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

Electrohydrodynamic Simulations of Capsule Deformation Using a Dual Time-Stepping Lattice Boltzmann Scheme

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs due to fluid motion and electrical forces that arise due to differences in the electrical properties between the internal fluid, external fluid, and cell membrane. The electrostatic equations are solved using the immersed interface method. A finite element method is used to compute the membrane’s elastic forces and the membrane’s bending resistance is described by the Helfrich bending energy functional. The membrane forces are coupled to the fluid equations through the immersed boundary method, where the elastic, bending, and electric forces appear as force densities in the Navier-Stokes equations. The fluid equations are solved using a novel dual time-stepping (DTS) lattice Boltzmann method (LBM), which decouples the fluid and capsule discretizations. The computational efficiency of the DTS scheme is studied for capsules in shear flow where it is found that the newly proposed scheme decreases computational time by a factor of 10 when compared to the standard LBM capsule model. The method is then used to study the dynamics of spherical and biconcave capsules in a combined shear flow and DC electric field. For spherical capsules the effect of field strength, shear rate, membrane capacitance, and membrane conductance are studied. For biconcave capsules the effect of the electric field on the tumbling and tank-treading modes of biconcave capsules is discussed

Studies of propellant sloshing under low-gravity conditions Final report, 4 Jan. 1966 - 10 oct. 1970

Studies of propellant sloshing under low gravity condition

Electrohydrodynamic model of vesicle deformation in alternating electric fields

We develop an analytical theory to explain the experimentally-observed morphological transitions of giant vesicles induced by AC electric fields (1). The model treats the inner and suspending media as lossy dielectrics, while the membrane as an ion-impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, and bending stresses exerted on the membrane. Considering a nearly spherical vesicle, the solution to the electrohydrodynamic problem is obtained as a regular perturbation expansion in the excess area. The theory predicts that stationary vesicle deformation depends on field frequency and conductivity conditions. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasi-spherical rest shape. The analysis shows that the evolution towards the stationary vesicle deformation strongly depends on membrane properties such as viscosity. The model can be applied to rationalize the transient and steady deformation of biological cells in electric fields

Fluid Vesicles in Flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.Comment: 13 pages, 13 figures. Adv. Colloid Interface Sci., 201

An immersed boundary method for particles and bubbles in magnetohydrodynamic flows

This thesis presents a numerical method for the phase-resolving simulation of rigid particles and deformable bubbles in viscous, magnetohydrodynamic flows. The presented approach features solid robustness and high numerical efficiency. The implementation is three-dimensional and fully parallel suiting the needs of modern high-performance computing. In addition to the steps towards magnetohydrodynamics, the thesis covers method development with respect to the immersed boundary method which can be summarized in simple words by From rigid spherical particles to deformable bubbles. The development comprises the extension of an existing immersed boundary method to non-spherical particles and very low particle-to-fluid density ratios. A detailed study is dedicated to the complex interaction of particle shape, wake and particle dynamics. Furthermore, the representation of deformable bubble shapes, i.e. the coupling of the bubble shape to the fluid loads, is accounted for. The topic of bubble interaction is surveyed including bubble collision and coalescence and a new coalescence model is introduced. The thesis contains applications of the method to simulations of the rise of a single bubble and a bubble chain in liquid metal with and without magnetic field highlighting the major effects of the field on the bubble dynamics and the flow field. The effect of bubble coalescence is quantified for two closely adjacent bubble chains. A framework for large-scale simulations with many bubbles is provided to study complex multiphase phenomena like bubble-turbulence interaction in an efficient manner

Stratospheric constituent measurements using UV solar occultation technique

The photochemistry of the stratospheric ozone layer was studied as the result of predictions that trace amounts of pollutants can significantly affect the layer. One of the key species in the determination of the effects of these pollutants is the OH radical. A balloon flight was made to determine whether data on atmospheric OH could be obtained from lower resolution solar spectra obtained from high altitude during sunset

The effects of electrostatic forces on the distribution of drops in a channel flow: Two-dimensional oblate drops

Numerical simulations are used to examine the effect of an electrostatic field on an emulsion of drops in a channel. The leaky-dielectric theory of Taylor is used to find the electric field, the charge distribution on the drop surface, and the resulting forces. The Navier-Stokes equations are solved using a front-tracking/finite-volume technique. Depending on the ratios of conductivity and permittivity of the drop fluid and the suspending fluid the drops can become oblate or prolate. In addition to normal forces that deform the drops, tangential forces can induce a fluid motion either from the poles of the drops to their equator or from the equator to the poles. In this paper we focus on oblate drops, where both the dielectrophoretic and the electrohydrodynamic interactions of the drops work together to “fibrate” the emulsion by lining the drops up into columns parallel to the electric field. When the flow through the channel is slow, the fibers can extend from one wall to the other. As the flow rate is increased the fibers are broken up and drops accumulate at the channel walls. For high enough flow rate, when the drop interactions are dominated by the fluid shear, the drops remain in suspension. Only two-dimensional systems are examined here, but the method can be used for fully three-dimensional systems as well.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87286/2/093302_1.pd