Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution, that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell-Wagner-O'Konski process associated with the counterions condensation layer, is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.Comment: J. Colloid Interface Sci., in press, 13 pages, 9 figure

Electrophoretic mobility of a charged colloidal particle: A computer simulation study

We study the mobility of a charged colloidal particle in a constant homogeneous electric field by means of computer simulations. The simulation method combines a lattice Boltzmann scheme for the fluid with standard Langevin dynamics for the colloidal particle, which is built up from a net of bonded particles forming the surface of the colloid. The coupling between the two subsystems is introduced via friction forces. In addition explicit counterions, also coupled to the fluid, are present. We observe a non-monotonous dependence of the electrophoretic mobility on the bare colloidal charge. At low surface charge density we observe a linear increase of the mobility with bare charge, whereas at higher charges, where more than half of the ions are co-moving with the colloid, the mobility decreases with increasing bare charge.Comment: 15 pages, 8 figure

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Statistical-mechanical theory of ultrasonic absorption in molecular liquids

We present results of theoretical description of ultrasonic phenomena in molecular liquids. In particular, we are interested in the development of microscopical, i.e., statistical-mechanical framework capable to explain the long living puzzle of the excess ultrasonic absorption in liquids. Typically, ultrasonic wave in a liquid can be generated by applying the periodically alternating external pressure with the angular frequency that corresponds to the ultrasound. If the perturbation introduced by such process is weak - its statistical-mechanical treatment can be done with the use of the linear response theory. We treat the liquid as a system of interacting sites, so that all the response/aftereffect functions as well as the energy dissipation and generalized (wave-vector and frequency dependent) ultrasonic absorption coefficient are obtained in terms of familiar site-site static and time correlation functions such as static structure factors or intermediate scattering functions. To express the site-site intermediate scattering functions we refer to the site-site memory equations in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors, direct and total correlation functions are deduced from the integral equation theory of molecular liquids known as RISM or one of its generalizations. All the formalism is phrased in a general manner, hence the obtained results are expected to work for arbitrary type of molecular liquid including simple, ionic, polar, and non-polar liquids.Comment: 14 pages, 1 eps-figure, RevTeX4-forma

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation is obtained and solved numerically for a totally asymmetric primitive model electrolyte around a spherical macroparticle. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential vs charge relationship, radial distribution functions, mean electrostatic potential and cumulative reduced charge for representative cases of 1:1 and 2:2 salts with a size asymmetry ratio of 2. Our results are collated with those of the Modified Gouy-Chapman (MGC) and unequal radius Modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size asymmetry effects. One of the most striking characteristics found is that,\textit{contrary to the general belief}, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e. \textit{counterions do not always dominate}. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features can not be described by traditional mean field theories like MGC, URMGC or even by enhanced formalisms, like HNC/MSA, if they are based on the RPM.Comment: 29 pages, 13 figure

Can airborne ultrasound monitor bubble size in chocolate?

Aerated chocolate products consist of solid chocolate with the inclusion of bubbles and are a popular consumer product in many countries. The volume fraction and size distribution of the bubbles has an effect on their sensory properties and manufacturing cost. For these reasons it is important to have an online real time process monitoring system capable of measuring their bubble size distribution. As these products are eaten by consumers it is desirable that the monitoring system is non contact to avoid food contaminations. In this work we assess the feasibility of using an airborne ultrasound system to monitor the bubble size distribution in aerated chocolate bars. The experimental results from the airborne acoustic experiments were compared with theoretical results for known bubble size distributions using COMSOL Multiphysics. This combined experimental and theoretical approach is used to develop a greater understanding of how ultrasound propagates through aerated chocolate and to assess the feasibility of using airborne ultrasound to monitor bubble size distribution in these systems. The results indicated that a smaller bubble size distribution would result in an increase in attenuation through the product

Nonlinear electrochemical relaxation around conductors

We analyze the simplest problem of electrochemical relaxation in more than one dimension - the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasi-neutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.Comment: 25 pages, 17 figures, 4 table

Characterizing generated charged inverse micelles with transient current measurements

We investigate the generation of charged inverse micelles in nonpolar surfactant solutions relevant for applications such as electronic ink displays and liquid toners. When a voltage is applied across a thin layer of a nonpolar surfactant solution between planar electrodes, the generation of charged inverse micelles leads to a generation current. From current measurements it appears that such charged inverse micelles generated in the presence of an electric field behave differently compared to those present in equilibrium in the absence of a field. To examine the origin of this difference, transient current measurements in which the applied voltage is suddenly increased are used to measure the mobility and the amount of generated charged inverse micelles. The mobility and the corresponding hydrodynamic size are found to be similar to those of charged inverse micelles present in equilibrium, which indicates that other properties determine their different behavior. The amplitude and shape of the transient currents measured as a function of the surfactant concentration confirm that the charged inverse micelles are generated by bulk disproportionation. A theoretical model based on bulk disproportionation with simulations and analytical approximations is developed to analyze the experimental transient currents