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.     

Breakup of a Multiple Emulsion Drop in a Uniform Electric Field

The steady deformation and breakup of emulsion drops in a uniform electric field are considered experimentally. Due to the low volume fraction of inner drops, the emulsions can be effectively assumed as Newtonian fluids with spatial nonuniformity. The measurements of the electrical properties show that the oil-in-water (o/w) emulsion drop behaves like a conducting drop. On the other hand, the water-in-oil (w/o) emulsion drops can be regarded as inhomogeneous leaky dielectric drops. It is found that the viscosity ratio is not an important parameter within the small deformation limit and breakup mode of the o/w emulsion drops. In the case of w/o emulsion drops, however, the breakup mode depends on the viscosity ratio. Inherent nonuniformity of the emulsion drops makes drop more deformable and unstable. The tip-streaming is the dominant breakup mode of o/w emulsion drops when the nonuniformity of drop phase is appreciable. Copyright 1999 Academic Press.     

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.     

Effects of Applied Electric Fields on Drop—Interface and Drop—Drop Coalescence*

In this work, coalescence of a single organic or aqueous drop with its homophase at a horizontal liquid interface was investigated under applied electric fields. The coalescence time was found to decrease for aqueous drops as the applied voltage was increased, regardless of the polarity of the voltage. For organic drops, the coalescence time increased with increasing applied voltage of positive polarity and decreased with increasing applied voltage of negative polarity. Under an electric field, the coalescence time of aqueous drops decreases due to polarization of both the drop and the flat interface. The dependency of organic drop-interface coalescence on the polarity of the electric field may be a result of the negatively charged organic surface in the aqueous phase. Due to the formation of a double layer, organic drops are subjected to an electrostatic force under an electric field, which, depending on the field polarity, can be attractive or repulsive. Pair-drop coalescence of aqueous drops in the organic phase was also studied. Aqueous drop-drop coalescence is facilitated by polarization and drop deformation under applied electric fields. Without applied electric fields, drop deformation increases the drainage time of the liquid film between two approaching drops. Therefore, a decrease in the interfacial tension, which causes drop deformation, accelerates drop-drop coalescence under an electric field and inhibits drop coalescence in the absence of an electric field.     

液态Wood合金在NaOH电解质溶液中的电毛细变形现象

本文研究了液态Wood合金在氢氧化钠电解质溶液中,通过施加外电场,进而诱发液态金属电毛细变形的现象. 当石墨电极伸入金属液滴内部时,通电后在金属表面发生的电极反应,促使金属表面形成氧化膜或去除氧化膜. 由于氧化膜与液态金属的表面张力存在巨大差异,通电后电极极性的变化可实现金属液滴形状的快速可逆变形.在液态金属与电解质溶液之间形成的双电子层中,当两侧聚集同极性电荷时将降低界面张力.为维持通电后体系自由能最小,将迫使液体金属增大与溶液之间的界面面积,在宏观上表现为液体金属的变形,由于液态金属与氢氧化钠反应后自身携带负电荷,在电场力的作用下可有效地驱动液态金属在电解质溶液中的运动.     

Electroviscous cylinder-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle-wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.     

Hydrodynamic forces acting on a microscopic emulsion drop growing at a capillary tip in relation to the process of membrane emulsification

Here, we calculate the hydrodynamic ejection force acting on a microscopic emulsion drop, which is continuously growing at a capillary tip. This force could cause drop detachment in the processes of membrane and microchannel emulsification, and affect the size of the released drops. The micrometer-sized drops are not deformed by gravity and their formation happens at small Reynolds numbers despite the fact that the typical period of drop generation is of the order of 0.1 s. Under such conditions, the flow of the disperse phase through the capillary, as it inflates the droplet, engenders a hydrodynamic force, which has a predominantly viscous (rather than inertial) origin. The hydrodynamic boundary problem is solved numerically, by using appropriate curvilinear coordinates. The spatial distributions of the stream function and the velocity components are computed. The hydrodynamic force acting on the drop is expressed in terms of three universal functions of the ratio of the pore and drop radii. These functions are computed numerically. Interpolation formulas are obtained for their easier calculation. It turns out that the increase in the viscosity of each of the two liquid phases increases the total ejection force. The results could find applications for the interpretation and prediction of the effect of hydrodynamic factors on the drop size in membrane emulsification.     

