Constant Surface Charge Research Articles

Collision rate coefficient for charged dust grains in the presence of linear shear.

Like and oppositely charged particles or dust grains in linear shear flows are often driven to collide with one another by fluid and/or electrostatic forces, which can strongly influence particle-size distribution evolution. In gaseous media, collisions in shear are further complicated because particle inertia can influence differential motion. Expressions for the collision rate coefficient have not been developed previously which simultaneously account for the influences of linear shear, particle inertia, and electrostatic interactions. Here, we determine the collision rate coefficient accounting for the aforementioned effects by determining the collision area, i.e., the area of the plane perpendicular to the shear flow defining the relative initial locations of particles which will collide with one another. Integration of the particle flux over this area yields the collision rate. Collision rate calculations are parametrized as an enhancement factor, i.e., the ratio of the collision rate considering potential interactions and inertia to the traditional collision rate considering laminar shear only. For particles of constant surface charge density, the enhancement factor is found dependent only on the Stokes number (quantifying particle inertia), the electrostatic energy to shear energy ratio, and the ratio of colliding particle radii. Enhancement factors are determined for Stokes numbers in the 0-10 range and energy ratios up to 5. Calculations show that the influences of both electrostatic interactions and inertia are significant; for inertialess (St=0) equal-sized and oppositely charged particles, we find that even at energy ratios as low as 0.2, enhancement factors are in excess of 2. For the same situation but like-charged particles, enhancement factors fall below 0.5. Increasing the Stokes number acts to mitigate the influence of electrostatic potentials for both like and oppositely charged particles; i.e., inertia reduces the enhancement factor for oppositely charged particles and increases it for like-charged particles. Uniquely, at elevated Stokes numbers with attractive potentials we find collisionless "pockets" within the collision area, which are regions completely bounded by the collision area but within which collisions do not occur. Regression equations to results are provided, enabling calculation of the enhancement factor as a function of energy ratio and Stokes number. In total, this study both leads to insight into the collision dynamics of finite-inertia, charged particles in shear flows, and provides a means to simply calculate the particle-particle collision rate coefficient.

Development of 3D BEM code for Computation of a Transformer Winding’s Capacitance Matrix

In this paper, a method for computation of capacitance matrix for a transformer geometry is presented. Computation is based on boundary elements methods and point-matching. Unknown charge distribution on a triangular surface mesh of a winding is modeled with constant surface charge density over a triangle. Capacitance matrix is then obtained from known potentials in nodes of the system. Computation of relevant capacitances is benchmarked using the professional finite element method (FEM) based software.

Electroosmotic Flow through a Tubular Channel

In this study, the electroosmotic flow in a charge-regulated tubular channel is considered at low potential and arbitrary double layer thickness. Analytical expressions for the flow velocity and the corresponding asymptotic results for thick double layers that are readily applicable to experimentalists are recovered. For the range of salt concentration usually encountered in practice, the mean flow velocity for the case of constant surface potential differs both quantitatively and qualitatively from that for the case of constant surface charge density. Since this difference is both quantitative and qualitative, the true charged conditions on a channel wall can be inferred by appropriately designed experiments. Using an equivalent circular channel to simulate an elliptic one is inappropriate; in general, neither is assuming electroneutrality on the channel axis even when double layer is ca. 1/3 of the equivalent channel radius.

Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density

The pressure–driven electrolyte transport through nanofiltration membrane pores with constant surface potential or charge density is investigated theoretically. Two approaches are employed in the study. The first one is based on one–dimensional Nernst–Planck equation coupled with electroneutrality, zero current, and Donnan equilibrium conditions. This model is extended to account for interfacial effects by using a smooth approximation of step function for the volume charge density. The second approach is based on two–dimensional Nernst–Planck, Poisson, and Navier–Stokes equations, which are solved in a high aspect ratio nanopore connecting two reservoirs with much larger diameter. The modification of equations on the basis of Slotboom transformation is employed to speed up the convergence rate. The distributions of potential, pressure, ion concentrations and fluxes due to convection, diffusion, and migration in the nanopore and reservoirs are discussed and analyzed. It is found that for constant surface charge density, the convective flux of counter–ions in the nanopore is almost completely balanced by the opposite migration flux, while for constant surface potential, the convective flux is balanced by the opposite diffusion and migration fluxes. The co–ions in the nanopore are mainly transported by diffusion. A particular attention is focused on describing the interfacial effects at the nanopore entrance/exit. Detailed comparison between one– and two–dimensional models is performed in terms of rejection, pressure drop, and membrane potential dependence on the surface potential/charge density, volume flux, ion concentration, and pore radius. A good agreement between these models is found when the Debye length is smaller than the pore radius and the surface potential or charge density are sufficiently low.

