Transient dynamic electrophoresis of a soft particle.

We introduce a general theory that explains the transient dynamic electrophoresis of a soft particle in an electrolyte solution when an oscillating electric field is suddenly applied. A simple approximate analytic expression is derived for the transient dynamic electrophoretic mobility of a soft particle that can be applied to practical situations. It is found that the mobility shows a damped oscillation, approaching its final value, similar to the behavior of a hard particle.

Dynamic Electrophoresis of a Hydrophobic and Dielectric Fluid Droplet.

Dynamic electrophoresis is the foundation for electroacoustical measurements, in which the electroacoustical signals may be used to analyze the size and electrostatic charge of colloidal entities by means of the results for dynamic electrophoretic mobility. Thus, the electrophoresis under an alternating electric field is the key foundation for electroacoustic theory. In this article, we develop a tractable analytical theory for the dynamic electrophoresis of hydrophobic and dielectric fluid droplets possessing uniform surface charge density. The tiny fluid droplets possess charged mobile surfaces and have found widespread applications in our day-to-day life. For dielectric fluid droplets (e.g., oil-water emulsions), the tangential electric stress at the interface is nonzero, which significantly affects its electrohydrodynamics under an oscillatory electric field, which has, however, a negligible impact on the electrophoretic motion of conducting droplets (e.g., mercury droplets). Besides, the micro/nanoscale fluid droplets often show hydrophobicity when they are immersed in an aqueous medium, and the impact of the electric field on hydrophobic surfaces remains a research frontier in the chemical discipline. Whereas a number of approximate expressions for electrophoretic mobility have been derived for the conducting droplet, none of them are applicable to such generic hydrophobic fluid droplets with dielectric permittivity that is significantly lower than or comparable to that of an aqueous medium. In this work, within the Debye-Hückel electrostatic framework, we elaborate an original analytical expression of dynamic electrophoretic mobility for this generic dielectric fluid droplet with a hydrophobic surface considering that the droplet retains its spherical shape during its oscillatory motion. We further derived a set of simplified expressions for dynamic electrophoretic mobility deduced under several limiting cases. The results are further illustrated, indicating the impact of pertinent parameters.

Transient dynamic electrophoresis of a spherical colloidal particle.

A general theory is presented for the transient dynamic electrophoresis of a spherical colloidal particle in an electrolyte solution under a suddenly applied oscillating electric field. An approximate analytic expression is derived for the transient dynamic electrophoretic mobility, which is applicable for low particle zeta potentials and arbitrary Debye length. It is found that the electrophoretic mobility shows a damped oscillation, approaching its final value, unlike the case where a step electric field is applied.

Transient Gel Electrophoresis of a Spherical Colloidal Particle.

The general theory is developed for the time-dependent transient electrophoresis of a weakly charged spherical colloidal particle with an electrical double layer of arbitrary thickness in an uncharged or charged polymer gel medium. The Laplace transform of the transient electrophoretic mobility of the particle with respect to time is derived by considering the long-range hydrodynamic interaction between the particle and the polymer gel medium on the basis of the Brinkman-Debye-Bueche model. According to the obtained Laplace transform of the particle's transient electrophoretic mobility, the transient gel electrophoretic mobility approaches the steady gel electrophoretic mobility as time approaches infinity. The present theory of the transient gel electrophoresis also covers the transient free-solution electrophoresis as its limiting case. It is shown that the relaxation time for the transient gel electrophoretic mobility to reach its steady value is shorter than that of the transient free-solution electrophoretic mobility and becomes shorter as the Brinkman screening length decreases. Some limiting or approximate expressions are derived for the Laplace transform of the transient gel electrophoretic mobility.

Impact of hydrodynamics and rheology of the ion partitioning effect on electrokinetic flow through a soft annulus with a retentive and absorptive wall.

