Soft lubrication: the elastohydrodynamics of conforming and non-conforming contacts

We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples
tangential and normal forces and thus generates lift. We consider materials that deform easily, due
to either geometry
e.g., a shell or constitutive properties
e.g., a gel or a rubber, so that the effects
of pressure and temperature on the fluid properties may be neglected. Four different system
geometries are considered: a rigid cylinder moving parallel to a soft layer coating a rigid substrate;
a soft cylinder moving parallel to a rigid substrate; a cylindrical shell moving parallel to a rigid
substrate; and finally a cylindrical conforming journal bearing coated with a thin soft layer. In
addition, for the particular case of a soft layer coating a rigid substrate, we consider both elastic and
poroelastic material responses. For all these cases, we find the same generic behavior: there is an
optimal combination of geometric and material parameters that maximizes the dimensionless
normal force as a function of the softness parameter
= hydrodynamic pressure/elastic stiffness
= surface deflection/ gap thickness, which characterizes the fluid-induced deformation of the
interface. The corresponding cases for a spherical slider are treated using scaling concepts.

How the Venus Flytrap snaps

The rapid closure of the Venus flytrap (Dionaea muscipula) leaf
in about 100 ms is one of the fastest movements in the plant
kingdom. This led Darwin to describe the plant as “one of the
most wonderful in the world”1
. The trap closure is initiated by
the mechanical stimulation of trigger hairs. Previous studies2–7
have focused on the biochemical response of the trigger hairs to
stimuli and quantified the propagation of action potentials in the
leaves. Here we complement these studies by considering the
post-stimulation mechanical aspects of Venus flytrap closure.
Using high-speed video imaging, non-invasive microscopy techniques and a simple theoretical model, we show that the fast
closure of the trap results from a snap-buckling instability, the
onset of which is controlled actively by the plant. Our study
identifies an ingenious solution to scaling up movements in non-muscular engines and provides a general framework for understanding nastic motion in plants.

Solenoids and Plectonemes in stretched and twisted elastomeric filaments

We study the behavior of a naturally straight highly extensible elastic filament subjected to large
extensional and twisting strains. We find that two different phases can coexist for a range of parameter
values: the plectoneme and the solenoid. A simple theory based on a neo-Hookean model for the material
of the filament and accounting for the slender geometry suffices to explain these observations, and leads to
a phase diagram that is consistent with observations. Extension and relaxation experiments on these
phases show the presence of large hysteresis loops and sawtoothlike force-displacement curves which are
different for the plectoneme and the solenoid.

Hydrodynamical models for the chaotic dripping faucet

We give a hydrodynamical explanation for the chaotic behaviour of a dripping
faucet using the results of the stability analysis of a static pendant drop and a
proper orthogonal decomposition (POD) of the complete dynamics. We find that the
only relevant modes are the two classical normal forms associated with a saddle–
node–Andronov bifurcation and a Shilnikov homoclinic bifurcation. This allows
us to construct a hierarchy of reduced-order models including maps and ordinary
differential equations which are able to qualitatively explain prior experiments and
numerical simulations of the governing partial differential equations and provide
an explanation for the complexity in dripping. We also provide a new mechanical
analogue for the dripping faucet and a simple rationale for the transition from
dripping to jetting modes in the flow from a faucet.

Self-organized origami

The controlled folding and unfolding of maps,
space structures, wings, leaves, petals, and other
foldable laminae is potentially complicated by the
independence of individual folds; as their number increases, there is a combinatorial explosion in the number of folded possibilities. The
artificially constructed Miura-ori (1) pattern,
with a periodic array of geometrically and
elastically coupled mountain and valley folds
(Fig. 1A), circumvents this complication by
allowing the entire structure to be folded or
unfolded simultaneously. Making such a pattern is not easy, so it may be surprising to find
an elegant natural counterpart that is a few
hundred millennia old. In Fig. 1B, we show the
different stages of the opening of a hornbeam
leaf that starts life in its bud as a Miura-ori
folded pattern (2). Similar structures arise in
insect wings (3) and elsewhere in nature (4),
suggesting that these origami patterns are a
result of convergent design. This raises a question of mechanism: How might this spatial
organization of folds be brought about?