Magnetic fields produced by rotating symmetrical bodies with homogeneous surface charge density

We present a numerical calculation for the stationary magnetic field produced by different rotating bodies with homogeneous and constant surface charge density. The calculation is done by superposing the magnetic field produced by a set of loops of current which mimic the magnetic field produced by belts of current defined by slices of fixed width. We consider the cases of a sphere, ellipsoids, open and closed cylinders and a combination of these in a dumbbell-like shell. We also plot their magnetic field lines using a technique that make use of the Runge–Kutta fourth-order method. Up to our knowledge, the case of closed cylinders was not calculated before. In contrast to previous results, we find that the magnetic field inside finite hollow bodies is homogeneous only in the case of a sphere. This is consequence of the fact that, for the sphere, the surface of any slice taken perpendicularly to the rotation axis, depends only on its thickness, like in the case of an infinite cylinder.

Electrophoresis and electric conduction in a suspension of charged soft particles

A thorough analytical study of the electrophoresis and electric conduction in a suspension of charged soft particles in an arbitrary electrolyte solution is presented through the use of a unit cell model. Each soft particle is a spherical hard core of radius r 0 and constant surface charge density σ covered with a permeable porous layer of constant thickness a − r 0 and uniform fixed charge density Q. Solving the relevant electrostatic and electrokinetic differential equations, we obtain closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension. These results are expressed as linear functions of σ and Q for arbitrary values of r 0/a, λa, κa, and the particle volume fraction of the suspension, where λ is the reciprocal of the Brinkman permeation length of the surface layer of each particle, and κ is the reciprocal of the Debye screening length. The effects of the surface layer characteristics and particle interactions on the electrophoretic mobility and effective conductivity are interesting, significant, and complicated. The general results for a suspension of charged soft spheres, which reduce to those of hard spheres and porous spheres in the limits r 0 = a and r 0 = 0, respectively, provide valuable information for interpreting experimental data.

Effect of eccentricity on the electroosmotic flow in an elliptic channel

The electroosmotic flow in an elliptic channel having constant surface potential (CSP) or charge density (CSCD) is considered at low potential and arbitrary double layer thickness. Analytical expressions for the flow velocity and the corresponding asymptotic results for thick double layers that are readily applicable to experimentalists are recovered. For the range of salt concentration usually encountered in practice, the mean flow velocity for the case of CSP differs both quantitatively and qualitatively from that for the case of CSCD. Using an equivalent circular channel to simulate an elliptic one is inappropriate, in general, neither is assuming electroneutrality on the channel axis even when double layer is ca. 1/3 of the equivalent channel radius.

Energy harvesting performance of viscoelastic polyacrylic dielectric elastomers

Viscoelasticity dissipates the mechanical energy, leading to a reduction of energy conversion efficiency in both dielectric elastomer (DE) actuators and generators. By measuring the uniaxial tension-recovery experiments of very-high-bond-based DE, this article quantitatively presents the effect of viscoelasticity on energy harvesting performance of DE generators. By employing a DE strip energy harvester with constant surface charge, an analytical model is established to calculate the generated electrical energy and energy conversion efficiency. Numerical results demonstrate that viscoelasticity has a significant influence on DE energy harvesting performance.

Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation.

Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. We study here ionic transport through single putatively neutral hydrophobic nanopores with high aspect ratio (of length L = 6 μm with diameters ranging from 1 to 10 nm) and with a well controlled cylindrical geometry. We develop a detailed hybrid mesoscopic theoretical approach for the electrolyte conductivity inside nanopores, which considers explicitly ion advection by electro-osmotic flow and possible flow slip at the pore surface. By fitting the experimental conductance data we show that for nanopore diameters greater than 4 nm a constant weak surface charge density of about 10−2 C m−2 needs to be incorporated in the model to account for conductance plateaus of a few pico-siemens at low salt concentrations. For tighter nanopores, our analysis leads to a higher surface charge density, which can be attributed to a modification of ion solvation structure close to the pore surface, as observed in the molecular dynamics simulations we performed.

Analysis of electro-osmotic flow in a microchannel with undulated surfaces

The electro-osmotic flow through a channel between two undulated surfaces induced by an external electric field is investigated. The gap of the channel is very small and comparable to the thickness of the electrical double layers. A lattice Boltzmann simulation is carried out on the model consisting of the Poisson equation for electrical potential, the Nernst–Planck equation for ion concentration, and the Navier–Stokes equations for flows of the electrolyte solution. An analytical model that predicts the flow rate is also derived under the assumption that the channel width is very small compared with the characteristic length of the variation along the channel. The analytical results are compared with the numerical results obtained by using the lattice Boltzmann method. In the case of a constant surface charge density along the channel, the variation of the channel width reduces the electro-osmotic flow, and the flow rate is smaller than that of a straight channel. In the case of a surface charge density distributed inhomogeneously, one-way flow occurs even under the restriction of a zero net surface charge along the channel.

