"Blue energy" from ion adsorption and electrode charging in sea- and river water

A huge amount of entropy is produced at places where fresh water and seawater mix, for example at river mouths. This mixing process is a potentially enormous source of sustainable energy, provided it is harnessed properly, for instance by a cyclic charging and discharging process of porous electrodes immersed in salt and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. Here we employ a modified Poisson-Boltzmann free-energy density functional to calculate the ionic adsorption and desorption onto and from the charged electrodes, from which the electric work of a cycle is deduced. We propose optimal (most efficient) cycles for two given salt baths involving two canonical and two grand-canonical (dis)charging paths, in analogy to the well-known Carnot cycle for heat-to-work conversion from two heat baths involving two isothermal and two adiabatic paths. We also suggest a slightly modified cycle which can be applied in cases that the stream of fresh water is limited.Comment: 7 Figure

Double layer in ionic liquids: Overscreening vs. crowding

We develop a simple Landau-Ginzburg-type continuum theory of solvent-free ionic liquids and use it to predict the structure of the electrical double layer. The model captures overscreening from short-range correlations, dominant at small voltages, and steric constraints of finite ion sizes, which prevail at large voltages. Increasing the voltage gradually suppresses overscreening in favor of the crowding of counterions in a condensed inner layer near the electrode. The predicted ion profiles and capacitance-voltage relations are consistent with recent computer simulations and experiments on room-temperature ionic liquids, using a correlation length of order the ion size.Comment: 4 pages + supplementary informatio

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.Comment: 30 pages, 17 eps-figures, RevTe

Bubble size distribution and energy dissipation in foam mixers

The bubble size distribution of a foam produced in a rotor-stator mixer has been determined as a function of several mixing parameters such as the rotor speed, residence time, gas/liquid ratio and the viscosity of the liquid used. A Newton-Reynolds expression for a foam mixer has been determined using energy consumption measurements. Two types of shear fields have been distinguished in the foam mixer, laminar and turbulent, the type of shear field depending on the properties of the foam mixer. After a certain mixing time the bubble size distribution characterised by the mean bubble size was found to reach a stationary value. The stationary bubble size distribution has been correlated with the mixing conditions by a critical Weber number. Both in the laminar and in the turbulent shear field bubble size distributions have been determined as a function of several mixing parameters

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

Streaming potential measurements 2. Relationship between electrical and hydraulic flow patterns from rock samples during deformation

Streaming potential and resistivity measurements have been performed on Fontainebleau sandstone and Villejust quartzite samples in a triaxial device during compaction, uniaxial compression, and rupture. Measurements on individual samples do not show any clear intrinsic dependence of the streaming potential coefficient with permeability. An apparent dependence of the streaming potential coefficient with permeability is, however, observed during deformation. The effect of surface conductivity is taken into account and is small compared with the observed changes in the streaming potential coefficient. The observed dependence is therefore interpreted in terms of a difference in the evolution of the electrical and hydraulic connectivity patterns during deformation. This effect causes the streaming potential coefficient, and consequently the inferred ξ potential, to be reduced by a geometrical factor R_G representing the electrical efficiency of the hydraulic network. Estimates of the R_G factor varying between 0.2 and 0.8 for electrolyte resistivity larger than 100 Ωm are obtained by comparing the values of the ξ potential inferred from intact rock samples with the values obtained from crushed rock samples, where the geometrical effects are assumed to be negligible. The reduction of the streaming potential coefficient observed during compaction or uniaxial compression suggests that the tortuosity of the hydraulic network increases faster than the tortuosity of the electrical network. Before rupture, an increase in the streaming potential coefficient associated with the onset of dilatancy was observed for three samples of Fontainebleau sandstone and one sample of Villejust quartzite. The changes in streaming potential coefficient prior to failure range from 30% to 50%. During one experiment, an increase in the concentration of sulfate ions was also observed before failure. These experiments suggest that observable streaming potential and geochemical variations could occur before earthquakes

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