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through a polyelectrolyte layer (PEL) coated cylindrical annulus with reversible and irreversible wall reactions. The ion partitioning effect is observed due to the difference in permittivity of the PEL and the electrolyte solution, which is accounted for by the Born energy. Considering ion partitioning effects, analytical solutions for induced potential and axial velocity are presented, respectively in both the PEL and electrolyte region from the modified Poisson-Boltzmann equation and the Cauchy momentum equation with a proper constitutive equation, respectively. The Maxwell fluid and classical viscous Newtonian fluid models can be achieved separately by adjusting the relaxation and retardation time in the constitutive equation of this model. The analytical solution of the convection-diffusion equation for solute transport is established in the full domain. The separation of species is found to be dependent mainly on the Damköhler number, absorption parameter, phase partitioning coefficient, etc. It is observed that the osmotic pressure increases with the thickness and fixed charge density of the PEL. The velocity decreases with an increase in the permittivity difference of these layers. Our results suggest that the separation may be achieved through a difference in absorption kinetics.

Transient electrophoresis of a spherical colloidal particle with a slip surface.

We derive the general expression for the transient electrophoretic mobility of a spherical colloidal particle with a slip surface in an electrolyte solution. From the general mobility expression, we derive an analytic mobility expression, which is applicable for low particle zeta potentials and arbitrary Debye length. This expression corresponds to the time-dependent transient Henry function.

Diffusiophoresis of a cylindrical colloidal particle oriented parallel to an electrolyte concentration gradient field.

We derive the general expression for the diffusiophoretic mobility of a cylindrical particle oriented parallel to an applied electrolyte concentration gradient field in a symmetrical electrolyte solution. From the general mobility expression as combined with an approximate analytic expression with negligible error for the electric potential distribution around a cylinder, an accurate analytic mobility expression is obtained, which is applicable for arbitrary values of the particle zeta potential and the electrical double layer thickness. It is also found that the low zeta potential approximation is an excellent approximation for low-to-moderate values of the particle zeta potential.

Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle.

The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh.

Diffusiophoresis of a moderately charged spherical colloidal particle.

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.

Electrophoretic Mobility of a Water-in-Oil Droplet Separately Affected by the Net Charge and Surface Charge Density.

Water-in-oil emulsions and droplets exhibit physicochemical properties completely different from those of oil-in-water emulsions and droplets. Thus, directly applying a standard theoretical model to water-in-oil systems cannot describe these anomalous properties. Here, the electrophoretic mobility of a water-in-oil droplet is analytically investigated using Debye-Hückel linearization and neglecting the Marangoni effect. The resulting electrophoretic mobility is shown to be separately dependent on the net charge of the droplet and the surface charge density at the droplet interface. Furthermore, when the net charge is negligible, the electrophoretic mobility is proportional to the surface charge density with a negative coefficient. This indicates that the internal electric double layer inversely contributes to the electrophoresis. This theory is applied to experimental data of water-in-oil emulsions and droplets in the literature, and qualitative and quantitative verification of the theory is discussed.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH-regulated and highly charged polyelectrolyte layer.

Electrophoresis of core-shell composite soft particles possessing hydrophobic inner core grafted with highly charged polyelectrolyte layer (PEL) has been studied analytically. The PEL bears pH-dependent charge properties due to the presence of zwitterionic functional groups. The dielectric permittivity of the PEL and bulk aqueous medium were taken to be different, which resulted in the ion-partitioning effect. Objective of this study was to provide a simple expression for the mobility of such core-shell soft particles under Donnan limit where the thickness of the PEL well exceeds the electric double layer thickness. Going beyond the widely used Debye-Hückel linearization, the nonlinear Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations was solved to determine the electrophoretic mobility. The derived expression further recovers all the existing results for the electrophoretic mobility under various simplified cases. The graphical presentation of the results illustrated the impact of pertinent parameters on the electrophoretic mobility of such a soft particle.

Approximate analytic expressions for the diffusiophoretic velocity of a spherical colloidal particle.