The electroviscous force between charged particles: beyond the thin-double-layer approximation

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95-112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye-Hückel approximation.     

Electrical charging of a conducting water droplet in a dielectric fluid on the electrode surface

It has been conceived that a charged droplet driven by Coulombic force can be used as a droplet-based microreactor. As a basic research for such applications, electrical charging of a conducting water droplet is studied experimentally. The effects of electric field, medium viscosity, and droplet size are investigated. It is found that the amount of electrical charging increases with the droplet size and the electric field. However, the medium viscosity does not have a significant effect in the range of the present study. A scaling law is derived from the experimental results. Unlike the case of a perfect conductor, the estimated amount of electrical charge (Q(est)) of a water droplet is proportional to the 1.59 power of the droplet radius (R) and the 1.33 power of the electric field strength (E). (For a spherical perfect conductor, Q is proportional to R(2) and E.) In order to understand these differences, numerical simulations are performed for the idealized droplets of perfect conductor. Comparison of the numerical and experimental results suggests that the differences are mainly due to incomplete charging of a water droplet resulted from the combined effect of electrochemical reaction at electrode and the relatively low conductivity of water.     

Transport and deformation of droplets in a microdevice using dielectrophoresis

In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop-drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results.     

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.     

Vertical motion of a charged colloidal particle near an AC polarized electrode with a nonuniform potential distribution: theory and experimental evidence

Electroosmotic flow in the vicinity of a colloidal particle suspended over an electrode accounts for observed changes in the average height of the particle when the electrode passes alternating current at 100 Hz. The main findings are (1) electroosmotic flow provides sufficient force to move the particle and (2) a phase shift between the purely electrical force on the particle and the particle's motion provides evidence of an E2 force acting on the particle. The electroosmotic force in this case arises from the boundary condition applied when faradaic reactions occur on the electrode. The presence of a potential-dependent electrode reaction moves the likely distribution of electrical current at the electrode surface toward uniform current density around the particle. In the presence of a particle the uniform current density is associated with a nonuniform potential; thus, the electric field around the particle has a nonzero radial component along the electrode surface, which interacts with unbalanced charge in the diffuse double layer on the electrode to create a flow pattern and impose an electroosmotic-flow-based force on the particle. Numerical solutions are presented for these additional height-dependent forces on the particle as a function of the current distribution on the electrode and for the time-dependent probability density of a charged colloidal particle near a planar electrode with a nonuniform electrical potential boundary condition. The electrical potential distribution on the electrode, combined with a phase difference between the electric field in solution and the electrode potential, can account for the experimentally observed motion of particles in ac electric fields in the frequency range from approximately 10 to 200 Hz.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Electrohydrodynamics of a drop under nonaxisymmetric electric fields

We consider the electrohydrodynamics of a spherical drop in a nonaxisymmetric electric field, which can be approximated by the sum of a uniform field and a linear straining field. We obtain the analytic solution of the three-dimensional flow fields inside and outside a drop for the Stokes flow regime by using Lamb's general solution and the leaky dielectric model. With the analytic solution, the dielectrophoretic migration velocity of a drop is obtained as a function of the type and the frequency of the imposed electric field. The direction of drop motion is found to be parallel to the dielectrophoretic force. The analytic solution is also used to investigate the characteristics of the interfacial flow under various nonaxisymmetric electric fields. While investigating the interfacial flow, we find a surface vortex structure under certain nonaxisymmetric electric fields, which is found to be related to the chaotic mixing inside the drop. Finally, we consider the chaotic features of three-dimensional flows inside the drop under static nonaxisymmetric electric fields.     

