Transmembrane voltage induced on a cell membrane in suspensions exposed to an alternating field: a theoretical analysis

We present analytical equations for the transmembrane voltage (DeltaPsi) induced by an alternating field on spherical cells arranged in orderly suspensions. For physiologically normal cells, the cell membrane was assumed to be non-conductive. With increasing alternating field frequency, capacitive property of the cytoplasm and the external medium become increasingly important and thus must be accounted for. Considering the symmetry of the arrayed cells and the tiny volume of the unit cell compared to that of the suspensions, the influence exerted on a unit cell by other cells was posited to be approximately symmetrical with respect to the symmetrical axis. This implies that the shape of the equipotential plane of spherical cells in the suspensions is similar to that of the single cell exposed to the external field, though the value of the potential of both cells should be different. Therefore, the internal field of the cytoplasm and the equivalent body of a unit cell in the suspensions should be approximately constant. This allows for calculating the effective average field in the equivalent body with Maxwell-Wagner and Bruggeman-Hanai equations for low and high cell concentrations, respectively. We investigated the conditions, under which the local electric field of a unit cells in suspension is approximately equal to that of a single cell. Under these conditions the analytical solution for DeltaPsi induced by alternating fields on cells in suspensions can be derived from that of the single cell.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Electrically developed morphology of carbon nanoparticles in suspensions monitored by in situ optical observations under sinusoidal electric field

In situ optical observations were performed for suspensions composed of carbon nanoparticles under the sinusoidal electric field with an amplitude around 20 kV/mm (volt per micrometer) and various frequencies. For extremely diluted suspensions of mixed fullerenes or multiwalled carbon nanotubes (MWNTs) in a silicone oil, the dark-field optical microscopy was effective for the in situ observation of the particle behavior under the electric field. The nanoparticles in a fullerene suspension under the sinusoidal electric field with a frequency of 100 Hz (in short, 100 Hz electric field) were aggregated to form a rigid spherical microstructure around the halfway between the electrodes. On the other hand, the nanoparticles in an MWNT suspension under 100 Hz electric field were also aggregated but aligned to form a chain-like microstructure which spans the electrodes. Both of the aggregated particles were stable even after the removal of the electric field, and they were redispersed by application of 10 Hz electric field.     

Dependence of the dielectric properties of suspensions on the volume fraction of suspended particles

It is shown that the fundamental expression for the complex permittivity epsilons* of a dilute suspension of monodispersed, spherical particles, epsilons*=epsilone*(1+3phid*), where epsilone* is the complex permittivity of the suspending medium and d* the dipolar coefficient, is strictly valid for any value of the volume fraction phi of particles in the suspension, provided that d* is interpreted as the ensemble average value of the dipolar coefficient of the particles and is defined in terms of the macroscopic electric field in the suspension.     

A new pulsed electric field microreactor: comparison between the laboratory and microtechnology scale

This paper presents a new microreactor dedicated for pulsed electric field treatment (PEF), which is a pasteurization method that inactivates microorganisms with short electric pulses. The PEF microreactor consists of a flow-through channel with a constriction where the electric field is focussed. Compared to a laboratory-scale setup 25 times lower voltages were needed to obtain the same electric field strength due to the close electrode spacing. A finite element model showed that the electric field intensity is very homogeneous throughout the channel, which is crucial for the pasteurization processes. Experiments where artificial vesicles, loaded with carboxyfluorescein, were electroporated showed that the maximum transmembrane potential adequately described the processes both in the microreactor and the laboratory-scale setup, although the length scales are different. Electroporation started at a transmembrane potential of 0.5 V, reaching a maximum fraction of electroporated vesicles of 51% at a transmembrane potential of 1.5 V. The partial electroporation is not a result of the heterogenity of the vesicles or the electric field. With this new PEF microreactor it is possible to study the PEF process in more detail.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Dynamic electrophoresis of droplet dispersions at low surface potentials

The dynamic electrophoresis of a dispersion of spherical droplets under conditions of low surface potential and arbitrary double-layer thickness and droplet volume fraction is analyzed. A cell model with the Shilov-Zharkikh boundary condition for the electric potential is adopted to simulate a dispersion, and the governing equations and the associated boundary conditions are solved by a pseudo-spectral method based on Chebyshev polynomials. The influence of the frequency of the applied electric field, the volume fraction of the droplets, the thickness of the double layer, and the relative magnitude of the viscosity of the droplet fluid on the electrophoretic behavior of a dispersion is discussed.     

