Showing papers by "Jyh-Ping Hsu published in 2000"

Electrophoresis of concentrated spherical particles with a charge-regulated surface

Abstract: The electrophoretic behavior of spherical colloidal particles is modeled theoretically. The classic analysis is extended to the case of a concentrated dispersion in which the double layer surrounding a particle can assume an arbitrary thickness, and the effect of double-layer polarization is taken into account. Also, the surface of a particle is charge regulated, which leads to a general mixed-type boundary condition, and simulates entities bearing dissociable functional groups such as biological cells and particles with a membrane layer. We show that the absolute surface potential decreases with the increase in κa, κ and a are, respectively, the reciprocal Debye length and the radius of a particle. The variation of the absolute electrophoretic mobility as a function of κa is found to have a local maximum. The higher the surface potential the more significant the effect of double-layer polarization, and it becomes insignificant if κa approaches infinity.

Electrophoretic mobility of concentrated spheres with a charge‐regulated surface

Abstract: The electrophoretic behavior of a concentrated spherical colloidal particle is modeled theoretically under the Debye-Huckel condition. The surface of a particle contains dissociable functional groups, the dissociation of which yields negative fixed charges. The model derived is applicable to an arbitrarily thick double layer. We show that the absolute surface potential decreases with the increase in kappa(a); kappa and a are the reciprocal Debye length and the radius of a particle, respectively. Moreover, the variation of the absolute electrophoretic mobility as a function of kappa(a) has a maximum.

Electrokinetic flow in a planar slit covered by an ion‐penetrable charged membrane

Abstract: The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.

Current Efficiency of an Ion-Exchange Membrane: Effect of Piecewise Continuous Fixed Charge Distribution

Abstract: The current efficiency η for the transport of ions through an ion-exchange membrane is analyzed theoretically. In particular, the effect of discretizing the fixed charges contained in the membrane into charged intervals on η is investigated. We show that if the applied current density I is low, a membrane with a continuous linear fixed charge distribution has a higher η than a membrane with evenly distributed charged intervals, and the larger the number of charged intervals the lower the η. If I is high, a membrane with randomly distributed charged intervals may have a higher η than that of a membrane with a continuous linear fixed charge distribution. It can be inferred that, as far as raising η is concerned, distributing fixed charges discretely and/or randomly in a membrane has no practical advantage.

Sedimentation of a Nonconducting Sphere in a Spherical Cavity

Abstract: The sedimentation of a nonconducting spherical particle in a spherical cavity is analyzed theoretically. We show that, for the case where the former is positively charged and the latter uncharged, the sedimentation velocity of the particle decreases with κa, κ and a being respectively the reciprocal Debye length and the radius of a particle. If the surface potential of the particle φr is high, the sedimentation potential has a local maximum as κa varies, which becomes inappreciable if the surface potential is low. If φr is sufficiently high, the sedimentation potential has a local maximum as λ (= radius of particle/radius of cavity) varies. It is not observed, however, if κa is large. If an uncharged particle is placed in a positively charged cavity, the sedimentation potential may reverse its sign, and may have a local minimum as κa varies.

Sedimentation of concentrated charged spheres at low surface potentials

Abstract: The sedimentation of concentrated charged spherical particles in an electrolyte solution is investigated theoretically for an arbitrarily thick double layer taking the effect of double-layer polarization into account. We show that the ratio E*/U* (=scaled sedimentation potential per scaled sedimentation velocity) is a constant if κa is either very small or very large, κ and a being respectively the reciprocal Debye length and the radius of a particle. The variation of E*/U* as a function of κa has a minimum at a medium κa. This minimum increases with the increase in particle concentration. The scaled sedimentation velocity approaches a constant if κa is small, and its variation as a function of κa has a maximum at a medium κa. This maximum decreases with the decrease in particle concentration.

Modeling Fluctuations in the Growth Rate of a Single Crystal

Abstract: The growth rate of a single crystal depends on various mesoscopic variables, e.g., irregularities such as defects and steps in the surface. It is highly plausible that such irregularities render the growth rates of crystals of an identical size to vary randomly. This work aims at modeling stochastically the fluctuations in the growth rate of a single crystal in a crystallizer. The crystal size in any of the equally-divided domains is considered as the random variable defining the state of the system. The transition of the crystal size from one state to another is characterized by a set of transition-intensity functions which, as for the case of the deterministic growth rate, exhibit a power-law dependence on the size. The master equation for the system is formulated through probabilistic balance around a particular state by taking into account all mutually exclusive events. The resultant nonlinear master equation has been expanded in power series of a small parameter, i.e., the reciprocal of the maximum crystal size obtainable, by means of the system-size expansion. This has yielded expressions for the means and variances of the size of a single particle. Comparison of the simulated crystal size with available experimental data indicates that the present stochastic model adequately portrays the dynamic behavior of a single crystal.