The general expression is derived for the diffusiophoretic velocity of a spherical colloidal particle of radius a in a concentration gradient of symmetrical electrolyte. On the basis of this expression, simple approximate analytic expressions for the diffusiophoretic velocity correct up to the order of 1/κa is derived, where κ is the Debye-Hückel parameter. It is found that the approximate expression correct to order unity can be applied for κa ≥ 50 with negligible errors, while the approximate expression correct to order 1/κa can be applied for κa ≥ 20 with negligible errors.

Thyroid-related ophthalmopathy development in concurrence with growth hormone administration.

BACKGROUND: Thyroid stimulating hormone (TSH) receptor and local infiltrate lymphocytes have been considered as major pathological factors for developing thyroid-related ophthalmopathy. Overexpression of insulin-like growth factor-I (IGF-I) receptor has emerged as a promising therapeutic target for refractory patients. However, the relationship between activation of growth hormone (GH)/IGF-I receptor signaling and development or exacerbation of thyroid ophthalmopathy has not been elucidated. Herein we describe a case that provides further clarification into the association between thyroid-related ophthalmopathy and GH/IGF-I receptor signaling. CASE PRESENTATION: A 62-year-old Japanese female diagnosed with thyroid-related ophthalmopathy was admitted to Kurume University Hospital. She had received daily administration of GH subcutaneously for severe GH deficiency; however, serum IGF-I levels were greater than + 2 standard deviation based on her age and sex. She exhibited mild thyrotoxicosis and elevation in levels of TSH-stimulating antibody. Discontinuation of GH administration attenuated the clinical activity scores of her thyroid-related ophthalmopathy. Additionally, concomitant use of glucocorticoid and radiation therapies resulted in further improvement of thyroid-related ophthalmopathy. The glucocorticoid administration was reduced sequentially, followed by successful termination. Thereafter, the patient did not undergo recurrence of thyroid-related ophthalmopathy and maintained serum IGF-I levels within normal physiological levels. CONCLUSIONS: We describe here a case in which development of thyroid-related ophthalmopathy occurred upon initiation of GH administration. GH/IGF-I signaling was highlighted as a risk factor of developing thyroid-related ophthalmopathy. Additionally, aberrant TSH receptor expression was suggested to be a primary pathophysiological mechanism within the development of thyroid-related ophthalmopathy. Physicians should be aware of the risks incurred via GH administration, especially for patients of advanced age, for induction of thyroid-related ophthalmopathy.

Approximate analytic expressions for the electrophoretic mobility of spherical soft particles.

Approximate analytic expressions are derived for the electrophoretic mobility of a weakly charged spherical soft particle consisting of the particle core covered with a surface layer of polymers in an electrolyte solution. The particle core and the surface polymer layer may be charged or uncharged. The obtained electrophoretic mobility expressions, which involve neither numerical integration nor exponential integrals, are found to be in excellent agreement with the exact numerical results. It is also found that the obtained mobility expressions reproduce all the previously derived limiting expressions and approximate analytic expressions for the electrophoretic mobility of a weakly charged spherical soft particle.

Settling of a charged hydrophobic rigid colloid in aqueous media under generalized gravitational field.

The hindrance created by the induced electric filed on the sedimentation of a charged colloid in an aqueous media is studied through numerical modeling. The colloid is considered to be hydrophobic, sedimenting under gravity or a centrifugal force (generalized gravity). The deformation of the charge cloud around the colloid induces an electric field, which generates electrical dipole force on the colloid. The sedimentation velocity is governed by the balance of an electric force, hydrodynamic drag, and gravitational force. Governing equations based on the first principle of electrokinetics is solved numerically through a control volume approach. The dependence of the sedimentation velocity on the electrical properties and slip length of the colloid is investigated. The sedimentation velocity of the charged colloid is slower than the corresponding uncharged particle and this deviation magnifies as the charge density as well as particle slip length is increased. An enhanced g-factor creates a size dependency of the charged colloids. The induced sedimentation field is obtained to analyze the electrokinetics. Surface hydrophobicity enhances the sedimentation velocity, which in turn manifests the induced sedimentation field. However, the sedimentation velocity of a charged hydrophobic colloid is lower than the corresponding uncharged hydrophobic particle and this deviation manifests as slip length is increased.

