(250e) Surface-Tension Effects in Oscillatory Squeeze Flow Rheometry

We report experiments, numerical simulations, and analytical models of low- and high-viscosity fluids undergoing oscillatory squeezing between two parallel plates in a commercial extensional rheometer. We show that surface tension modifies the low-frequency response of a viscous fluid, resulting in an ``apparent elasticity'' akin to a Kelvin-Voigt solid. This response is highly sensitive to the amplitude of the imposed oscillation, due to the influence of the meniscus profile on the capillary force exerted at the plate edge. At sufficiently small strain amplitudes ε << 1, the liquid bridge is weakly perturbed from its initial cylindrical shape and the measured elastic stress depends linearly on the applied strain. We show that large-amplitude (nonlinear) effects can be quantified via a free-energy minimization of the static meniscus shape at different time points. The rheometric response is well-modeled by a complex shear modulus G*(ω) = iμω+ 4φγ/R, where ω is the angular frequency of oscillation, μ is the shear viscosity, γ is the surface tension, R is the radius of the plates, and φ is an O(1) correction factor that depends only on the amplitude of oscillation and fluid volume (for thin films and small enough strains, φ = 1). Surface-tension effects dominate the response when the capillary number Ca = μωR/γ is small compared to unity. Other physical effects, including gravity and fluid inertia, are considered and shown to be irrelevant under the conditions of our study. The overall impact of this work is twofold. First, surface-tension effects oftentimes emerge as an unwanted artifact in linear and nonlinear viscoelastic measurements of bulk material properties. Our analysis precisely isolates and quantifies this undesired contribution and, therefore, may be used to properly interpret measurements of low-viscosity fluids at low frequencies. Second, the agreement between our experimental measurements and models suggest the use of oscillatory squeezing as a method of measuring the surface tension or, more generally, surface viscoelastic properties of liquids. We propose that subsequent studies focus on adapting and optimizing oscillatory squeeze flow devices, which are traditionally used for bulk rheometry, to additionally measure the surface properties of thin films. Our experimentally validated computer models and scaling relations provide useful benchmarks for any future experimental work.