Electrophoresis of a charge-regulated soft sphere in a charged cylindrical pore.

The boundary effect on the electrophoresis of a soft spherical particle, which comprises a rigid core and a porous layer, along the axis of a cylindrical pore is analyzed under the conditions of low surface potential and weak applied electric field. The porous layer of the particle is of charge-regulated nature where the distribution of fixed charge depends on the degree of dissociation/association reaction of the ionizable function groups contained in the porous layer. The pore might be charged, implying that the effect of electroosmotic flow can play a role. The influences of the nature of the porous layer of a particle, the thickness of the double layer, the pH of the bulk liquid, and the relative size of a pore on the electrophoretic behavior of the particle are investigated. Several unexpected and interesting results are obtained. For instance, if the pH value of the bulk liquid or the thickness of the membrane layer takes a medium large value, the electrophoretic mobility of the particle has a local maximum as the thickness of the double layer varies.

Diffusiophoresis of a sphere along the axis of a cylindrical pore.

The diffusiophoresis of a charged spherical particle along the axis of an uncharged cylindrical pore filled with an electrolyte solution is analyzed theoretically. The influence of chemiphoresis, which includes two types of double-layer polarization, and that of electrophoresis arising from the difference in the diffusivities of the ionic species on the diffusiophoretic behavior of the particle are discussed. We have underlined the important difference between two cases: the first is a possibility for a particle to migrate to the low concentration side at low surface potentials ( approximately 25mV) along the axis of a cylindrical pore, while the second is that this migration occurs at high surface potentials ( approximately 150mV) in the case of a sphere in a spherical cavity.

Electrophoretic behaviors of human hepatoma HepG2 cells.

The electrophoretic mobility of HepG2 cells was measured and a charge-regulated model was proposed to simulate the results obtained. Here, a cell was simulated by a rigid core and an ion-penetrable membrane layer containing both acidic and basic functional groups. The influences of the key parameters, including the pH, the ionic strength, the thickness of the membrane layer of a cell, the density and the dissociation constant of the dissociable functional groups in the membrane layer, and the binding constant of divalent cations on the electrophoretic mobility of a cell were investigated. In particular, the role of the buffer used in the experiment was discussed; this effect was neglected in almost all the relevant theoretical analyses in the literature. We showed that the binding ability of divalent cations to the dissociated functional groups in the membrane layer of a cell ranks as Ca(2+)>Mg(2+)>hexamethonium.

Electrophoresis of a charge-regulated toroid normal to a large disk.

The electrophoresis of a charge-regulated toroid (doughnut-shaped entity) normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. The system considered is capable of modeling the electrophoretic behavior of various types of biocolloids such as bacterial DNA, plasmid DNA, and anabaenopsis near a perfectly conducting planar wall. The influences of the size of the toroid, the separation distance between the toroid and the disk, the charged conditions on the surfaces of the toroid and the disk, and the thickness of electric double layer on the electrophoretic mobility of the toroid are discussed. The results of numerical simulation reveal that under typical conditions the electrophoretic behavior of the toroid can be different from that of an integrated entity. For instance, if the surface of the toroid carries both acidic and basic functional groups, its mobility may have a local maximum as the thickness of double layer varies. We show that the electrophoretic behavior of the toroid is different, both qualitatively and quantitatively, from that of the corresponding integrated particle (particle without hole).

Effect of charged boundary on electrophoresis: Sphere in spherical cavity at arbitrary potential and double-layer thickness.

The boundary effect on electrophoresis is investigated by considering a spherical particle at an arbitrary position in a spherical cavity. Our previous analysis is extended to the case where the effect of double-layer polarization can be significant. Also, the effect of a charged boundary, which yields an electroosmotic flow and a pressure gradient, thereby making the problem under consideration more complicated, is investigated. The influences of the level of the surface potential, the thickness of double layer, the relative size of a sphere, and its position in a cavity on the electrophoretic behavior of the sphere are discussed. Some results that are of practical significance are observed. For example, if a positively charged sphere is placed in an uncharged cavity, its mobility may have a local minimum as the thickness of the double layer varies. If an uncharged sphere is placed in a positively charged cavity, the mobility may have a local minimum as the position of the sphere varies. Also, if the size of a sphere is fixed, its mobility may have a local minimum as the size of a cavity varies. These provide useful information for the design of an electrophoresis apparatus.

