Surface-charge-mobility-modulated electrokinetic energy conversion in graphene nanochannels

Abstract

In recent years, electrokinetic energy conversion for pressure-driven flow through hydrophobic nanochannels has attracted increasing attention from numerous researchers. However, the reported electrokinetic energy conversion efficiencies may be overestimated owing to neglect of the surface charge mobility effect of hydrophobic nanochannels. In fact, both the effective slip length and the induced streaming potential are influenced by the surface charge mobility. In this paper, a theoretical model for electrokinetic energy conversion through graphene nanochannels is developed with consideration of the influence of surface charge mobility. The surface charge density σ s varies from very low to considerably high. A numerical solution to the electric potential is obtained by using the finite difference method. We also derive analytical solutions for two limiting cases, namely, the case with a low zeta potential and the case without considerable electric double layer overlap. Our results reveal that consideration of the surface charge mobility leads to a 44% reduction in the maximum conversion efficiency. The predicted maximum efficiency is approximately 5.9% at σ s=−0.0162 C/m2. Our results may prove useful for predicting and optimizing the electrokinetic conversion efficiency in hydrophobic nanochannels.

Energy harvesting from water streaming at charged surface

“…These changes can be attributed to the zeta potential enhanced whereas slip length inhibited by constantly increasing the surface charge density, which impacts the EKEC efficiency. This brings the conflict-high surface charge density versus slip length-possibly results in lower efficiency than the predictions and was verified by Liu et al in the recent work [153]. Thus, the maximum value of the figure of merit can be reached with the surface charge density satisfies 𝜒 −1∕2 .…”

“…[140–148], respectively), boundary slip from number 47 to 55 (Refs. [80, 88, 116, 125, 128, 149–153], respectively), and microjets/droplets from number 56 to 61 (Refs. [14–, 74, 87, 154], respectively).…”

“…respectively), ion layering from number 38 to 46 (Refs [140][141][142][143][144][145][146][147][148],. respectively), boundary slip from number 47 to 55 (Refs [80,88,116,125,128,[149][150][151][152][153],. respectively), and microjets/droplets from number 56 to 61 (Refs.…”

Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid

“…However, both theoretical and numerical models can be implemented for any type of monovalent or charge asymmetric multivalent electrolytes. Several previous studies ,, consider the physisorbed ions on hydrophobic surfaces as OH – with the effective hydrodynamic radius (τ) as 0.15 nm, which leads to the friction coefficient of mobile surface ions with water (λ s ) to be 2.8274 × 10 –12 kg/s and α s = 0.8. We denote the variables with the superscript “*” for the dimensionless variables.…”

“…The force balance condition for the negative physisorbed ion on the particle surface with lateral velocity u – relative to the fluid is 0 = prefix− λ s ( u − − u ) − λ w u − + ( − e ) E t where λ s and λ w are the friction coefficient of the surface mobile ion with water and wall, respectively, and E t ( = − 1 r ∂ ϕ ∂ θ ) is the tangential electric field at the surface. Thus u − = λ normals λ s + λ w u + − e λ s + λ w E t We denote α s = λ normals λ s + λ w as the surface charge mobility . Note that the velocity of the physisorbed ion vanishes when the friction of the ion with the wall becomes infinite, i.e., λ w → ∞.…”