Self-similar solutions in ion-exchange membranes and their stability

Polyanskikh, S. V.; Demekhin, E. A.

doi:10.1134/s1028335810100071

Cited by 11 publications

(14 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On dimensional grounds, the only diffusion length which can give a proper characteristic size that includes time and is, hence, dynamical, is 4Dt -and the behavior of the solution has to be self-similar. These intermediate times vary from milliseconds to seconds (for details see [9][10][11]). the corresponding old variables, ν, j and ∆V , by the relations…”

Section: Formulationmentioning

confidence: 99%

“…The two-parameter family of self-similar solutions for the parameters ∆Φ and ε is found in [9][10][11] and now is compared with the DNS of (1)-(3). In Fig.…”

Section: Formulationmentioning

confidence: 99%

“…The time dependence of the thickness of the diffusion layer∆ is taken in dimensional variables. Excluding very short times of establishment, up to 8.9 s of evolution, the solution in zone I follows the self-similar law proportionally to √t (dash-and-dot line); then the self-similar process is violated by the loss of stability Figure 5: Time dependence of the thickness of the diffusion layer∆ in dimensional variables for ∆Ṽ = 2.5 V,L = 1 mm,D = 5 · 10 −9 m 2 /s and ν = 0.001 [10]. (1) Selfsimilar solution, (2) numerical solution, I is the self-similarity range, and II is the stability loss by the trivial solution and the appearance of electroconvection.…”

Section: Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

2011

Self Cite

View full text Add to dashboard Cite

In the present work, four nontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes system: (i) a stage of the influence of the initial conditions (milliseconds); (ii) one-dimensional (1D) self-similar evolution (milliseconds-seconds); (iii) a primary instability of the self-similar solution (seconds); (iv) a nonlinear stage with secondary instabilities. The self-similar character of evolution at moderately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toward overlimiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest a self-similar growth of the diffusion layer. It also specifies its characteristic length as was first experimentally predicted by Yossifon and Chang [G. Yossifon and H.-C. Chang, Phys. Rev. Lett. 101, 254501 (2008)]. A novel principle for the characteristic wave-number selection from the broadband initial noise is established.

show abstract

Section: Formulationmentioning

confidence: 99%

“…The two-parameter family of self-similar solutions for the parameters ∆Φ and ε is found in [9][10][11] and now is compared with the DNS of (1)-(3). In Fig.…”

Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…The linear stability theory of the one-dimensional (1D) quiescent steadystate solution, based on a systematic asymptotic analysis of the problem, was developed by Zaltzman and Rubinstein [14]. Different aspects of the linear stability of the 1D solution were also studied in [15][16][17]. A qualitative discussion of the basic mechanisms of the electrokinetic instability can be found in [18].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional coherent structures of electrokinetic instability

2014

Self Cite

View full text Add to dashboard Cite

A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge-selective surface (electric membrane, electrode, or system of micro- or nanochannels) has been carried out and analyzed. A special finite-difference method has been used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. The calculations employ parallel computing. Three characteristic patterns, which correspond to the overlimiting currents, are observed: (a) two-dimensional electroconvective rolls, (b) three-dimensional regular hexagonal structures, and (c) three-dimensional structures of spatiotemporal chaos, which are a combination of unsteady hexagons, quadrangles, and triangles. The transition from (b) to (c) is accompanied by the generation of interacting two-dimensional solitary pulses.

show abstract

“…Theoretical predictions have shown that the ratio between the wavelength of a vortex pair to the DL, λ/L, is between 0.7 and 1.2 [15], while experimental observations have shown this ratio to be approximately 1.25 [16]. Using the latter observed value while taking the diffusive scaling for the DL growth, L = √ 2Dt [32], allows the wave number to be modeled as…”

Section: Experimental Techniques and Resultsmentioning

confidence: 94%

Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind

Green

Yossifon

2013

Phys. Rev. E

View full text Add to dashboard Cite

By applying a stepwise overlimiting voltage to a nanoslot system in equilibrium, it is possible to follow the time evolution of the electroconvective instability vortex array via the depletion dynamics or, alternatively, by following dielectrophoretically trapped particles at the stagnation points of each of the hydrodynamic vortex pairs. Particles are advected to the stagnation point by the hydrodynamics, where they are trapped by a shortrange dielectrophoretic force. It is experimentally confirmed that the wavelength selection process occurs at the diffusive time scale and that the wavelength selection mechanism, started by the Rubinstein and Zaltzman electroconvective instability is eventually determined by the system lateral geometry and dictated by Dukhin's electro-osmosis of the second kind. The steady-state case was numerically studied by solving the fully coupled electroconvective problem, confirming that the vortex stagnation point is indeed of a converging type. The particle's planar (two-dimensional) equations of motion are solved after adding a dielectrophoretic force that accounts for quasi-three-dimensional effects. It is shown that this force can account for trapping at the nanoslot interface.

show abstract

Self-similar solutions in ion-exchange membranes and their stability

Cited by 11 publications

References 6 publications

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

Linear and nonlinear evolution and diffusion layer selection in electrokinetic instability

Three-dimensional coherent structures of electrokinetic instability

Dynamical trapping of colloids at the stagnation points of electro-osmotic vortices of the second kind

Contact Info

Product

Resources

About