Electrophoresis of two spheres: Influence of double layer and van der Waals interactions

Considering recent applications of electrophoresis conduced in nanoscaled devices, where particle–particle interaction can play a role, we studied for the first time the electrophoresis of two rigid spheres along their center line, taking account of the hydrodynamic, electric, and van der Waals interactions between them. Under the conditions of constant surface potential and surface charge density, the influences of the level of surface potential/charge density, the bulk salt concentration, and the particle–particle distance on their electrokinetic behaviors are examined. Numerical simulation reveals that these behaviors are much more complicated and interesting than those of isolated particles. In particular, we show that care must be taken in choosing an appropriate particle concentration in relevant experiment to avoid obtaining unreliable mobility data.

Molecular dynamics study of electric double layer in nanochannel

The Electric Double Layer for electroosmotic flow of NaCl aqueous solution in nanochannels is studied numerically in this paper using Molecular Dynamics (MD) approach. For an electrolyte solution flowing in 40 nm nanochannel, two different conditions for charge on channel wall are defined; first the charge on the wall is held as equal to the amount that was previously reported by the experiment when charge dissociation on silicon dioxide wall occurs and second the constant surface charge density on the wall is assumed. The MD based numerical results show great agreement with experimental data for zeta potential in the range of 10−2−10−1 M. The MD simulations show that Debye length decreases as NaCl concentration increases. Moreover the electric conductance and velocity profile in nanochannel could be extracted from MD results. Performance of the MD approach as a most promising numerical method to study electrokinetic phenomena in nanoscale devices is then verified.

Surface Charge Properties of Nanoparticle: Size Dependency and Boundary Effect

Surface charge properties of nanoparticles play an important role in many applications, such as drug delivery, cellular uptake and their separation. Surface charge properties of silica nanoparticles are investigated as functions of particle’s size, solution properties including pH and background salt concentration, and separation distance from a flat silica surface using a multi-ion charge-regulation model. In contrast to most previous studies utilizing constant surface charges regardless of the local solution properties, surface chemical reactions in the presence of multiple ionic species are considered in this study. The obtained results agree with experimental data available from the literature. Results show that the magnitude of nanoparticle’s surface charge density increases with its size due to the curvature effect and the presence of the nearby boundary induces spatially non-uniform surface charge around the nanoparticle as while decreasing the k h, the degree of nonhomogeneous distribution increases. Due to the surface chemical reactions, both pH and background salt concentration significantly affect the charge properties of silica nanoparticles.

Induced hydraulic pumping via integrated submicrometer cylindrical glass capillaries.

Here, we report on a micropump that generates hydraulic pressure owing to a mismatch in EOF rates of microchannels and submicrometer cylindrical glass capillaries integrated on silicon. The electrical conductance of such capillaries in the dilute limit departs from bulk linear behavior as well as from the surface-charge-governed saturation in nanoslits that is well described by the assumption of a constant surface charge density. The capillaries show rather a gradual decrease in conduction at low salt concentrations, which can be explained more aptly by a variable surface charge density that accounts for chemical equilibrium of the surface. The micropump uses a traditional cross-junction structure with ten identical capillaries integrated in parallel on a side arm and each with a 750 nm diameter and 3 mm length. For an applied voltage of 700 V, a hydraulic pressure up to 5 kPa is generated with a corresponding flow velocity nearly 3 mm/s in a straight field-free branch 20 μm wide, 10 μm deep, and 10 mm long. The micropump utility has been demonstrated in an open tubular LC of three fluorescently labeled amino acids in just less than 20 s with minimal plate height values between 3 and 7 μm. The submicrometer capillaries are self-enclosed and produced through a unique process that does not require high-resolution advanced lithography or wafer-bonding techniques to define their highly controlled precise structures.

Influence of ionic strength on the surface charge and interaction of layered silicate particles

The surface charge densities and surface potentials of selected phyllosilicate surfaces were calculated from AFM surface force measurements and reported as a function of ionic strength at pH 5.6. The results show that the silica faces of clay minerals follow the constant surface charge model because of isomorphous substitution in the silica tetrahedral layer. A decreasing surface charge density sequence was observed as follows: muscovite silica face>kaolinite silica face>talc silica face, which is expected to be due to the extent of isomorphous substitution. In contrast, at pH 5.6, the alumina face and the edge surface of kaolinite follow the constant surface potential model with increasing ionic strength, and the surface charge density increased with increasing ionic strength.The cluster size of suspended kaolinite particles at pH 5.6 was found to increase with increasing ionic strength due to an increase in the surface charge density for the alumina face and the edge surface. However, the cluster size decreased at 100mM KCl as a result of an unexpected decrease in the surface charge of the alumina face. When the ionic strength continued to increase above 100mM KCl, the van der Waals attraction dominated and larger clusters of micron size were stabilized.

