Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

Abstract

The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics, and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong prestretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Föppl-von Kármán equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and timescale on the spatial wavenumber, as well as the transition between stretchingand bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Föppl-von Kármán equations and present the deformation behavior as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

Nonuniform Electro-osmotic Flow Drives Fluid-Structure Instability

“…Such deformations were also recently studied in the context of EOF-driven flows by Mukherjee et al. [5], de Rutte et al [6] and Boyko et al [7]. In all of those studies, the fluid-structure interaction exhibited stable behavior.…”

“…To understand the physical mechanisms underlying the instability, we perform a linear stability analysis of Eq. (7). We consider a small perturbation of the rigid body from its equilibrium height is some small perturbation and σ is the non-dimensional growth rate.…”

Hydrodynamic Bulge Testing: Materials Characterization Without Measuring Deformation

“…The proposed hydrodynamic bulge testing technique could also be extended to handle liquid blister tests [49], which are used to measure the strength of bonding (via the work of adhesion), if the fluid layer is made much thinner than the solid film. Beyond bulge tests, the FSI between a viscous fluid and a pre-stressed platelike elastic structure can be harnessed to create soft microfluidic actuators [19]. Similar multiphysics problems can also be motivated by biomedical and physiological applications, such as the reopening of strongly collapsed airways [18].…”

“…The X → −X symmetry of the boundary-value problem (BVP) specified by Eq. (19) and its BCs requires that C 1 (Z) = C 2 (Z) and C 4 (Z) = 0. Thus, the general solution (22) can be rewritten as…”

“…Often, bulge testing techniques discussed in the literature have focused on circular membranes [2], with only a few studies addressing the case of rectangular membranes with prestress [10,11,12,17] using energy minimization methods [1]. Residual pre-stress (pre-tension) is common in samples being tested because the thin film of material has to be stretched taut over an orifice (say, a rectangular microchannel) to ensure that it is flat before the commencement of the experiment [18,19]. Furthermore, most of the bulge testing theories in the literature assume that the film has negligible thickness and deformations due to shear along the transverse direction are, thus, not accounted for.…”