Robert D. Deegan

Capillary flow as the cause of ring stains from dried liquid drops

When a spilled drop of coffee dries on a solid surface, it leaves a dense, ring-like deposit along the perimeter (Fig. 1a). The coffee—initially dispersed over the entire drop—becomes concentrated into a tiny fraction of it. Such ring deposits are common wherever drops containing dispersed solids evaporate on a surface, and they influence processes such as printing, washing and coating. Ring deposits also provide a potential means to write or deposit a fine pattern onto a surface. Here we ascribe the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior. The resulting outward flow can carry virtually all the dispersed material to the edge. This mechanism predicts a distinctive power-law growth of the ring mass with time—a law independent of the particular substrate, carrier fluid or deposited solids. We have verified this law by microscopic observations of colloidal fluids.

Complexities of splashing

We study the impact of a drop of liquid onto a thin layer of the same liquid. We give an overview of the sequence of events that occur as the two most important dimensionless control parameters are varied. In particular, multiple cohorts of droplets can be ejected at different stages after impact due to different mechanisms. Edgertons famous Milkdrop Coronet is only observed for a narrow range of parameters. Outside this range, the splash is either qualitatively different, or suffers from a much lower level of regularity.

Wavelength selection in the crown splash

The impact of a drop onto a liquid layer produces a splash that results from the ejection and dissolution of one or more liquid sheets, which expand radially from the point of impact. In the crown splash parameter regime, secondary droplets appear at fairly regularly spaced intervals along the rim of the sheet. By performing many experiments for the same parameter values, we measure the spectrum of small-amplitude perturbations growing on the rim. We show that for a range of parameters in the crown splash regime, the generation of secondary droplets results from a Rayleigh–Plateau instability of the rim, whose shape is almost cylindrical. In our theoretical calculation, we include the time dependence of the base state. The remaining irregularity of the pattern is explained by the finite width of the Rayleigh-Plateau dispersion relation. Alternative mechanisms, such as the Rayleigh–Taylor instability, can be excluded for the experimental parameters of our study.

Crumpling, buckling, and cracking: Elasticity of thin sheets

Deforming thin surfaces creates a rich set of structural and dynamical problems combining physics and geometry.

Finessing the fracture energy barrier in ballistic seed dispersal

Fracture is a highly dissipative process in which much of the stored elastic energy is consumed in the creation of new surfaces. Surprisingly, many plants use fracture to launch their seeds despite its seemingly prohibitive energy cost. Here we use Impatiens glandulifera as model case to study the impact of fracture on a plant’s throwing capacity. I. glandulifera launches its seeds with speeds up to 4 m/s using cracks to trigger an explosive release of stored elastic energy. We find that the seed pod is optimally designed to minimize the cost of fracture. These characteristics may account for its success at invading Europe and North America.

Localized structures in vibrated emulsions

We report our observations of localized structures in a thin layer of an emulsion subjected to vertical oscillations. We observe persistent holes, which are voids that span the layer depth, and kinks, which are fronts between regions with and without fluid. These structures form in response to a finite amplitude perturbation. Combining experimental and rheological measurements, we argue that the ability of these structures to withstand the hydrostatic pressure of the surrounding fluid is due to convection within their rim. For persistent holes the oscillatory component of the convection generates a normal stress which opposes contraction, while for kinks the steady component of the convection generates a shear stress which opposes the hydrostatic stress of the surrounding fluid.

Electrowetting on semiconductors

Applying a voltage difference between a conductor and a sessile droplet sitting on a thin dielectric film separating it from the conductor will cause the drop to spread. When the conductor is a good metal, the change of the drops contact angle due to the voltage is given by the Young-Lippmann (YL) equation. Here, we report experiments with lightly doped, single crystal silicon as the conductive electrode. We derive a modified YL equation that includes effects due to the semiconductor and contact line pinning. We show that light induces a non-reversible wetting transition, and that our model agrees well with our experimental results.

Weakly and strongly coupled Belousov-Zhabotinsky patterns

We investigate experimentally and numerically the synchronization of two-dimensional spiral wave patterns in the Belousov-Zhabotinsky reaction due to point-to-point coupling of two separate domains. Different synchronization modalities appear depending on the coupling strength and the initial patterns in each domain. The behavior as a function of the coupling strength falls into two qualitatively different regimes. The weakly coupled regime is characterized by inter-domain interactions that distorted but do not break wave fronts. Under weak coupling, spiral cores are pushed around by wave fronts in the other domain, resulting in an effective interaction between cores in opposite domains. In the case where each domain initially contains a single spiral, the cores form a bound pair and orbit each other at quantized distances. When the starting patterns consist of multiple randomly positioned spiral cores, the number of cores decreases with time until all that remains are a few cores that are synchronized with a partner in the other domain. The strongly coupled regime is characterized by interdomain interactions that break wave fronts. As a result, the wave patterns in both domains become identical.

Droplet Translation Actuated by Photoelectrowetting

In traditional electrowetting-on-dielectric (EWOD) devices, droplets are moved about a substrate using electric fields produced by an array of discrete electrodes. In this study, we show that a drop can be driven across a substrate with a localized light beam by exploiting the photoelectrowetting (PEW) effect, a light-activated variant of EWOD. Droplet transport actuated by PEW eliminates the need for electrode arrays and the complexities entailed in their fabrication and control, and offers a new approach for designing lab-on-a-chip applications. We report measurements of the maximum droplet speed as a function of frequency and magnitude of the applied bias, intensity of illumination, volume of the droplet, and viscosity and also introduce a model that reproduces these data.

Quantized orbits in weakly coupled Belousov-Zhabotinsky reactors

Using numerical and experimental tools, we study the motion of two coupled spiral cores in a light-sensitive variant of the Belousov-Zhabotinsky reaction. Each core resides on a separate two-dimensional domain, and is coupled to the other by light. When both spirals have the same sense of rotation, the cores are attracted to a circular trajectory with a diameter quantized in integer units of the spiral wavelength λ. When the spirals have opposite senses of rotation, the cores are attracted towards different but parallel straight trajectories, separated by an integer multiple of λ/2. We present a model that explains this behavior as the result of a spiral wavefront-core interaction that produces a deterministic displacement of the core and a retardation of its phase.