Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0511183

Transport coefficients for electrolytes in arbitrarily shaped nano and micro-fluidic channels

N. A. Mortensen·L. H. Olesen·H. Bruus
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider laminar flow of incompressible electrolytes in long, straight channels driven by pressure and electro-osmosis. We use a Hilbert space eigenfunction expansion to address the general problem of an arbitrary cross section and obtain general results in linear-response theory for the hydraulic and electrical transport coefficients which satisfy Onsager relations. In the limit of non-overlapping Debye layers the transport coefficients are simply expressed in terms of parameters of the electrolyte as well as the geometrical correction factor for the Hagen-Poiseuille part of the problem. In particular, we consider the limits of thin non-overlapping as well as strongly overlapping Debye layers, respectively, and calculate the corrections to the hydraulic resistance due to electro-hydrodynamic interactions.

Explore related subjects

physics.flu-dyncond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

N. A. Mortensen, L. H. Olesen, H. Bruus. 2006-02-20. Transport coefficients for electrolytes in arbitrarily shaped nano and micro-fluidic channels. https://doi.org/10.1088/1367-2630%2F8%2F3%2F037

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Statistical State Dynamics based study of turbulence in Eady fronts. Part 1. Instability

The streamwise roll and streak structure (RSS) is prominent in observations of the planetary boundary layer in the atmosphere and ocean and in unstratified wall-bounded shear flows. Although the RSS in these systems is structurally similar, the mechanism forming and maintaining the RSS in both remains controversial. This study demonstrates that the same turbulence-sustaining mechanism identified to underlie the RSS in the Statistical State Dynamics (SSD) formulation of unstratified wall-bounded shear flow dynamics (Farrell & Ioannou 2012; Farrell et al. 2016) also operates in the Eady front. We analyze the mechanism by which turbulence and symmetric instability interact to form the RSS in the baroclinic stratified Eady front model by adapting to the Eady front problem the stability analysis of the second order closure of the SSD used previously to study roll formation in unstratified wall-bounded shear flows. Our findings advance mechanistic understanding of RSS formation in the turbulent geostrophic front regime and establish foundational parallels between geophysical turbulent front dynamics and turbulence dynamics in engineering-scale shear flows.

physics.flu-dyn↗
arXiv2026

Statistical state dynamics based study of turbulent Eady fronts. Part 2. Finite amplitude equilibria

Streamwise roll circulations commonly observed in frontal regions are primary agents of momentum and tracer transport in the planetary boundary layer (PBL) both in the atmosphere and ocean. Traditionally, the formation of the streamwise roll/streak structure (RSS) has been ascribed to symmetric instability (SI). In part 1, we studied RSS formation in the classical Eady front problem using statistical state dynamics (SSD), which allows incorporating the Reynolds stress (RS) torque instability mechanism together with SI in the dynamics underlying RSS formation. We found using SSD theory that the RS torque mechanism acts synergistically with the SI mechanism in forcing symmetric circulations in fronts when Richardson number Ri < 1, and also that the turbulence-mediated RS torque mechanism supports RSS formation in fronts with Ri > 1 for which the SI mechanism does not operate. Although SI theory provides an explanation for initial roll formation, it leaves open the question of RSS equilibration. An advantage of the SSD formulation of RSS dynamics is that it consistently incorporates the equilibration process. In this paper, we extend perturbation analysis of RSS dynamics in the SSD framework to a nonlinear analysis to understand roll formation, equilibration, and maintenance in the turbulent RSS regime.

physics.flu-dyn↗
arXiv2026

Small-Scale Dynamo for Full Spectrum of Hydrodynamic Turbulence in Kazantsev Model

A method is proposed for computing coefficients in the Kazantsev equation of small-scale dynamo for the full spectrum of hydromagnetic turbulence comprising the inertial range together with the range of viscous dissipation. The dynamo equation with so-defined coefficients is solved numerically for magnetic (Rm) and hydrodynamic (Re) Reynolds numbers from $10^2$ to $10^8$. The threshold value ${\rm Rm}_c$ for onset of dynamo increases initially with Re but then saturates at a constant value of ${\rm Rm}_c \simeq 300$ for ${\rm Re}\geq 10^5$. In the case of small Prandtl number Pm = Rm/Re << 1, the field growth rate is also small and depends logarithmically on Rm. In this case, the magnetic energy spectrum peaks around the scale of Ohmic dissipation, which decreases with increasing Pm. The decrease stops at the scale of viscous dissipation while the growth rate increases sharply when Pm approaches the value of one. The increase in the growth rate proceeds to ${\rm Pm} > 1$ but slows down and then saturates at a value somewhat below the inverse lifetime of most short-living eddies. An explanation of the results is proposed.

physics.flu-dyn↗