Parametric study on the onset of Faraday waves in a Hele–Shaw cell

This work investigates the onset of Faraday instabilities in Hele–Shaw cells. The influence of kinematic viscosity, surface tension, and forcing frequency on the stability threshold is systematically studied for two gap widths. Acceleration, wave amplitude, and wavelength at the onset of instability are measured for 37 different configurations. In parallel, gap-averaged Navier–Stokes simulations are performed for these configurations, showing reasonable agreement with experiments in most cases. The results are also compared with predictions from linear stability theories. When represented as a function of a newly defined capillary-number-like parameter, all experimental and numerical data collapse onto a single master curve. This study provides a unique experimental dataset for model validation and highlights the limitations of current simulation strategies and theoretical approaches.