Electroosmotic lubrication flow in constricted microchannels with a compliant wall and DLVO interactions

TL;DR

This work tackles electroosmotic flow in constricted soft microchannels where wall deformation, lubrication pressures, and short-range intermolecular DLVO forces interact nonlinearly. A nonlinear framework couples electroosmotic slip, lubrication dynamics, elastic bending of a clamped Kirchhoff–Love wall, and DLVO disjoining pressure in the thin EDL limit, and is analyzed via asymptotics and spectral collocation simulations using a six-parameter nondimensional set $C$, $\mathcal{B}$, $\kappa^*$, $\Pi_{\mathrm{el}}$, $\Pi_{\mathrm{vdW}}$, and $Du$. The study identifies three regimes—stiff-wall, deformation-limited, and repulsion-stabilized—and derives compact scaling relations such as $Q \sim -s_\zeta \sqrt{C} K(Du)$ in strong constriction, $\delta_{\max} \sim F_{\mathrm{DLVO}}/(\mathcal{B}C^2)$, and $\Delta Q \sim F_{\mathrm{DLVO}}/(\mathcal{B}C^{3/2})$, providing design rules in terms of $\mathcal{B}C^2$ and $Du$. The results reveal how elasticity, geometry, and molecular forces jointly regulate EOF under nanometric confinement and offer guidelines for creating compliant electrokinetic channels with tunable throughput and stability. This framework supports simulations and experimental validation in soft microfluidics, biosensing, and iontronic devices where controlled deformation and DLVO interactions are central.

Abstract

We develop a nonlinear model for electroosmotic transport in a constricted microchannel with a compliant lower wall, with applications to soft microfluidics, bio-inspired sensing, and energy harvesting. The formulation couples electroosmotic slip-driven flow under a globally constrained electric field with pressure-driven lubrication and elastic wall deformation, modeled as a clamped Kirchhoff-Love plate. Short-range intermolecular stresses are incorporated through an extended Derjaguin-Landau-Verwey-Overbeek framework combining electrostatic double-layer repulsion and van der Waals attraction, enabling us to probe the nonlinear coupling between intermolecular forces, wall deformation, and electroosmotic flow in compliant microchannels. The flow is governed by six nondimensional parameters: wall compliance, geometric curvature, electrostatic and van der Waals strengths, scaled Debye length, and Dukhin number. Asymptotic analysis clarifies the role of these parameters in limiting regimes. In the stiff-wall limit, electroosmotic slip acts as a uniform offset to the pressure-driven flow. Fully coupled spectral collocation simulations confirm the asymptotic predictions and capture nonlinear feedback between pressure, deformation, and intermolecular stresses. Three regimes emerge: a stiff-wall regime with negligible deformation, a deformation-limited regime in which elastic narrowing strongly suppresses flux, and a repulsion-limited regime where DLVO forces cap wall deflection and prevent collapse. These results show how elasticity, geometry, and molecular forces jointly regulate electroosmotic lubrication and provide scaling rules for the design of compliant electrokinetic channels operating under nanometric confinement.

Figures (7)

• Figure 1: Electroosmotic lubrication in a constricted microchannel with a rigid curved upper wall and a compliant lower wall. A prescribed potential drop $\Delta\phi$ produces an axial electric field $E_x(x)$ in a symmetric $z:z$ electrolyte. Under quasi one dimensional conduction the field intensifies where the gap is small and this strengthens the Helmholtz Smoluchowski electroosmotic slip. The compliant wall deforms under the normal traction due to hydrodynamic pressure and disjoining stresses.
• Figure 2: Model validation and numerical convergence. (a) Constant-gap benchmark: computed flux $Q$ versus Dukhin number $Du$ compared with Eq. \ref{['eq:Q_constgap']}. (b) Stiff-wall benchmark: augmented-pressure profile $\hat{P}(x)=P(x)-P(0)$ compared with the reference solution from Eq. \ref{['eq:stiff_ref_Pprime']}. (c) Grid refinement: relative errors in flux, deformation, and pressure, $e_Q$, $e_\delta$, and $e_p$, defined in Eqs. \ref{['eq:eQ_def']} and \ref{['eq:profile_errors']}, as functions of the number of Chebyshev modes $N$.
• Figure 3: Compliance-controlled response for several constriction amplitudes $C$. (a) Normalized flux $Q/Q_{\mathrm{rigid}}$ as a function of the dimensionless bending stiffness $B$. (b) Maximum wall deflection $\delta_{\max}$ shown in rescaled form $C^2\delta_{\max}$ versus $1/B$. (c) Normalized flux deficit $(Q_{\mathrm{rigid}}-Q)/Q_{\mathrm{rigid}}$ versus the combined compliance parameter $C^2/B$.
• Figure 4: Effect of geometric modulation and surface conduction. (a) Flux magnitude $-Q$ versus constriction amplitude $C$ on logarithmic axes for several Dukhin numbers $Du$. (b) Representative axial profiles of the hydrodynamic pressure $p(x)$ (solid lines, left axis) and wall deflection $\delta_s(x)$ (dashed lines, right axis) for increasing $C$ at fixed $Du=0.1$. (c) Rescaled flux $-Q/\sqrt{C}$ versus $Du$ for different $C$, illustrating the collapse predicted by the strong-constriction scaling.
• Figure 5: Narrow-gap scaling in the DLVO-influenced regime. (a) Maximum deflection $\delta_{\max}$ versus constriction amplitude $C$ for several bending stiffness values $B$, showing the $C^{-2}$ trend. (b) Flux variation $|\Delta Q|$ versus the rescaled forcing $F_{\mathrm{DLVO}}/(B C^{3/2})$, illustrating collapse of the numerical results.