导电原子力显微镜对蛋白质在分子水平上的电学表征

蛋白质电子传递的研究不仅对阐述生物能量传递具有重要的意义,而且有助于促进生物分子在分子电子器件中的应用．金属蛋白以其固有的电化学和电学特性,在光合作用和呼吸作用中起到重要作用．其中铜蓝蛋白具有良好的电化学性质和明确的分子结构,常常用作研究蛋白质电子传递的模型分子。很多具有微观尺度表征能力的分析仪器可用于研究表面吸附的蛋白质分子。     

Low-capacity channel designed for particle separation with controlled electric fields and evaluation of involved forces

Electric field is one of the suitable physical fields applicable to particle separations. Although long rectangular channel is used for particle separation in usual electrical field flow fractionation (FFF), a short low-capacity channel can replace it if the field is precisely controlled. Several separation principles are proposed with this channel. The elution behavior of particles has revealed that the gravitational, diffusion, and hydrodynamic lift force (HLF) play important roles in the determination of the elution behavior of particles. The elution threshold voltage (V(th)) was defined and experimentally determined for various system configurations and particles. The electric force no longer overcomes the other forces, and particles are taken off the wall, when the applied voltage becomes lower than V(th). V(th) values have allowed us not only to estimate surface charge density of a particle but also to evaluate the hydrodynamic lift force against particle.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.     

Force acting on a dielectric particle in a concentration gradient by ionic concentration polarization under an externally applied DC electric field

There is a concentration-polarization (CP) force acting on a particle submerged in an electrolyte solution with a concentration (conductivity) gradient under an externally applied DC electric field. This force originates from the two mechanisms: (i) gradient of electrohydrodynamic pressure around the particle developed by the Coulombic force acting on induced free charges by the concentration polarization, and (ii) dielectric force due to nonuniform electric field induced by the conductivity gradient. A perturbation analysis is performed for the electric field, the concentration field, and the hydrodynamic field, under the assumptions of creeping flow and small concentration gradient. The leading order component of this force acting on a dielectric spherical particle is obtained by integrating the Maxwell and the hydrodynamic stress tensors. The analytical results are validated by comparing the surface pressure and the skin friction to those of a numerical analysis. The CP force is proportional to square of the applied electric field, effective for electrically neutral particles, and always directs towards the region of higher ionic concentration. The magnitude of the CP force is compared to that of the electrophoretic and the conventional dielectrophoretic forces.     

Electrophoretic motion of a spherical particle in a converging-diverging nanotube

A charged spherical particle is concentrically positioned in a converging-diverging nanotube filled with an electrolyte solution, resulting in an electric double layer (EDL) forming around the particle's surface. In the presence of an axially applied electric field, the particle electrophoretically migrates along the axis of the nanotube due to the electrostatic and hydrodynamic forces acting on the particle. In contrast to a cylindrical nanotube with a constant cross-sectional area in which the electric field is almost uniform, the presence of a converging-diverging section in a nanotube alters the electric field, perturbs the charge distribution, and induces a pressure gradient and a recirculating flow that affect the electrostatic and hydrodynamic forces acting on both the particle and the fluid. Depending on the magnitude of the surface charge density along the nanotube's wall, the particle's electrophoretic motion may be significantly accelerated as the particle transverses the converging-diverging section. A continuum model consisting of the Nernst-Planck, Poisson, and Navier-Stokes equations for the ionic concentrations, electric potential, and flow field is implemented to compute the particle's velocity as a function of the particle's size, the nanotube's geometry, surface charges, electric field intensity, bulk electrolyte concentration, and the particle's location. When the particle is negatively charged and the wall of the nanotube is uncharged, the particle migrates in the direction opposite to that of the applied electric field and the presence of the converging-diverging section significantly accelerates the particle's motion. This, however, is not always true when the nanotube's wall is charged with the same sign as that of the particle. Once the ratio of the surface charge density of the nanotube's wall to that of the particle exceeds a certain value, the negatively charged particle will not translocate through the tube toward the anode and does not attain the maximum velocity at the throat of the converging-diverging section. One can envision such a device to be a nanofilter that allows molecules with surface charge densities much higher than that of the wall to go through the nanofilter, while preventing molecules with surface charge densities lower than that of the wall from passing through the nanofilter. The induced recirculating flow may be used to enhance mixing and to stretch, fold, and trap molecules in nanofluidic detectors and reactors.