Evaluation of the electric force in electrophoresis.

A new expression for the evaluation of the electric force acting on a colloidal particle in an applied electric field is derived under the condition of weak applied electric field. The expression derived, which is based on the Maxwell stress tensor, is applicable to both rigid and soft particles for various types of surface conditions and to both symmetric and asymmetric geometries. We show that, depending upon the electrophoresis conditions, the electric force evaluated by the methods commonly used in the literature can be overestimated, thereby leading to incorrect electrophoretic mobility.

Electrophoresis of a toroid along the axis of a cylindrical pore.

The electrophoresis of a toroid (doughnut-shaped entity) along the axis of a long cylindrical pore is analyzed under the conditions of low surface potential and weak applied electric field. The system under consideration is capable of modeling the electrophoretic behavior of various types of biocolloid such as bacterial DNA, plasmid DNA, and anabaenopsis, in a confined space. The influences of the key parameters of the problem, including the sizes of a toroid, the radius of a pore, and the thickness of the double layer, on the electrophoretic mobility of a toroid are discussed. We show that the electrophoretic behavior of a toroid under typical conditions can be different from that of an integrated entity. For instance, although the presence of the pore wall has the effect of retarding the movement of a particle, it becomes advantageous if a toroid is sufficiently close to the boundary. Several interesting behaviors are also observed, for example, the mobility of a toroid when the boundary effect is significant can be larger than that when it is insignificant.

Electrophoresis of a charge-regulated sphere normal to a large disk.

The electrophoresis of a rigid, charge-regulated, spherical particle normal to a large disk is investigated under the conditions of low surface potential and weak applied electric field. We show that, although the presence of a charged disk does not generate an electroosmotic flow, it affects particle motion appreciably through inducing charge on its surface and establishing an osmotic pressure field. The competition between the hydrodynamic force and the electric force may yields a local extremum in mobility; it is also possible that the direction of particle movement is reversed. In general, if a particle remains at constant surface potential, a decrease in the thickness of double layer has the effect of increasing the electrostatic force acting on it so that its mobility increases. However, this might not be the case for a charged-regulated particle because an excess hydrodynamic force is enhanced. For a fixed separation distance, the influence of a charged disk on mobility may reduce to a minimum if the bulk concentration of hydrogen ion is equal to the dissociation constant of the monoprotic acidic functional groups on particle surface.

Boundary effect on electrophoresis: finite cylinder in a cylindrical pore.

The boundary effect on electrophoresis is investigated by considering a finite cylindrical particle moving along the axis of a long cylindrical pore under conditions of low surface potential and weak applied electric field. The influence of the thickness of the double layer, the aspect ratio of a particle, the ratio particle radius/pore radius, and the charged conditions of the surfaces of the particle and pore on the electrophoretic behavior of a particle are investigated. We show that the effect of the aspect ratio of a particle on its electrophoretic behavior for the case where the particle is charged and the pore is uncharged is larger than that for the case where the particle is uncharged and the pore is charged. Also, depending on the parameters chosen, increasing the aspect ratio of a particle can either promote or hinder its movement, which is not reported in previous studies, and can play a role in electrophoresis measurements. Because both the electric and the flow fields in the gap between the particle and the pore are mediated by those near the top and the end of the particle, the end effect is large when the double layer is thick.

Electrophoresis of a spherical particle along the axis of a cylindrical pore: effect of electroosmotic flow.

The electrophoresis of a spherical particle along the axis of a cylindrical pore is investigated under conditions of low surface potential and thick double layer. In particular, the effect of electroosmotic flow is taken into account. The results of numerical simulation reveal that if both particle and pore are positively charged, the variation of the mobility of a particle may have a local minimum as the thickness of the double layer varies, which is not reported in the literature. This is mainly due to the charge induced on the particle surface, which arises from the presence of the charged boundary. Depending upon the level of the surface potential of the pore, the presence of the local minima may lead to a reversal in the direction of particle movement as the thickness of the double layer surrounding it varies: if the surface potential is either too low or too high, reversal does not occur; if it has a medium level, reversal occurs twice. This interesting observation can play a role in electrophoresis measurements. Previous analysis predicts that reversal always occurs once, regardless of the level of the surface potential of the pore.