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.

A thin stream or rope of viscous fluid falling from a sufficient height onto a surface forms a steadily rotating helical coil. Tabletop laboratory experiments in combination with a numerical model for slender liquid ropes reveal that finite-amplitude coiling can occur in four distinct regimes (viscous, gravitational, inertio-gravitational, and inertial) corresponding to different balances among the three principal forces acting on the rope. The model further shows that the onset of coiling has distinct viscous, gravitational, and inertial modes that connect smoothly with the corresponding finite-amplitude regimes. In addition to steady coiling, slender liquid ropes falling onto surfaces can exhibit a remarkable variety of nonstationary behaviors, including propagating spiral waves of air bubbles, supercoiling, the leaping-shampoo (Kaye) effect for non-Newtonian fluids, and the fluid-mechanical sewing machine in which the rope leaves complex stitch patterns on a moving surface.

We present an experimental study of the coiling instability of a liquid “rope” falling on a solid surface. Coiling can occur in three different regimes—viscous, gravitational, or inertial—depending on the fluid viscosity and density, the fall height, and the flow rate. The competition among the different forces causes the coiling frequency first to decrease and subsequently to increase with increasing height. We also observe an oscillation between two coiling states in the gravitational-to-inertial transitional range, reflecting the multivaluedness of the dependence of coiling frequency on fall height. The data can be rescaled in a universal way, and agree very well with numerically predicted coiling frequencies.

Numerous materials, from biopolymers to filled rubbers, exhibit strain softening at high strain amplitudes during a strain sweep in oscillatory rheology: The modulus decreases with increasing deformation. On the other hand, if the nonlinear elastic response is analyzed within a single oscillation cycle (described by a Lissajous curve), these systems are often reported to exhibit strain hardening. We compare strain sweeps and single cycle LAOS (large amplitude oscillatory shear) analyses of stress vs strain on three very different materials. We conclude that the reported strain hardening is due to the use of a tangent modulus in the LAOS analysis, and that the overall rheology remains strain softening. To show that this conclusion is robust, we demonstrate a rescaling of the modulus that collapses the data from all the oscillatory measurements onto a single master curve that clearly exhibits the correct strain softening behavior.

Just a bit of water enables one to turn a pile of dry sand into a spectacular sandcastle. Too much water however will destabilize the material, as is seen in landslides. Here we investigated the stability of wet sand columns to account for the maximum height of sandcastles. We find that the columns become unstable to elastic buckling under their own weight. This allows to account for the maximum height of the sand column; it is found to increase as the 2/3 power of the base radius of the column. Measuring the elastic modulus of the wet sand, we find that the optimum strength is achieved at a very low liquid volume fraction of about 1%. Knowing the modulus we can quantitatively account for the measured sandcastle heights.

A thin “rope” of viscous fluid falls from a sufficient height of coils as it approaches a rigid surface. Here we perform a linear stability analysis of steady coiling, with particular attention to the “inertio-gravitational” regime in which multiple states with different frequencies exist at a fixed fall height. The basic states analyzed are numerical solutions of asymptotic “thin-rope” equations that describe steady coiling. To analyze their stability, we first derive in detail a set of more general equations for the arbitrary time-dependent motion of a thin viscous rope. Linearization of these equations about the steady coiling solutions yields a boundary-eigenvalue problem of order 21 which we solve numerically to determine the complex growth rate. The multivalued portion of the curve of steady coiling frequency vs height comprises alternating stable and unstable segments whose distribution agrees closely with high-resolution laboratory experiments. The dominant balance of (perturbation) forces in the instability is between gravity and the viscous resistance to bending of the rope; inertia is not essential, although it significantly influences the growth rate.