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.

Effect of electroosmotic flow on the electrophoresis of a membrane-coated sphere along the axis of a cylindrical pore.

The electrophoresis of a membrane-coated spherical particle along the axis of a long, charged cylindrical pore was analyzed theoretically under the conditions of low surface potential and weak applied electrical field. The influences of the thickness of the double layer, the pore radius, the nature of the membrane layer, and the charged conditions of the particle and the pore on the electrophoretic behavior of the particle were investigated. The occurrence of the electroosmotic flow and the presence of the membrane layer were found to have a significant influence on the mobility of the particle. For instance, because the direction of electrophoresis does not depend solely on the applied electrical field and the nature of the charge carried by the particle, care must be taken in interpreting electrophoresis data. Furthermore, the magnitude of the electrophoretic mobility of a particle can show a local maximum as the concentration of electrolytes varies, which is of practical significance if electrophoresis is employed, for example, as a separation tool.

Boundary effect on diffusiophoresis: spherical particle in a spherical cavity.

The boundary effect on the diffusiophoretic behavior of a particle is analyzed theoretically by considering the diffusiophoresis of a charged sphere under arbitrary surface potential and double-layer thickness at an arbitrary position in an uncharged spherical cavity. We show that the phenomenon under consideration is governed by double-layer relaxation, chemiosmotic/diffusioosmotic flow, and two types of competing double-layer polarization. The presence of the cavity has a profound influence on the diffusiophoretic behavior of the particle, especially when the surface potential is high. For instance, the scaled diffusiophoretic velocity of the particle has a local maximum as the position of the particle varies; it may have a local maximum and local minimum as the thickness of the double-layer varies. The significance of the effect of double-layer relaxation depends upon the level of surface potential and magnitude of the electric Peclet number.

Effects of double-layer polarization and electroosmotic flow on the electrophoresis of an ellipsoid in a spherical cavity.

The electrophoresis of a rigid, positively charged ellipsoidal particle at the center of a spherical cavity is investigated theoretically under the conditions where the effects of double-layer polarization and the presence of an electroosmotic flow can be important. The equations governing the problem under consideration and the associated boundary conditions are solved numerically, and the influences of the key parameters on the electrophoretic mobility of the particle are discussed. We show that if the cavity is uncharged, the effect of double-layer polarization yields a local minimum in the electrophoretic mobility as the thickness of the double layer varies. This local minimum disappears if the cavity is also positively charged. In addition to reducing the scaled mobility of an ellipsoid, the presence of the boundary is also capable of influencing the relative magnitudes of the scaled mobility for particles of various shapes. For instance, if the volume of an ellipsoid is fixed, the scaled mobility ranks as prolate > sphere > oblate if the boundary effect is unimportant, but that order is reversed if the boundary effect is important.

Electrophoresis of an ellipsoid along the axis of a cylindrical pore: effect of a charged boundary.

The influence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering the electrophoresis of a nonconducting ellipsoid along the axis of a cylindrical pore at the level of the linear Poisson-Boltzmann equation ignoring the polarization effect. The problem considered simulates the electrophoresis conducted in a narrow space such as capillary electrophoresis and electrophoresis through a porous medium. Here, because the effect of electroosmotic flow can be important the electrophoretic behavior is much more complicated than that for the case where a boundary is uncharged. The influences of the thickness of double layer, the aspect ratio of an ellipsoid, the relative radius of a pore, and the charge conditions on the ellipsoid and pore surfaces on the mobility of the ellipsoid are discussed. Several interesting but nonintuitive electrophoretic behaviors are observed.

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.

Electrophoresis of a sphere along the axis of a cylindrical pore: effects of double-layer polarization and electroosmotic flow.

The electrophoresis of a rigid sphere along the axis of a cylindrical pore is investigated theoretically. Previous analysis is extended to the case where the effects of double-layer polarization and electroosmotic flow can be significant. The influences of the surface potential, the thickness of the double layer, and the relative size of a pore on the electrophoretic behavior of a sphere are discussed. Some interesting results are observed. For example, if both a sphere and a pore are positively charged, then the mobility of the sphere has a local minimum as the thickness of its double layer varies. Depending upon the level of the surface potential of a sphere and the degree of significance of the boundary effect, the mobility of the sphere may change its sign twice as the thickness of its double layer varies. This result can play a significant role in electrophoresis measurements.

Effect of a charged boundary on electrophoresis: a sphere at an arbitrary position in a spherical cavity.

The effect of the presence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering a sphere at an arbitrary position in a spherical cavity under conditions of low surface potential and weak applied electric field. Previous analyses are modified by using a more realistic electrostatic force formula and several interesting results, which are not reported in the literature, are observed. We show that the qualitative behavior of a particle depends largely on its position, its size relative to that of a cavity, and the thickness of the electric double layer. In general, the presence of a cavity has the effect of increasing the conventional hydrodynamic drag on a particle through a nonslip condition on the former. Also, a decrease in the thickness of the double layer surrounding a sphere has the effect of increasing the electrostatic force acting on its surface so that its mobility increases. However, this may not be the case when an uncharged particle in placed in a positively charged cavity, where the electroosmotic flow plays a role; for example, the mobility can exhibit a local maximum and the direction of electrophoresis can change.