Byung Jun Yoon

The effective conductivities of composites with cubic arrays of spheroids and cubes

A boundary element method is developed for computing the effective conductivity of a composite material containing periodic arrays of particles of arbitrary shape. Utilizing the periodic nature of the problem, steady conduction through a unit cell is analyzed by solving the integral representation of the Laplace equation. The accuracy of the method is validated by comparing the numerical results with analytic solutions for periodic arrays of spherical and spheroidal particles, in particular at high particle volume fractions. The utility of the boundary element method is demonstrated by determining the effective conductivities of simple-cubic, body-centered-cubic, and face-centered-cubic arrays of spheroids and cubes over the entire range of the particle volume fraction.

Diffusive transport of macromolecules across the arterial wall

A mathematical model of diffusive transport of macromolecules across the arterial wall was developed in order to analyze the enhancement of molecular transport into the media in the presence of the endothelial injuries. The model is based on the continuum description of the distribution of macromolecules in the arterial wall with multiple injuries periodically dispersed on the endothelial surface. A boundary element method is successfully employed to model the problem geometry along with the relevant boundary conditions. The concentration and surface flux are computed for various physical conditions of the artery. Among other factors, the proper estimation of the mass transfer resistance, characterized by the Biot number, of the endothelial surface is crucial for the analysis. In addition the curvature effects are negligible when the vessel radius is larger than 10 times the wall thickness.

High-order field electrophoresis theory for a nonuniformly charged sphere

An electrophoresis theory is developed for a rigid sphere in a general nonuniform electric field. The zeta potential distribution and the double-layer thickness are both arbitrary. The zeta potential of the sphere is assumed to be small so that the deformation of the double layer can be neglected. Explicit expressions for the translational and rotational velocities of the sphere are derived in terms of the multipole moments of the zeta potential distribution and the tensor coefficients of the applied electric field. The presence of the kth-order component in the electrical potential field applied to the sphere results in a translation of the sphere only when the sphere possesses the (k-1)th- or (k+1)th-order multipole moments of the zeta potential distribution. In addition, the kth-order component in the electrical potential field causes a rotation of the sphere only when the sphere possesses the kth-order moment of the zeta potential distribution. As an illustrative example for the utility of our theory, we theoretically devise an electrophoresis analysis scheme for estimating the dipole moment of a dipolar sphere by observing the electrophoretic translation of the sphere in a quadratic potential field.

ELECTROOSMOTIC HELICAL FLOW PRODUCED BY COMBINED USE OF LONGITUDINAL AND TRANSVERSAL ELECTRIC FIELDS IN A RECTANGULAR MICROCHANNEL

We theoretically devise and simulate a microelectrode system that produces electroosmotic helical flow in a straight rectangular microchannel. In addition to a pair of primary electrodes that generate a longitudinal electric field, sets of secondary electrodes are installed to produce a transversal electric field. The secondary electrode system consists of point electrodes embedded along two edges of the bottom surface of the channel. The transversal electric field developed across the bottom surface causes the electroosmotic motion of fluid at the bottom of the channel along the transversal direction. As a combined effect of the primary electrode system that produces unidirectional longitudinal flow along the channel and the secondary electrode system that produces transversal flow across the bottom surface, the flow inside a rectangular microchannel follows a helical pattern. After simulating the electroosmotic helical flows developed in microchannels we analyze the mixing of sample liquid in such flow fields by calculating the trajectories of fluid particles.

Theoretical Study of AC Electroosmotic Flows in Non-Uniformly Charged Microchannels

We report the utility of AC electroosmosis as an effective means for fluid mixing in a microchannel where the channel surface is non-uniformly charged. AC electroosmotic flows near a single plate and between two parallel plates are analyzed theoretically. The effects of the AC frequency and non-uniform surface potential distribution on the mixing of sample liquid are investigated.

Application of Reptation Model on Brownian Dynamics for Electrophoresis of Single DNA in Polymer Solution

Brownian dynamcis(BD) simulation is performed to study electrophoretic motion of a single DNA moecule in polymer solution. When a DNA is forced to pass through pores in polymer solution under electrophoresis, the motion of DNA is strongly influence by surrounding entangled polymer molecules. We following the concept in the reptation model to represent the dynamics of DNA in polymer solution. Using the cubic Bezier spline, we manifest the contour of DNA to apply the constraint force from entangled polymer molecules surrounding the DNA. U-shaped, I-shaped migration, and periodic motions of DNA correspoding to each concentration of polymers solution under DC field, and the dynamics of DNA under AC field are simulated. We derive electrophoretic mobility using BD model with the constraint force to compare with experiment. We make the empirical correlation of the constraint force with concentration of polymer solution.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Continuum theory for ionic field charging of spheroidal aerosols in nonuniform electric field

Classical theory for the ionic field charging previously developed for a spherical particle in a uniform electric field is extended for prolate and oblate spheroidal particles in uniform and nonuniform electric fields. Spheroidal particles are either dielectrics or perfect conductors. The nonuniform electric field is modeled as a two-dimensional linear field commonly developed in wire-cylinder and wire-plate electrodes systems. Assuming that the particle orientation remains unchanged during the charging process the saturation charge and the time evolution of the particle charge are determined as functions of the aspect ratio and orientation of the particle. Although the saturation charge depends strongly on the particle shape and orientation, the results for spherical particles apply to within an order of magnitude to spheroidal particles in most cases. For a collection of spheroidal particles with a uniform orientation distribution the ensemble averages for the saturation charge and the time evolution of the particle charge are also determined. A simple formula is proposed as an approximate expression for the ensemble average for the saturation charge. It is found that the ensemble average for the time evolution of the relative saturation for a spheroidal particle with a moderate aspect ratio can be approximated using the well-known formula for a spherical particle in a uniform electric field.