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Register a new userInduced Charge Capacitive Deionization: The electrokinetic response of a porous particle to an external electric field
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We demonstrate the phenomenon of induced-charge capacitive deionization (ICCDI) that occurs around a porous and conducting particle immersed in an electrolyte, under the action of an external electric field. The external electric field induces an electric dipole in the porous particle, leading to its capacitive charging by both cations and anions at opposite poles. This regime is characterized by a long charging time which results in significant changes in salt concentration in the electrically neutral bulk, on the scale of the particle. We qualitatively demonstrate the effect of advection on the spatio-temporal concentration field which, through diffusiophoresis, may introduce corrections to the electrophoretic mobility of such particles.
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The influence of the texture of a hydrophobic surface on the electro-osmotic slip of the second kind and the electrokinetic instability near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a simple model based on the Rubinstein-Zaltzman approach. A simple formula is derived to evaluate the decrease in the instability threshold due to hydrophobicity. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a hydrophobic membrane surface. Theory predicts a significant enhancement of the ion flux to the surface and shows a good qualitative agreement with the available experimental data.
Over the past decade, capacitive deionization (CDI) has realized a surge in attention in the field of water desalination and can now be considered as an important technology class, along with reverse osmosis and electrodialysis. While many of the recently developed technologies no longer use a mechanism that follows the strict definition of the term capacitive, these methods nevertheless share many common elements that encourage treating them with similar metrics and analyses. Specifically, they all involve electrically driven removal of ions from a feed stream, storage in an electrode (i.e., ion electrosorption) and release, in charge/discharge cycles. Grouping all these methods in the technology class of CDI makes it possible to treat evolving new technologies in standardized terms and compare them to other technologies in the same class.
When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry induced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach proceeds through the application of the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely-extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely-large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cut-off length beyond which the bending forces become subdominant to an external body force.
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. Two kinds of initial conditions were considered: (a) white noise initial conditions to mimic room disturbances and subsequent natural evolution of the solution; (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution; two-dimensional steady electroconvective vortices (stationary point in a proper phase space); unsteady vortices aperiodically changing their parameters (homoclinic contour); periodic motion (limit cycle); and chaotic motion. The transition to chaotic motion did not include Hopf bifurcation. Numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics.
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