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

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.