Dynamic Interactions of Two Electrical Double Layers

Effect of Audible Sounds on the Forces Acting between Charged Surfaces in Water

We aimed to determine if audible sounds could change the forces acting between charged surfaces in water and their electric double layers (EDLs). This was achieved by using an atomic force microscope to measure force-distance curves between a microsized silica particle attached to a cantilever (probe) and a silicon wafer in water in the absence and presence of sound. Sound decreased the repulsive forces acting between the probe and silicon wafer, where the range and magnitude of the forces decreased with an increase in the sound frequency from 300 to 15000 Hz. The decrease in the force range was explained by a decrease in the EDL thickness. This result was explained by (1) the shrinkage of the EDL by a high-pressure region of the sound wave, where an increased sound frequency caused the number of high-pressure regions that passed between the probe and the substrate to increase and (2) the inability of the EDL to fully re-expand to its original thickness during the time that a low-pressure region of the sound wave was applied. The decrease in the force magnitude with a sound frequency increase was explained by the increased screening of charged surfaces that accompanies a decrease in the EDL thickness. An increase in the force measurement speed caused the sound waves to reduce the repulsive forces less. A faster speed decreased the time to measure a force curve, which reduced the number of high-pressure regions of the sound wave to pass through the water between the probe and the substrate. This reduced the number of times that the EDL was compressed by the sound wave.

Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute's mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman's model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

Transient electro-osmotic flow in cylindrical microcapillaries containing salt-free medium

A theoretical study on the transient electro-osmotic flow through a cylindrical microcapillary containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electro-osmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electro-osmotic flow is detailed. The general behavior of transient electro-osmotic flow in a cylindrical tube is similar to that observed in a microchannel containing an electrolyte solution. However, the steady-state electro-osmotic flow significantly deviates from the typical plug flow at higher surface charge and the rate of increase in the electro-osmotic mobility is strongly suppressed due to the effect of counterion condensation. In addition, the applicability limit of these solutions is also discussed.

Transient finite element analysis of electric double layer using Nernst–Planck–Poisson equations with a modified Stern layer

A finite element implementation of the transient nonlinear Nernst-Planck-Poisson (NPP) and Nernst-Planck-Poisson-modified Stern (NPPMS) models is presented. The NPPMS model uses multipoint constraints to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The Poisson-Boltzmann equation is used to provide a limited check of the transient models for low surface potential and dilute bulk solutions. The effects of the surface potential and bulk molarity on the electric potential and ion concentrations as functions of space and time are studied. The ability of the models to predict realistic energy storage capacity is investigated. The predicted energy is much more sensitive to surface potential than to bulk solution molarity.

Critical coagulation concentration for a suspension of cation-absorptive biocolloids

Critical coagulation concentration (CCC) of a biocolloidal suspension is investigated theoretically by taking into account the influences of cationic absorption in particulate membrane phase, variation in dielectric constant, size of charged species and nonuniform distribution of fixed membrane groups. Here, an increase in both valence and effective radius of the original functional group (OFG) via absorption of electrolyte cation(s) is especially considered. The simulated results indicate that stronger membrane electricity yields a larger electrostatic repulsion and a higher potential energy, which generates a higher CCC. A lower CCC can be resulted from a larger (1) cation-functional group complex (CFGC) for a fixed difference between the radius of CFGC and that of OFG, Delta, (2) number of OFG(s) involved in the formation of a CFGC, (3) Delta for a positively charged CFGC, (4) dielectric constant of main membrane phase, in general, (5) membrane thickness for a constant amount of space-average functional groups, and (6) effective radius of anions. CCC decreases with the following parameters: (1) Delta for a negatively charged CFGC, (2) equilibrium constant of the reaction of cationic absorption, (3) nonuniform feature index of fixed groups, and (4) effective radius of cations.

Effect of ionic size on the deposition of charge-regulated particles to a charged surface

The deposition of charge-regulated particles to a rigid, planar charged surface is modeled theoretically, taking the effects of the excluded area arising from deposited particles and finite ionic sizes into account. Here, a particle comprises a rigid core and an ion-penetrable charged membrane layer, which represents a general type of particle. If the membrane layer has a negligible thickness, the particle simulates a regular inorganic particle, and if the membrane layer has a finite thickness, it simulates biocolloids such as cells. The results of numerical simulation reveal that the rate of particle deposition is faster under the following conditions: (1) lower potential of the planar surface, (2) thicker membrane, (3) higher counterion valance, (4) lower fixed charge density, (5) smaller counterions, (6) larger co-ions, (7) larger functional group, and (8) lower pH. Neglecting the sizes of ionic species may lead to an appreciable deviation in both the electrical repulsive force between particle and surface and the rate of deposition. Typical deviation for the former is approximately 20%, and that for the latter is approximately -75%.

Electrical Interaction Energy between Two Charged Entities in an Electrolyte Solution

The electrical interaction energy between two charged entities in an electrolyte solution plays a significant role in various phenomena in colloid and interface science. Available methods for the estimation of this energy under the Debye-Huckel condition are discussed briefly, and a systematic approach based on a boundary integral method, which has the potential to yield an approximate analytical expression for various types of surfaces under a general surface condition, is introduced. The linear sizes of the interacting entities can be comparable or one is much larger than the other. A typical example for the former includes, for instance, the interaction between two colloidal particles. The stability behavior of a colloidal dispersion belongs to this category. That for the latter includes the interaction between a particle and a wall. The adsorption of particles to surfaces and the electrophoretic motion of particles near a boundary, for example, belong to this category. Extensions to more complicated cases, for example, multiple particles and arbitrary surfaces, are also discussed. Copyright 1999 Academic Press.