Temperature-gradient-induced electrokinetic flow and thermoelectricity of electrolyte solutions in a capillaries

TL;DR

This paper presents a semi-analytical model to study how temperature gradients induce electrokinetic flow and thermoelectric potential in electrolyte solutions within micro/nanocapillaries, revealing complex interactions among various parameters.

Contribution

It introduces a comprehensive semi-analytical model that accounts for multiple parameters influencing thermoelectric effects and electrokinetic flow in capillaries, advancing understanding of temperature-gradient-driven electrokinetics.

Findings

Thermoelectric field arises from ion Soret coefficient differences, ion diffusion, and fluid advection.

Thermoelectric effects depend on zeta potential and capillary size, with dominant mechanisms varying.

Electrokinetic flow is a superposition of electroosmotic and thermoosmotic flows, which can either cooperate or oppose.

Abstract

A systematic theoretical study of temperature-gradient-induced electrokinetic flow and thermoelectric potential of electrolyte solutions in a micro-/nanocapillary is presented. The study is based on a semi-analytical model developed by simultaneously solving the energy equation and the Poisson-Nernst-Planck/Navier-Stokes equations with the lubrication theory. The semi-analytical model is shown to be mainly governed by eight parameters, including two temperature-related parameters (temperature and its gradient), two electrokinetic parameters ($\zeta$ potential and the ratio of capillary radius to the Debye length $\kappa_0a$) and four physical properties of cation and anion (i.e. Soret coefficient difference $\Delta S_T$, average Soret coefficient $S_T$, normalized difference in diffusivities $\chi$ and intrinsic Peclet number $\lambda$). It is found that the thermoelectric field is induced by three effects, which are respectively due to (1) the difference in the Soret coefficients of cation and anion; (2) the selective ion diffusion resulting from the temperature-modified Boltzmann distribution of ions; (3) the advective transport of ions caused by the fluid flow. The first thermoelectric effect prevails for lower $\zeta$ potentials or large $\kappa_0a$, while the second is dominant for higher $\zeta$ potentials with very small $\kappa_0a$. The first two thermoelectric effects can cooperate or counteract depending on the sign of $\zeta\Delta S_T$. Finally, the temperature-gradient-induced electrokinetic flow is found to be a superposition of an electroosmotic flow component due to the thermoelectric field and a thermoosmotic flow component due to the combined effects of osmotic pressure and dielectric body force. These two flow components may cooperate or counteract depending on values of $\zeta$ and $\kappa_0a$.