Startup of electrophoresis in a suspension of colloidal spheres

The transient electrophoretic response of a homogeneous suspension of spherical particles to the step application of an electric field is analyzed. The electric double layer encompassing each particle is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is incorporated. The momentum equation for the fluid outside the double layers is solved through the use of a unit cell model. Closed‐form formulas for the time‐evolving electrophoretic and settling velocities of the particles in the Laplace transform are obtained in terms of the electrokinetic radius, relative mass density, and volume fraction of the particles. The time scale for the development of electrophoresis and sedimentation is significantly smaller for a suspension with a higher particle volume fraction or a smaller particle‐to‐fluid density ratio, and the electrophoretic mobility at any instant increases with an increase in the electrokinetic particle radius. The transient electrophoretic mobility is a decreasing function of the particle volume fraction if the particle‐to‐fluid density ratio is relatively small, but it may increase with an increase in the particle volume fraction if this density ratio is relatively large. The particle interaction effect in a suspension on the transient electrophoresis is much weaker than that on the transient sedimentation of the particles.     

Continuous flow microfluidic cell inactivation with the use of insulating micropillars for multiple electroporation zones

Electroporation is a powerful tool for inactivating cells and transfecting biological cells and has applications in biology, genetic engineering, medicine, environment, and many others. We report a new continuous flow device embedded with insulating micropillars to achieve better performance of cell inactivation. The use of micropillars creates multiple electroporation zones with enhanced local electric field strengths. Using a model solution of Saccharomyces cerevisiae, we examined the inactivation performance of the device under various applied electric voltages and flow rates. Results from the numerical simulations and experiments showed that even with an induced transmembrane potential of 0.58 V, close to 63% of cell inactivation was achieved at a flow rate of 2.5 mL/h. This was higher than the 24% cell inactivation observed for a reference device without micropillars that was subjected to the same conditions.     

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.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Three-dimensional Monte Carlo simulations of internal aggregate structures in a colloidal dispersion composed of rod-like particles with magnetic moment normal to the particle axis

We have treated a suspension composed of ferromagnetic rod-like particles with a magnetic moment normal to the particle axis in order to investigate aggregation phenomena of such a suspension by means of cluster-moving Monte Carlo simulations. In the present study, we have considered a three-dimensional mono-dispersed model system composed of such rod-like particles. Internal structures of self-assembled clusters have been discussed quantitatively in terms of radial distribution, pair correlation, orientational pair correlation functions, number distributions of clusters, and order functions. The main results obtained here are summarized as follows. Rod-like particles tend to aggregate to form raft-like clusters along the magnetic moment direction more significantly with magnetic particle-particle interactions. In such raft-like clusters, the direction of each particle axis has a tendency to incline in parallel formation, but is not so parallel as in a two-dimensional dispersion. As the volumetric fraction increases, longer raft-like clusters are formed, but such raft-like clusters do not aggregate further to form thicker clusters, which is in significantly contrast with a dispersion of spherical particles, where thicker chain-like clusters are observed under certain conditions. For the case of strong magnetic particle-particle interactions, sufficiently long raft-like clusters are formed along the magnetic field direction, even if the influence of an external magnetic field is of the same order of that of the thermal energy. However, rod-like particles in such clusters do not necessarily incline in significantly parallel formation along a certain direction. Self-assembled tube-like clusters are formed when magnetic particle-particle interactions are much more dominant than the rotational Brownian motion under circumstances of rod-like particles inclining in a certain direction.     

Electric birefringence of dispersions of platelets

This paper describes the electro-optic response of a suspension of disk-like colloids. We have considered aqueous suspensions of Gibbsite platelets and measured the electrically induced birefringence in the broad frequency range 10(2)-10(8) Hz. When simply dispersed in an electrolyte solution, these particles orient with their major axis parallel to the electric field at all frequencies. The spectral dependence of their Kerr coefficient features three regimes: an electrokinetic α-relaxation within the kHz range, a conductive Maxwell-Wagner-O'Konski (MWO) relaxation having characteristic frequency in the 1-10 MHz range, and a nonzero high frequency asymptote. We quantitatively analyze the MWO spectral component and the high-frequency asymptote on the basis of a model developed for oblate particles. This analysis enables us to obtain the relevant particle properties: surface conductivity, zeta potential, and intrinsic Gibbsite birefringence. When the particles are dispersed in a mixture that also contains smaller spherical particles that have a charge of the same sign, their electric birefringence becomes negative at low frequency. This anomalous orientation of the platelets is analogous to that observed in mixtures of prolate and spherical particles, and demonstrates the anomalous birefringence as a universal property of suspensions of nonspherical particles when surrounded by smaller charged particles.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

Sedimentation velocity and potential in concentrated suspensions of charged porous spheres

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter. An analytical expression for the settling velocity of the charged porous sphere 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 porous spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.     

