Experimental determination of forces applied by liquid water drops at high drop velocities impacting a glass plate with and without a shallow water layer using wavelet deconvolution

Time-dependent forces applied by 2 and 4.5 mm diameter drops of water (with velocities up to terminal velocity) impacting upon a glass plate with or without a water layer (up to 10 mm depth) have been measured using two different approaches, force transduction and wavelet deconvolution. Both approaches are in close agreement for drops falling on dry glass. However, only the wavelet approach is able to measure natural features of the splash on shallow water layers that impart forces to the plate after the initial impact. At relatively high velocities (including terminal velocity) the measured peak force from the initial impact is significantly higher than that predicted by idealised drop shape models and models from Roisman et al. and Marengo et al. Hence empirical formulae are developed for the initial time-dependent impact force from drops falling at (a) different velocities up to and including terminal velocity onto a dry glass surface, (b) terminal velocity onto dry glass or glass with a water layer and (c) different velocities below terminal velocity onto dry glass or glass with a water layer. For drops on dry glass, the empirical formulae are applicable to a glass plate or a composite layered plate with a glass surface, although they apply to other plate thicknesses and are applicable to any plate material with a similar surface roughness and wettability. The measurements also indicate that after the initial impact there can be high level forces when bubbles are entrained in the water layer.