Interfacial instability of thin films in soft microfluidic configurations actuated by electro-osmotic flow

Abstract

We analyze the interfacial instability of a thin film confined between a rigid surface and a pre-stretched elastic sheet, triggered by non-uniform electro-osmotic flow. We derive a nonlinear viscous−elastic equation governing the deformation of the elastic sheet, describing the balance between viscous resistance, the dielectric and electro-osmotic effects, and the restoring effect of elasticity. Our theoretical analysis, validated by numerical simulations, shows several distinct modes of instability depending on the electro-osmotic pattern, controlled by a non-dimensional parameter representing the ratio of electro-osmotic to elastic forces. We consider several limiting cases and present approximate asymptotic expressions predicting the electric field required for triggering of the instability. Through dynamic numerical simulations of the governing equation, we study the hysteresis of the system and show that the instability can result in an asymmetric deformation pattern, even for symmetric actuation. Finally, we validate our theoretical model with finite-element simulations of the two-way coupled Navier equations for the elastic solid, the unsteady Stokes equations for the fluid, and the Laplace equation for the electric potential, showing very good agreement. The mechanism illustrated in this work, together with the provided analysis, may be useful in toward the implementation of instability-based soft actuators for lab-on-a-chip and soft-robotic applications.

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

“…On the other hand, a computational study by de Rutte et al [221] on electroosmotic flow in a compliant microchannel concluded that a narrow and wide flow conduit can collapse over a range of imposed electric field strengths, and the effect is "exacerbated for soft materials such as PDMS." Boyko et al [222,223] expounded on this idea, showing that "above a certain electric field threshold, negative gauge pressure induced by electro-osmotic flow causes the collapse of its elastic wall." They experimentally demonstrated this novel type of fluid-structure instability and showed that an electroosmotic fluid-structure interaction parameter β ∝ B/(k w Lh 3 0 /η 0 ) (recall section 3.6) controls the (in)stability in a 2D Cartesian configuration as in figure 7(a).…”

“…To highlight the novel features of these electroosmotic flows in soft hydraulic conduits, it is instructive to consider the unsteady lubrication model from [223]. In this case, (60) becomes…”

“…Note that the electric field E is nonuniform in this narrow confinement, and it is given by the product of the second and third terms on the righthand side of (63). In model from [223], the pressure p(z, t) in ( 62) is not obtained from a local deformationpressure relation, as in section 3.5. Instead p(z, t) is related to ∂ 4 u y /∂z 4 , ∂ 2 u y /∂z 2 , ρgh, and εE 2 to account for axial bending, axial tension, gravity, and Maxwell stresses induced by the electric field, respectively (see also [224]).…”

Dynamics of fixed-volume pinned films – dealing with a non-self-adjoint thin-film problem

“…Another emerging application is in the field of reconfigurable microfluidics (Paratore et al 2022), where thin liquid films could be used to dynamically deform the surface of a thin membrane of a microfluidic chip, in order to control its functionality in real time. The film dynamics in such applications can be described by the same set of equations, whether a liquid-fluid or a liquid-membrane interface is used (Hosoi, Mahadevan & Peeling 2004;Kodio, Griffiths & Vella 2017;Boyko et al 2019Boyko et al , 2020. The ability to design such devices, predict their performance and understand their fundamental limitations, would greatly benefit from a theoretical framework that allows their analysis.…”

“…The film dynamics in such applications can be described by the same set of equations, whether a liquid-fluid or a liquid-membrane interface is used (Hosoi, Mahadevan & Peeling 2004; Kodio, Griffiths & Vella 2017; Boyko et al. 2019, 2020). The ability to design such devices, predict their performance and understand their fundamental limitations, would greatly benefit from a theoretical framework that allows their analysis.…”