Effective charge of cylindrical and spherical colloids immersed in an electrolyte: the quasi-planar limit

Šamaj, L.; Trizac, Emmanuel

doi:10.1088/1751-8113/48/26/265003

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…With the development of current nanotechnology in electrochemistry, 1,2 analysis of solutions to mathematical models with regulated parameters plays a more and more important role in investigating the distribution of electrostatic potential in electrolyte‐like solutions (cf. previous studies 3–12 ). In the past few decades, a key ingredient for understanding of such microscopic phenomena is the Poisson‐Boltzmann equation, 13–15 but which suffered from deficiencies that are well known.…”

Section: Introductionmentioning

confidence: 56%

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Lyu

Lee

Lin

2021

Math Methods in App Sciences

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This work is concerned with the stationary Poisson‐Nernst‐Planck equation with a large parameter which describes a huge number of ions occupying an electrolytic region. First, we focus on the model with a single specie of positive charges in one‐dimensional bounded domains due to the assumption that these ions are transported in the same direction along a tubular‐like mircodomain. We show that the solution asymptotically blows up in a thin region attached to the boundary and establishes the refined “near‐field” and “far‐field” expansions for the solutions with respect to the parameter. Moreover, we obtain the boundary concentration phenomenon of the net charge density, which mathematically confirms the physical description that the non‐neutral phenomenon occurs near the charged surface. In addition, we revisit a charge‐conserving Poisson‐Boltzmann model for monovalent binary ions and establish a novel comparison for these two models.

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Section: Introductionmentioning

confidence: 56%

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Lyu

Lee

Lin

2021

Math Methods in App Sciences

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“…their charge can be estimated under salt-free conditions with the corresponding saturation charge. The magnitude of this charge can be obtained from PB theory [51][52][53] (18…”

Section: View Article Onlinementioning

confidence: 99%

Thickness of the particle-free layer near charged interfaces in suspensions of like-charged nanoparticles

et al. 2021

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“…Indeed, in order to develop theoretical frameworks for the EDL, most PB type equations have been investigated via numerical simulations [6,18,22,48,50,52,54], multiple-scale method [41] and the method of matched asymptotic expansions [46]. Such frameworks focus mainly on the linear PB theory (Debye-Hückel approximation [8,9]).…”

Section: Background and Problem Formulationmentioning

confidence: 99%

Thin layer analysis of a non-local model for the double layer structure

Lee

2019

Journal of Differential Equations

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For the structure of the thin electrical double layer (EDL) and the property related to the EDL capacitance, we analyze boundary layer solutions (corresponding to the electrostatic potential) of a non-local elliptic equation which is a steady-state Poisson-Nernst-Planck equation with a singular perturbation parameter related to the small Debye screening length. Theoretically, the boundary layer solutions describe that those ions exactly approach neutrality in the bulk, and the extra charges are accumulated near the charged surface. Hence, the non-neutral phenomenon merely occurs near the charged surface. To investigate such phenomena, we develop new analysis techniques to investigate thin boundary layer structures. A series of fine estimates combining the Pohožaev's identity, the inverse Hölder type estimates and some technical comparison arguments are developed in arbitrary bounded domains. Moreover, we focus on the physical domain being a ball with the simplest geometry and gain a clear picture on the effect of the curvature on the boundary layer solutions. The content involves three contributions. The first one focuses mainly on the boundary concentration phenomena. We show that the net charge density behaves exactly as Dirac delta measures concentrated at boundary points. The second one is devoted to pointwise descriptions with curvature effects for the thin boundary layer. An interesting outcome shows that the significant curvature effect merely occurs in the part of the boundary layer close to the boundary, and this part is extremely thinner than the whole boundary layer. The third contribution gives a connection to the EDL capacitance. We provide a theoretical way to support that the EDL has higher capacitance in a quite thin region near the charged surface, not in the whole EDL. In particular, for the cylindrical electrode, our result has a same analogous measurement as the specific capacitance of the well-known Helmholtz double layer.Mathematics Subject Classification. 34E05 · 35J67 · 35Q92 · 35R09.

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Effective charge of cylindrical and spherical colloids immersed in an electrolyte: the quasi-planar limit

Cited by 13 publications

References 25 publications

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Near‐ and far‐field expansions for stationary solutions of Poisson‐Nernst‐Planck equations

Thickness of the particle-free layer near charged interfaces in suspensions of like-charged nanoparticles

Thin layer analysis of a non-local model for the double layer structure

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