Experimental Verification of the Electroosmotic Mechanism of Overlimiting Conductance Through a Cation Exchange Electrodialysis Membrane

The paper is concerned with convection at an ion-exchange electrodialysis membrane induced by nonequilibrium electroosmosis as a source of overlimiting conductance current through the membrane. Derivation of nonequilibrium electroosmotic slip condition is recapitulated along with the results of linear stability analysis of quiescent electrodiffusion through a flat ion-exchange membrane. Results of numerical calculation pertaining to nonlinear convection, developing from the respective instability, are reported along with those of recent experiments with modified membranes. These latter rule in favor of electroosmotic versus bulk electroconvective origin of overlimiting conductance through ion-exchange membranes.     

Vertex singularities associated with conical points for the 3D laplace equation

The solution u to the Laplace equation in the neighborhood of a vertex in a three‐dimensional domain may be described by an asymptotic series in terms of spherical coordinates $$u = \sum\nolimits_i {A_i}{\rho ^{{\nu _i}}}{f_i}(\theta ,\phi )$$ . For conical vertices, we derive explicit analytical expressions for the eigenpairs ν_i and f_i(θ, φ), which are required as benchmark solutions for the verification of numerical methods. Thereafter, we extend the modified Steklov eigen‐formulation for the computation of vertex eigenpairs using p/spectral finite element methods and demonstrate its accuracy and high efficiency by comparing the numerically computed eigenpairs to the analytical ones. Vertices at the intersection of a crack front and a free surface are also considered and numerical eigenpairs are provided. The numerical examples demonstrate the efficiency, robustness, and high accuracy of the proposed method, hence its potential extension to elasticity problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Diffusional mechanism of strong selection in ostwald ripening

The purpose of this paper is to show through a systematic asymptotic analysis that fluctuations, accounted for as a diffusional perturbation in the Lifshitz-Slyozov-Wagner (LSW) model of Ostwald ripening, provides, as conjectured previously by Meerson [Phys. Rev. E 60, 3072 (1999)], a "strong" selection of the limiting solution, out of a one-parameter family of similarity solutions with a finite support, as the sole attractor of time evolution. Throughout the latter, the previously described weak selection of other similarity solutions of that family, by the initial conditions with finite supports, occurs as intermediate time asymptotics. The respective mechanism is traced first for a simple instance of the LSW model with linear characteristic equations (integer power in the particle growth rate law equals -1), beginning with the analysis of steady states in the perturbed problem in similarity variables and weak selection in the unperturbed problem, followed by a detailed asymptotic analysis of the time-dependent perturbed problem, and generalized next for an arbitrary integer power in the range [-1,2]. The approximate asymptotic solutions obtained are compared with the exact numerical ones.     

Solvates of zafirlukast

The crystal structures of three solvates of zafirlukast [systematic name: cyclopentyl N‐{1‐methyl‐3‐[2‐methyl‐4‐(o‐tolylsulfonylaminocarbonyl)benzyl]‐1H‐indol‐5‐yl}carbamate], viz. the monohydrate, C₃₁H₃₃N₃O₆S·H₂O, (I), the methanol solvate, C₃₁H₃₃N₃O₆S·CH₃OH, (II), and the ethanol solvate, C₃₁H₃₃N₃O₆S·C₂H₅OH, (III), have been determined by single‐crystal X‐ray diffraction analysis. All three compounds crystallize in the monoclinic crystal system. Zafirlukast adopts a similar Z‐shaped conformation in all three solvates. The methanol and ethanol solvates are isostructural. The packing of the zafirlukast mol­ecules in all three crystal structures is similar and is expressed by hydrogen‐bonded mol­ecules that are related by translation, along (101) in (I) and along the b axis in (II) and (III). The methanol and ethanol solvent mol­ecules are hydrogen bonded to two mol­ecules of zafirlukast. The water mol­ecule, on the other hand, acts as a connector via hydrogen bonds between three mol­ecules of zafirlukast. The solvent mol­ecules are not released at temperatures below the melting points of the solvates.     

Multidimensional two-phase quasistationary stefan problem

Existence and uniqueness of the classic solution to a two-dimensional quasistationary Stefan problem are considered. The family of model problems dependent on the parameter ε>0 which defines a heat conductivity of a matter in the direction of thex-axis is analysed. When ε→0 it is approximated by the approximate model problem having less dimensions. Analogous results are also valid for a three-dimensional problem.     

Overlimiting current in a microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i)?surface conduction carried by excess counterions, which dominates for very thin channels, (ii)?convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.