is developed to simulate the time-dependent dynamics of an axisymmetric drop in an electric field. The second-order immersed interface method is applied to solving both the fluid velocity field and the electric field. To date this has not been done before in the literature. Detailed numerical studies on this new numerical scheme shows numerical convergence and good agreement with the large-deformation model. Dynamics of an axisymmetric viscous drop under an electric field is being simulated using this novel numerical code