Tuning diffusioosmosis of electrolyte solutions by hydrostatic pressure

TL;DR

This work develops a lubrication-approximation-based theory for diffusio-osmosis in a uniformly charged, thick slit connecting reservoirs of differing salinity, explicitly incorporating a hydrostatic pressure drop $Δp$. The authors show that the total flow rate $\mathcal{Q}$ is the sum of a salt-gradient–driven diffusio-osmotic term and a pressure-driven term, with the latter altering concentration and potential profiles while leaving the intrinsic slip response to salt gradients unchanged. They derive a closed-form expression for the midplane concentration $c_m(x)$ in terms of the flow rate $\mathcal{Q}$ and the concentration drop $Δc$, and relate the surface potential $φ_s$ to $c_m$, revealing strong spatial variation of $φ_s$ along the slit. The results explain experimental flow-rate trends, provide a direct way to infer internal concentration and surface-potential profiles from measurements, and suggest practical ways to tune diffusio-osmotic flows and sensing capabilities in nano/microfluidic devices.

Abstract

When two reservoirs of a distinct salinity are connected by channels or pores, a fluid flow termed diffusio-osmotic is generated. This article investigates the flow emerging in an uniformly charged long slit whose thickness exceeds the local Debye screening length. Attention is focussed on the role of hydrostatic pressure drop $Δp$ between reservoirs. For a thick slit we recover the known formula for a local diffusioosmotic slip over a single wall, which is determined by the surface potential, salt concentration and its gradient. An equation for the global fluid flow rate $\mathcal{Q}$ is presented as a sum of the diffusio-osmotic and pressure-driven contributions. Although the diffusio-osmotic term itself remains unaffected by $Δp$, the concentration and surface potential profiles along the slit, and consequently, the local slip velocity are dramatically modified. We present an equation relating the local concentration to $\mathcal{Q}$ and employ it to derive an expression describing the surface potential variation in the slit. Since $\mathcal{Q}$ can easily be tuned by $Δp$, the variety of possible concentration and surface potential profiles becomes very rich. Our theory provides a simple explanation of recent flow rate measurements and shows that experimental data provide rather direct information about concentration and surface potential profiles in the uniformly charged slit. The relevance of our results for sensing the salt dependence of surface potentials is discussed briefly.

Figures (12)

• Figure 1: Sketch of the microchannel of thickness $H$, length $L \gg H$ and constant surface charge density $\sigma$ that connects the "fresh" (left) and "salty" (right) bulk electrolyte reservoirs of concentrations $C_{0}$ and $C_{1}$ with hydrostatic pressures $P_{0}$ and $P_{1}$. The extension of electrostatic diffuse layers, which is of the order of the Debye length $\lambda_D \ll H$. It takes the upper value of $\lambda_D = \lambda_D^{\star}$ at $X=0$ and is reducing along the channel.
• Figure 2: $\mathcal{Q}$ as a function of $\ell_{GC}$ computed using $c_1 = 10^2$ and $\beta = -0.3$ for pressure drop $\Delta p = -10^{2}$ (solid curves) and $0$ (dotted curves). The dash-dotted curve corresponds to the case of $c_1 = 1$ and $\Delta p = -10^{2}$. Open and filled circles show calculations from Eqs. \ref{['qint_l']} and \ref{['eq:q_lin']}.
• Figure 3: The flow rate $\mathcal{Q}$ as a function of $\beta$ computed using $\ell_{GC} = -1$ nm for $c_1 = 10^2$, $\Delta p = -10^{2}$, 0 and $10^{2}$ (from top to bottom). Circles from left to right mark values of $\mathcal{Q}$ that correspond to LiI, LiNO$_3$, NaCl, LiCH$_3$COO, KBr, NaCH$_3$COO, and KCH$_3$COO.
• Figure 4: $\mathcal{J}$ as a function of $\mathrm{Pe}\mathcal{Q}$ computed using $\beta = -0.3$ and $c_1 = 1$ (dotted), $10$ (solid), $10^{2}$ (dashed), $10^{3}$ (dash-dotted). The square marks the point of $\mathcal{J} = \mathcal{Q} = 0$. Circles and triangles indicate $\mathcal{J} = 0$ and $\mathcal{Q} = 0$.
• Figure 5: Concentration $c_m$ as a function of $x$ for NaCl [$\mathrm{Pe} = 0.272$, $\beta = -0.208$]. Solid and dash-dotted curves show calculations using $\mathrm{Pe}\mathcal{Q} = -30$ and 30. Dashed and dotted curves correspond to the cases when $\mathcal{Q}=0$ and $\mathcal{J}=0$. Filled and open circles are obtained using Eqs. \ref{['cx_largePeQ']} and \ref{['cx_minus']}. Filled and open squares show predictions of Eqs. \ref{['cx_zeroJ']} and \ref{['eq:c_lin2']}.