Surface-tension effects in oscillatory squeeze flow rheometry

Oscillatory squeeze flow rheometry (OSFR) is a technique for measuring fluid viscosity and linear viscoelasticity between oscillating parallel plates. While several corrections to the basic viscous flow model for OSFR have been considered (e.g., due to inertial effects), the role of surface tension remains largely unexplored. The present work revisits the classical liquid bridge problem subject to an oscillatory squeeze flow and considers the role of viscosity and surface tension on the dynamic force exerted by the liquid on the supporting plates. Using a combination of theory and experiment, we show that the (dimensionless) force collapses onto a master curve when plotted against a modified capillary number (measuring the relative importance of viscosity and surface tension) and that this prediction is robust over a wide range of strain amplitudes and aspect ratios. In doing so, we also demonstrate the ability of OSFR to measure surface-tension forces with reasonably high resolution. We test this capability for several low-viscosity fluids, demonstrating that, with current instrumentation and protocol, OSFR can measure surface tension to within 20% relative error. Finally, we provide an operating diagram that demarcates the regimes in which either viscosity or surface tension can be ignored in OSFR measurements. The results of this study may be used to further develop OSFR as a tool for measuring dynamical surface phenomena in addition to bulk viscoelasticity.