Surface Charge of a Nanoparticle Interacting with a Flat Substrate

Electrostatic interactions between two charged dielectric objects highly depend on their surface charge. Most existing studies assume constant surface charge densities between the two interacting objects regardless of the separation distance between them. The surface charge of a spherical silica nanoparticle interacting with a flat silica plate is investigated numerically as a function of the separation distance normalized with the electrical double layer thickness (κh), pH, and background salt concentration. The numerical model employs Poisson–Nernst–Planck equations for ionic mass transport and considers surface charge regulation in the presence of multiple ionic species. Relatively weak interactions between the nanoparticle and the plate are observed for κh ≫ 1, resulting in uniform surface charge densities. Because of curvature, the surface charge density of the nanoparticle is higher than that of the plate. Strong interactions are observed for κh ≤ 1, leading to spatially nonuniform surface charge de...

Size Dependent Surface Charge Properties of Silica Nanoparticles

Nanoparticle surface charge density plays an important role in many applications, such as drug delivery and cellular uptake. In this study, surface charge properties of silica nanoparticles with different sizes are studied using a multi-ion surface charge-regulation model. In contrast to most previous studies utilizing constant surface charge, protonation and deprotonation surface reactions are used to obtain the local surface charge, which depends on the particle size and electrolyte solution properties, including the salt concentration and pH. For a fixed particle size, the magnitude of the surface charge typically increases with an increase in pH or background salt concentration. For fixed background salt concentration and pH, the magnitude of surface charge decreases with an increase in the particle size and reaches a constant when the particle size exceeds a critical value. Size dependent surface charge is further characterized by the ratio of electrical double layer thickness to the particle diameter, and the surface charge varies significantly when this dimensionless ratio is above 0.2.

Reluctance of a neutral nanoparticle to enter a charged pore

We consider the translocation of a neutral (uncharged) nanoparticle through a pore in a thin membrane with constant surface charge density. If the concomitant Debye screening layer is sufficiently thin, the resulting forces experienced by the particle on its way through the pore are negligible. But when the Debye length becomes comparable to the pore diameter, the particle encounters a quite significant potential barrier while approaching and entering the pore, and symmetrically upon exiting the pore. The main reason is an increasing pressure, which acts on the particle when it intrudes into the counter ion cloud of the Debye screening layer. In case the polarizability of the particle is different (usually smaller) than that of the ambient fluid, a second, much smaller contribution to the potential barrier is due to self-energy effects. Our numerical treatment of the problem is complemented by analytical approximations for sufficiently long cylindrical particles and pores, which agree very well with the numerics.

Calculating the Electrostatic Potential Profiles of Double Layers from Simulation Ion Density Profiles

Computer simulations of the planar double layer geometry provide the charge profile with statistical noise. To compute the mean electrostatic potential profile from the charge profile, one must solve Poisson’s equation with appropriate boundary conditions (BC). In this work, we show that it is advantageous to use the Neumann or Dirichlet BCs at the boundaries of the simulation domain with an integrated version of Poisson’s equation. This minimises errors from the simulation’s noisy density profiles, in contrast to traditional convolution integrals that amplify the noise. The Neumann BC, where the electric field is prescribed, can be used in both the constant surface charge and constant electrode voltage ensembles. In the constant voltage ensemble, where the potential difference between the confining electrodes is prescribed, one can also use the Dirichlet BC, where the potentials at the boundaries are set. We show that the new methods provide converged results for the potential profile faster than the convolution integral does.

The effect of the surface functionalization and the electrolyte concentration on the electrical conductance of silica nanochannels

It is known that the conductance of nanochannels as a function of electrolyte concentration deviates from a linearly proportional relationship and approaches a value independent of the concentration as the electrolyte concentration is lowered. Most of the proposed models account for this behavior by considering a constant surface charge density and an ideal electrolyte solution. However, at low electrolyte concentrations, the ideal electrolyte approximation is no longer valid because the ions that result from the atmospheric carbon dioxide dissolution in water dominate the ionic concentration. In this paper, arrays of silica nanochannels were electrically characterized via conductance measurements. The conductance at low salt concentrations is modeled by a variable surface charge model that accounts for all ionic species in solution. This model was used to determine the variable surface charge of the bare silica nanochannels as well as of chemically modified nanochannels. The model correctly predicted the variation of the nanochannel conductance observed after silane (aminopropyldimethylethoxysilane) functionalization and single-strand DNA immobilization. Finally, pH modification of bulk KCl solutions was employed as an alternative method of changing the surface charge of silica nanochannels. Surface charge calculated from conductance measurements performed at different bulk pH values confirmed that the surface charge of the silica nanochannel walls is sensitive to the H(+) concentration.