SUMMARYFlexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. In strong winds and flood waters, for example, leaves roll up into cone shapes that reduce drag compared with rigid objects of similar surface area. Less understood is how a leaf attached to a flexible leaf stalk will roll up stably in an unsteady flow. Previous mathematical and physical models have only considered the case of a flexible sheet attached to a rigid tether in steady flow. In this paper, the dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia and the wild violet Viola papilionacea are described using particle image velocimetry. The flows around the leaves are compared with those of simplified physical and numerical models of flexible sheets attached to both rigid and flexible beams. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In the physical model, a similar recirculation zone is observed within sheets constructed to roll up into cones with both rigid and flexible tethers. Numerical simulations and experiments show that flexible rectangular sheets that reconfigure into U-shapes, however, are less stable when attached to flexible tethers. In these cases, larger forces and oscillations due to strong vortex shedding are measured. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf. Supplementary material available online at

A jet of fluid flowing down a partially wetting inclined plane usually meanders. In this paper, we demonstrate that meandering on a smooth plane can be suppressed by maintaining a constant volume flow rate. In the absence of meandering, we experimentally observe the jet developing a braided structure with non-monotonic width. This flow pattern is theoretically explained as the result of the interplay between surface tension that tends to narrow the jet down and fluid inertia that drives the jet width to expand. The theory also predicts a bifurcation between the braiding regime and a non-meandering non-braiding flow, which is confirmed by experiment.

A stream of fluid flowing down a partially wetting inclined plane usually meanders, unless the volume flow rate is maintained at a highly constant value. Here we investigate whether the meandering of this stream is an inherent instability. In our experiment, we eliminate meandering on several partially wetting substrates by reducing perturbations entering the flow. By re-introducing controlled fluctuations, we show that they are responsible for the onset of the meandering. We derive a theoretical model for the stream shape, %from first principles which includes stream dynamics and forcing by external noise. The deviation h(x) from a straight linear stream h(x)=0 shows considerable variability as a function of downstream distance x. However, for an ensemble average of stream shapes acquired at different times, the power spectrum S(k) as a function of wavenumber k has a power-law scaling S(k) ~ k5/2. Moreover, the area A(x) swept by the stream at the distance x grows as A(x) ~ x1.75.

A promising method of particle self-assembly using patterned surfaces is described. A set of long (order of millimeters), nanoscale-width grooves is etched into a substrate, and an aqueous solution containing particles of ∼50- or 80-nm diameter is deposited on the surface. Upon the evaporation of the solution, the particles are dragged into the grooves by the receding contact line. A partial differential equation, incorporating screening, is constructed to investigate the final distribution of particles in the grooves. A complete analysis of the stationary states for the density equation in one and two dimensions is performed. Additionally, the nonlinear evolution of the density is studied numerically and the results compare well with both the analytic results and the experiments.

A jet of fluid flowing down a partially wetting, inclined plane usually meanders but--by maintaining a constant flow rate--meandering can be suppressed, leading to the emergence of a beautiful braided structure. Here we show that this flow pattern can be explained by the interplay between surface tension, which tends to narrow the jet, and fluid inertia, which drives the jet to widen. These observations dispel misconceptions about the relationship between braiding and meandering that have persisted for over 20 years.