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles.

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.

Analytic Expression for Electrophoretic Mobility of Soft Particles with a Hydrophobic Inner Core at Different Electrostatic Conditions.

This paper presents a simplified model for the electrophoresis of a soft particle with a nonwettable rigid core with charged polyelectrolyte corona under a weak-field and low-charge density consideration. We have derived a closed form solution for the mobility, which reduces to the well-known expressions for mobility as derived by Ohshima for limiting cases such as a hydrophilic charged core coated with an uncharged polymer (Ohshima, H. J. Colloid Interface Sci. 2002, 252, 119-125) or an uncharged no-slip core coated with a polyelectrolyte layer (Ohshima, H. Electrophoresis 2006, 27, 526-533). The generalized mobility expression reduces to the existing expression for mobility of a rigid hydrophobic colloid as the soft layer shrinks to zero. The general form of the mobility expression involves elliptic integrals, which can be computed easily through a software like Mathematica. We have derived analytical solutions for mobility pertaining to several particular cases. The occurrence of mobility reversal when the core and polyelectrolyte layer has a charge of opposite polarity is demonstrated in this paper.

Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow.

Within the framework of analytical theories for soft surface electrophoresis, soft particles are classically defined by a hard impermeable core of given surface charge density surrounded by a polyelectrolyte shell layer permeable to both electroosmotic flow and ions from background electrolyte. This definition excludes practical core-shell particles, e.g. dendrimers, viruses or multi-layered polymeric particles, defined by a polyelectrolytic core where structural charges are distributed and where counter-ions concentration and electroosmotic flow velocity can be significant. Whereas a number of important approximate expressions has been derived for the electrophoretic mobility of hard and soft particles, none of them is applicable to such generic composite core-shell particles with differentiated ions- and fluid flow-permeabilities of their core and shell components. In this work, we elaborate an original closed-form electrophoretic mobility expression for this generic composite particle type within the Debye-Hückel electrostatic framework and thin double layer approximation. The expression explicitly involves the screening Debye layer thickness and the Brinkman core and shell hydrodynamic length scales, which favors so-far missing analysis of the respective core and shell contributions to overall particle mobility. Limits of this expression successfully reproduce results from Ohshima's electrophoresis theory solely applicable to soft particles with or without hard core.

Electrokinetic phenomena in a dilute suspension of spherical solid colloidal particles with a hydrodynamically slipping surface in an aqueous electrolyte solution.

A review is given on the theory of the electrokinetics in a dilute suspension of spherical solid colloidal particles with a hydrodynamically slipping surface moving in an aqueous liquid medium containing electrolytes. For a solid particle with a slip surface, the Navier boundary condition is employed instead of the usual no-slip boundary condition on the particle surface. The effect of the hydrodynamic slip is characterized by the slipping length. The limiting case of zero slipping length corresponds to a hydrophilic surface. As the hydrophobicity of the particle surface increases, the slipping length increases. The limiting case of infinitely large slipping length corresponds to a completely hydrophobic surface. General formulas and approximate expressions of the electrophoretic mobility, the electrical conductivity, the sedimentation velocity and potential, and the diffusion constant are presented. The magnitudes of the electrophoretic mobility and the sedimentation potential, in particular, are found to increase with increasing slipping length. It is also shown that a spherical solid colloidal particle with a slip surface is hydrodynamically similar to a liquid drop.

Gel electrophoresis of a soft particle.

A review is given on the theory of the gel electrophoresis of a spherical soft particle, i.e., the electrophoresis of a spherical hard particle covered with an ion-penetrable surface layer of polyelectrolytes moving in a polymer gel medium, which may either be charged or uncharged. A detailed study is made on the fundamental electrokinetic equations describing the soft-particle gel electrophoresis due to the long-range hydrodynamic particle-gel interaction on the basis of the Brinkman-Debye-Bueche model. A general expression and several approximate analytic expressions are given for the electrophoretic mobility of a soft particle in a polymer gel medium.