Creeping motion of an assemblage of composite spheres relative to a fluid

The sedimentation of a homogeneous distribution of spherical composite particles and the fluid flow through a bed of these particles are investigated theoretically. Each composite particle is composed of a spherical solid core and a surrounding porous shell. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. The effect of interactions among the particles is taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of nonporous spheres within a fluid. In the limit of a small Reynolds number, the Stokes and Brinkman equations are solved for the flow field in a unit cell, and the drag force exerted by the fluid on the particle is obtained in a closed form. For a distribution of composite spheres, the normalized mobility of the particles decreases or the particle interactions increase monotonically with a decrease in the permeability of their porous shells. The effect of particle interactions on the creeping motion of composite spheres relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solutions describing the drag force or mobility for a suspension of composite spheres reduce to those for suspensions of solid spheres and of porous spheres. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability.     

Some solutions of a cell model for a suspension of spherical vesicles in osmophoresis

The problem of the osmophoretic motion of a homogeneous suspension of identical spherical vesicles is analyzed in the limit of negligible Reynolds and Peclet numbers. The effects of interaction among individual vesicles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical vesicle is envisaged to be surrounded by a concentric shell of suspending fluid, and the osmophoretic velocity of the vesicle is calculated for various cases. Analytical expressions of this mean vesicle velocity are obtained in closed form as functions of the volume fraction of the vesicles. Comparisons between the approximate ensemble-averaged osmophoretic velocity of a test vesicle in a dilute suspension and our cell-model results are made.     

Diffusiophoresis in a concentrated suspension of colloidal spheres in nonelectrolyte gradients

The diffusiophoretic motion of a homogeneous suspension of identical spherical particles is considered under conditions of small Reynolds and Peclet numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the diffusiophoretic velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. Comparisons between the ensemble-averaged diffusiophoretic velocity of a test particle in a dilute suspension and our cell-model results are made. Received: 30 June 1999 Accepted: 8 December 1999     

Dielectric versus optical response of chevron ferroelectric liquid crystals

Dielectric and optical methods to investigate the response of surface-stabilized ferroelectric liquid crystals (SSFLCs) of the chevron structure are examined and compared in the case of the azimuthal mode of collective relaxation processes. It is found that the variation of an effective (averaged over the chevron cell volume) dielectric permittivity tensor under the influence of a weak alternating external electric field is approximately equivalent to the transformation of this tensor as a consequence of the rotation of the laboratory frame around the axis perpendicular to the smectic plane about a small angle. Then, using an analytic solution of the equation of motion describing the azimuthal rotation of molecules, it is shown that both of the analysed approaches to calculate and measure the response of SSFLCs yield consistent results for these rotational dynamic processes. This allows the calculation of the spontaneous polarization of the unit volume of chevron slabs, provided that the pretilted azimuthal angle (in the absence of an applied electric field) within the smectic plane is known.     

Model of a confined spherical cell in uniform and heterogeneous applied electric fields

Cells exposed to electric fields are often confined to a small volume within a solid tissue or within or near a device. Here we report on an approach to describing the frequency and time domain electrical responses of a spatially confined spherical cell by using a transport lattice system model. Two cases are considered: (1) a uniform applied field created by parallel plane electrodes, and (2) a heterogeneous applied field created by a planar electrode and a sharp microelectrode. Here fixed conductivities and dielectric permittivities of the extra- and intracellular media and of the membrane are used to create local transport models that are interconnected to create the system model. Consistent with traditional analytical solutions for spherical cells in an electrolyte of infinite extent, in the frequency domain the field amplification, G(m) (f) is large at low frequencies, f<1 MHz. G(m) (f) gradually decreases above 1 MHz and reaches a lower plateau at about 300 MHz, with the cell becoming almost "electrically invisible". In the time domain the application of a field pulse can result in altered localized transmembrane voltage changes due to a single microelectrode. The transport lattice approach provides modular, multiscale modeling capability that here ranges from cell membranes (5 nm scale) to the cell confinement volume ( approximately 40 microm scale).     

Dielectric versus optical response of chevron ferroelectric liquid crystals

Dielectric and optical methods to investigate the response of surface‐stabilized ferroelectric liquid crystals (SSFLCs) of the chevron structure are examined and compared in the case of the azimuthal mode of collective relaxation processes. It is found that the variation of an effective (averaged over the chevron cell volume) dielectric permittivity tensor under the influence of a weak alternating external electric field is approximately equivalent to the transformation of this tensor as a consequence of the rotation of the laboratory frame around the axis perpendicular to the smectic plane about a small angle. Then, using an analytic solution of the equation of motion describing the azimuthal rotation of molecules, it is shown that both of the analysed approaches to calculate and measure the response of SSFLCs yield consistent results for these rotational dynamic processes. This allows the calculation of the spontaneous polarization of the unit volume of chevron slabs, provided that the pretilted azimuthal angle (in the absence of an applied electric field) within the smectic plane is known.     

