Making use of experimental and theoretical considerations, in this Letter we deduce a criterion to determine the critical velocity for which a drop impacting a smooth dry surface either spreads over the substrate or disintegrates into smaller droplets. The derived equation, which expresses the splash threshold velocity as a function of the material properties of the two fluids involved, the drop radius, and the mean free path of the molecules composing the surrounding gaseous atmosphere, has been thoroughly validated experimentally at normal atmospheric conditions using eight different liquids with viscosities ranging from μ=3×10(-4) to μ=10(-2)  Pa s, and interfacial tension coefficients varying between σ=17 and σ=72  mN m(-1). Our predictions are also in fair agreement with the measured critical speed of drops impacting in different gases at reduced pressures given by Xu et al. [Phys. Rev. Lett. 94, 184505 (2005).

An experimental investigation of the flow generated by a homogeneous population of bubbles rising in water is reported for three different bubble diameters (d= 1.6, 2.1 and 2.5 mm) and moderate gas volume fractions (0.005 ≤ α ≤ 0.1). The Reynolds numbers,Re=V0d/ν, based on the rise velocityV0of a single bubble range between 500 and 800. Velocity statistics of both the bubbles and the liquid phase are determined within the homogeneous bubble swarm by means of optical probes and laser Doppler anemometry. Also, the decaying agitation that takes place in the liquid just after the passage of the bubble swarm is investigated from high-speed particle image velocimetry measurements. Concerning the bubbles, the average velocity is found to evolve asV0α−0.1whereas the velocity fluctuations are observed to be almost independent of α. Concerning the liquid fluctuations, the probability density functions adopt a self-similar behaviour when the gas volume fraction is varied, the characteristic velocity scaling asV0α0.4. The spectra of horizontal and vertical liquid velocity fluctuations are obtained with a resolution of 0.6 mm. The integral length scale Λ is found to be proportional toV02/gor equivalently tod/Cd0, wheregis the gravity acceleration andCd0the drag coefficient of a single rising bubble. Normalized by using Λ, the spectra are independent on both the bubble diameter and the volume fraction. At large scales, the spectral energy density evolves as the power −3 of the wavenumber. This range starts approximately from Λ and is followed for scales smaller than Λ/4 by a classic −5/3 power law. Although the Kolmogorov microscale is smaller than the measurement resolution, the dissipation rate is however obtained from the decay of the kinetic energy after the passage of the bubbles. It is found to scale as α0.9V03/Λ. The major characteristics of the agitation are thus expressed as functions of the characteristics of a single rising bubble. Altogether, these results provide a rather complete description of the bubble-induced turbulence.