Electrophoresis of solid particles at large Peclet numbers

A theory of concentration polarization of a thin electrical double layer (DL) on a spherical particle is developed for the regime of large Peclet numbers which is realized in strong electric fields. In this regime, the concentration field arising outside DL is estimated under influence of diffusion and convection. According to the theory developed, polarization of DL at large Peclet numbers causes a change in the Stern potential, the formation of a dipole moment and the long-range potential. The diffuse layer deviates strongly from spherical symmetry and electroneutrality, and the screen of the surface charge is provided not only by the diffuse atmosphere but also by the charge induced in the convective-diffusion layer. The effect of electric field on the induced charge gives rise to the additional electroosmotic slip, that was called "secondary electroosmosis". Thus, a nonlinear additional term for the Smoluchowski formula of electrophoretic velocity is based on the changes of zeta-potential and on the secondary electroosmotic slip. The comparison of theory with experimental results revealed considerable fitting.     

Osmotically induced membrane tension facilitates the triggering of living cell electropermeabilization

Very little is known about the molecular mechanisms supporting living cell membrane electropermeabilization. This concept is based on the local membrane permeability induced by cell exposure to brief and intense external electric field pulses. During the electric field application, an electro-induced membrane electric potential difference is created that is locally associated with the dielectric properties of the plasma membrane. When the new membrane electric potential difference locally reaches a critical value, a local alteration of the membrane structure is induced and leads to reversible permeabilization. In our study, we attempted to determine whether mechanical tension could modulate the triggering of membrane electropermeabilization. Change in lateral tension of Chinese Hamster Ovary cell membrane has been osmotically induced. Cell electropermeabilization was performed in the minute time range after the osmotic stress, i.e., before the regulatory volume decrease being activated by the cell. Living cell electropermeabilization was analyzed on cell population using flow cytometry. We observed that electropermeabilization triggering was significantly facilitated when the lateral membrane tension was increased. The main conclusion is that the critical value of transmembrane potential needed to trigger membrane electropermeabilization, is smaller when the membrane is under lateral mechanical constraint. This supports the hypothesis that both mechanical and electrical constraints play a key role in transient membrane destabilization.     

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.     

Direct measurement of depletion and structural forces in polydisperse, charged systems

The effect of polydispersity in macromolecule size or surface potential on the depletion interaction between a spherical silica particle and a silica flat in solutions containing two different types of nonadsorbing charged spherical macromolecules was studied with an atomic force microscope (AFM). The macromolecules used here were negatively charged nanospheres of either polystyrene or silica. To investigate the effect of size polydispersity, experiments were performed under the condition of either constant macromolecule number density or constant volume fraction as the relative proportions of smaller and larger polystyrene nanospheres in the suspension were varied. Similarly, for the experiments with surface potential polydispersity, the suspensions contained varying fractions of more highly charged (polystyrene) and less highly charged (Ludox silica) nanospheres at constant number density. The experimental results were compared to the predictions of the modified force-balance model of Piech and Walz and semiquantitative agreement was found. In particular, the maximum attraction and repulsion observed in the measured force profiles were found to agree with the predicted trends as the makeup of the macromolecules was varied. The trend in the maximum attraction was also consistent with predictions made using a simple "scaling" analysis derived using the equation for hard-sphere interactions.     

Monodisperse conducting colloidal dipoles with symmetric dimer structure for enhancing electrorheology properties

This study introduces an electrorheological (ER) approach that allows us to obtain remarkably enhanced ER properties by using monodisperse colloidal dimer particles. Two sets of colloidal particles, which are spheres and symmetric dimers, were synthesized employing the seeded polymerization technique. The aspect ratio of dimer particles was ~1.43. Then, the surface of the particles was coated with polyaniline by using the chemically oxidative polymerization method. After preparation of the particle suspensions having the same particle volume and concentration, their ER behavior was investigated with changing the electric field strength. At the same experimental condition, both shear stress and shear yield stress of the dimer particle suspension remarkably increased, compared with those of the spherical particle suspension. This attributes to the fact that the shape anisotropy of suspending particles effectively led to increase in the dipole moment under the electric field, thus resulting in formation of a well-structured colloidal chains between the electrodes.