The response of a colloidal suspension to an alternating electric field

This paper is concerned with the calculation of the complex conductivity K* of a suspension, a quantity which may be determined experimentally from the measurement of the alternating current which flows between a pair of electrodes in the suspension due to an alternating voltage difference. A semi-analytic formula is derived for the complex conductivity of a dilute suspension of spherical particles with small dielectric constant which is reasonably accurate for ?-potentials of less than 50 mV. For such suspensions this formula represents a very economical alternative to the exact computer calculation of K* described by DeLacey and White (ref. 2). Although the formula for K* is derived for particles with fixed surface charge, it is shown that the formula can also be applied to a more general class of suspensions, in which the surface charge arises from the dissociation of a single type of surface group.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.     

Numerical study of the electrical conductivity and polarization in a suspension of spherical cells

The spatial distribution of electrical potential and current in a suspension of spherical cells under an applied electric field was numerically obtained using the equivalent circuit method (ECM). The effect of the proximity of the cells was studied in a set of simulations where the volumetric fraction varied from 0.24 to 0.66. The results show that the transmembrane potential for cells in the suspension is lower than the theoretically predicted value for a single dielectric membrane under a uniform electric field. It was also observed that as the volumetric fraction is increased, the transmembrane potential on the pole of the cells decreases linearly. Furthermore, the conductivity of the suspension was also observed to be a function of the volumetric fraction and this result is in a good agreement with the Maxwell's model for spherical particles suspended in a volume conductor.     

Field induced anisotropy of charged magnetic colloids: a rescaled mean spherical approximation study

The liquidlike structure of colloidal suspensions with both electrostatic and magnetic interactions is investigated by means of small angle x-ray scattering (SAXS) dependent on an external magnetic field. For weak magnetic interactions, without external field, the magnetic dipoles are randomly oriented. Under this condition, isotropic structures are observed. In an external field, however, the magnetic momenta arrange parallel to the external field and induce anisotropic liquidlike structures. For weak magnetic interactions, the structure factor can be described within the framework of the rescaled mean spherical approximation. Due to the high experimental accuracy of synchrotron SAXS, from the anisotropic distortion of liquidlike structures, interparticle forces smaller than 10(-15) N can easily be detected.     

Cellular absorption of electric field energy: influence of molecular properties of the cytoplasm

Molecular dispersions may significantly alter the frequency dependence of structural polarizations. Consequently, the molecular properties cannot be neglected when the energy absorption is calculated with a subcellular resolution. Our example presents calculations that explain the absorption in single human red blood cells. The molecular properties of the cytoplasm have been derived from literature data on the impedance of Hb suspensions. The resulting cell properties were then compared to own data obtained by single cell dielectric spectroscopy.     

Simultaneous stochastic effects of a thermal reservoir and an electromagnetic field on the optical susceptibility of a two-level system

In this paper we derive analytical expressions for the optical susceptibility of a two-level system immersed in a thermal bath and interacting with an external electromagnetic field, where both of them are considered as noise sources. The dynamics of the system is described by a set of optical stochastic Bloch equations. The noise sources are modeled as Ornstein-Uhlenbeck processes. The optical stochastic Bloch equations are perturbatively solved up to second order in the external field. We found that each noise affects the dynamics in a different manner. Thus, at first order, the bath modifies the transverse relaxation time, whereas the effect of a random field can only be appreciated if the expansion is calculated up to second order, where correlations begin to be important.     

Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.     

Cell membrane electropermeabilization by symmetrical bipolar rectangular pulses. Part I. Increased efficiency of permeabilization

The paper presents a comparative study of electropermeabilization of cells in suspension by unipolar and symmetrical bipolar rectangular electric pulses. While the parameters of electropermeabilization by unipolar pulses have been investigated extensively both in cell suspensions and in tissues, studies using bipolar pulses have been rare, partly due to the lack of commercially available bipolar pulse generators with pulse parameters suitable for electropermeabilization. We have developed a high-frequency amplifier and coupled it to a function generator to deliver high-voltage pulses of programmable shapes. With symmetrical bipolar pulses, the pulse amplitude required for the permeabilization of 50% of the cells was found to be approximately 20% lower than with unipolar pulses, while no statistically significant difference was detected between the pulse amplitudes causing the death of 50% of the cells. Bipolar pulses also led to more than 20% increase in the uptake of lucifer yellow. We show that these results have a theoretical background, because bipolar pulses (i) counterbalance the asymmetry of the permeabilized areas at the poles of the cell which is introduced by the resting transmembrane voltage, and (ii) increase the odds of permeabilization of cells having a nonspherical shape or a nonhomogeneous membrane. If similar results are also obtained in tissues, bipolar pulse generators could in due course gain a wide, or even a predominant use in cell membrane electropermeabilization.     

