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We study the evaporation rate from single drops as well as collections of drops on a solid substrate, both experimentally and theoretically. For a single isolated drop of water, in general the evaporative flux is limited by diffusion of water through the air, leading to an evaporation rate that is proportional to the linear dimension of the drop. Here, we test the limitations of this scaling law for several small drops and for very large drops. We find that both for simple arrangements of drops, as well as for complex drop size distributions found in sprays, cooperative effects between drops are significant. For large drops, we find that the onset of convection introduces a length scale of approximately 20 mm in radius, below which linear scaling is found. Above this length scale, the evaporation rate is proportional to the surface area.

We present a study of hydraulic jumps with flow predominantly in one direction, created either by confining the flow to a narrow channel with parallel walls or by providing an inflow in the form of a narrow sheet. In the channel flow, we find a linear height profile upstream of the jump as expected for a supercritical one-dimensional boundary layer flow, but we find that the surface slope is up to an order of magnitude larger than expected and independent of flow rate. We explain this as an effect of turbulent fluctuations creating an enhanced eddy viscosity, and we model the results in terms of Prandtl's mixing-length theory with a mixing length that is proportional to the height of the fluid layer. Using averaged boundary-layer equations, taking into account the friction with the channel walls and the eddy viscosity, the flow both upstream and downstream of the jump can be understood. For the downstream subcritical flow, we assume that the critical height is attained close to the channel outlet. We use mass and momentum conservation to determine the position of the jump and obtain an estimate which is in rough agreement with our experiment. We show that the averaging method with a varying velocity profile allows for computation of the flow-structure through the jump and predicts a separation vortex behind the jump, something which is not clearly seen experimentally, probably owing to turbulence. In the sheet flow, we find that the jump has the shape of a rhombus with sharply defined oblique shocks. The experiment shows that the variation of the opening angle of the rhombus with flow rate is determined by the condition that the normal velocity at the jump is constant.

We study the rheology of a granular paste, i.e. a dense suspension of non-Brownian particles, quantitatively at steady state, in a cylindrical Couette cell. Previous studies have shown a discrepancy between local and global measurements of the viscosity for these materials, making it impossible to predict their resistance to flow. Using both MRI investigation techniques and classical rheology studies, we show that agreement between local and global measurements can be obtained, provided the migration of particles inside the gap is taken into account. As found by Leighton & Acrivos (J. Fluid Mech. vol. 181, 1987, p. 415), the migration leads to a particle density gradient in the flow, the highly sheared regions being less dense in particles. Here, by comparing the local viscosity and particle density measurements from MRI with the macroscopic relation between viscosity and the volume fraction, it is shown that global and local measurements agree with each other. This consequently allows us to define a viscosity for dense suspensions.

International audience; The evaporation of droplets on a substrate that is wetting to the liquid is studied. The radius $R(t)$ of the droplet is followed in time until it reaches zero. If the evaporation is purely diffusive, $R \propto \sqrt{t_0\,{-}\,t}$ is expected, where $t_0$ is the time at which the droplet vanishes; this is found for organic liquids, but water has a different exponent. We show here that the difference is likely to be due to the fact that water vapour is lighter than air, and the vapour of other liquids more dense. If we carefully confine the water so that a diffusive boundary layer may develop, we retrieve $R(t) \propto \sqrt{t_0\,{-}\,t}$. On the other hand, if we force convection for an organic liquid, we retrieve the anomalous exponent for water.

We study the viscous fingering or Saffman–Taylor instability in two different dilute or semi-dilute polymer solutions. The different solutions exhibit only one non-Newtonian property, in the sense that other non-Newtonian effects can be neglected. The viscosity of solutions of stiff polymers has a strong shear rate dependence. Relative to Newtonian fluids, narrower fingers are found for rigid polymers. For solutions of flexible polymers, elastic effects such as normal stresses are dominant, whereas the shear viscosity is almost constant. Wider fingers are found in this case. We characterize the non-Newtonian flow properties of these polymer solutions completely, allowing for separate and quantitative investigation of the influence of the two most common non-Newtonian properties on the Saffman–Taylor instability. The effects of the non-Newtonian flow properties on the instability can in all cases be understood quantitatively by redefining the control parameter of the instability.

We study the impact and subsequent retraction dynamics of liquid droplets upon high-speed impact on hydrophobic surfaces. Performing extensive experiments, we show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that when increasing the Ohnesorge number, $\Oh=\eta/\sqrt{\rho R_{\rm I} \gamma}$, the retraction, i.e. dewetting, dynamics crosses over from a capillaro-inertial regime to a capillaro-viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid-liquid contact line dynamics inspired by the standard theories for thin film dewetting.