Bacteria counting with impedance spectroscopy in a micro probe station

A method to quantify the density of viable biological cells in suspensions is presented. The method is implemented by low-frequency impedance spectroscopy and based on the finding that immobilized ions are released to move freely in the surrounding suspension when viable Escherichia coli cells are killed by a heat shock. The presented results show that an amount of ions corresponding to approximately 2 x 10(8) unit charges are released per viable bacterium killed. A micro probe station with coplanar Ti electrodes was electrically characterized and used as a measuring unit for the impedance spectroscopy recordings. This unit is compatible with common microfabrication techniques and should enable the presented method to be employed using a flow-cell device for viable bacteria counting in miniaturized on-line monitoring systems.     

Electrophoresis of a concentrated dispersion of spherical particles in a non-Newtonian fluid

Electrophoresis is one of the most widely used analytical tools for the quantification of the charged conditions on the surface of fine particles including biological entities. Although it has been studied extensively in the past, relevant results for the case when the dispersion medium is non-Newtonian are very limited. This may occur, for example, when the concentration of the dispersed phase is not low, which is not uncommon in practice. Here, the electrophoresis of a concentrated spherical dispersion in a Carreau fluid is analyzed theoretically under the conditions of low electric potential and weak external applied electrical field. A pseudospectral method coupled with a Newton-Raphson iteration procedure is used to solve the electrokinetic equations describing the phenomenon under consideration. We conclude that the more significant the shear thinning effect of the fluid, the larger the mobility, and this phenomenon is pronounced for the case when the double layer surrounding a particle is thin. We show that if the double layer is thin and the effect of shear thinning is significant, a second vortex can be observed in the neighborhood of a particle.     

Dielectric analysis of sheep erythrocyte ghost. Examination of applicability of dielectric mixture equations

The purpose of this study is to confirm the applicability of dielectric mixture equations in dielectric analysis of biological cell suspensions. Two dielectric mixture equations, the Pauly-Schwan (P-S) equation and the Hanai-Asami-Koizumi (H-A-K) equation were tested using sheep erythrocyte ghosts whose internal solution is identical with the external solution. Dielectric measurements were carried out for the ghost suspensions over a frequency range 10 kHz to 100 MHz; a single dielectric relaxation was found between 100 kHz and 10 MHz. From the dielectric relaxation, the conductivity and permittivity of the ghost interior and the capacitance of the cell membrane were calculated following the P-S and H-A-K equations. When the H-A-K equation was employed (and as expected from the property of the ghosts), the estimated internal conductivity was in good agreement with the external conductivity at volume fractions up to about 0.7. With the P-S equation, on the other hand, the same results as above were obtained but only at low volume fractions below about 0.3. In addition, the H-A-K equation provided a better simulation for the observed relaxation curves than did the P-S equation, especially at high volume fractions. It is, therefore, concluded that the H-A-K equation is applicable to a wider range of volume fraction than is the P-S equation.     

Electrorheological suspensions of laponite in oil: rheometry studies

We have studied the effect of an external direct current (DC) electric field ( approximately 1 kV/mm) on the rheological properties of colloidal suspensions consisting of aggregates of laponite particles in a silicone oil. Microscopy observations show that, under application of an electric field greater than a triggering electric field Ec approximately 0.6 kV/mm, laponite aggregates assemble into chain- and/or columnlike structures in the oil. Without an applied electric field, the steady-state shear behavior of such suspensions is Newtonian-like. Under application of an electric field larger than Ec, it changes dramatically as a result of the changes in the microstructure: a significant yield stress is measured, and under continuous shear the fluid is shear-thinning. The rheological properties, in particular the dynamic and static shear stress, were studied as a function of particle volume fraction for various strengths (including null) of the applied electric field. The flow curves at constant shear rate can be scaled with respect to both the particle fraction and electric field strength onto a master curve. This scaling is consistent with simple scaling arguments. The shape of the master curve accounts for the system's complexity; it approaches a standard power-law model at high Mason numbers. Both dynamic and static yield stresses are observed to depend on the particle fraction Phi and electric field E as PhibetaEalpha, with alpha approximately 1.85 and beta approximately 1 and 1.70 for the dynamic and static yield stresses, respectively. The yield stress was also determined as the critical stress at which there occurs a bifurcation in the rheological behavior of suspensions that are submitted to a constant shear stress; a scaling law with alpha approximately 1.84 and beta approximately 1.70 was obtained. The effectiveness of the latter technique confirms that such electrorheological (ER) fluids can be studied in the framework of thixotropic fluids. The method is very reproducible; we suggest that it could be used routinely for studying ER fluids. The measured overall yield stress behavior of the suspensions may be explained in terms of standard conduction models for electrorheological systems. Interesting prospects include using such systems for guided self-assembly of clay nanoparticles.