Joseph Paulsen

Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets

Significance Thin elastic sheets buckle and wrinkle to relax compressive stresses. Wrinkling metrologies have recently been developed as noninvasive probes of mechanical environment or film properties, for instance in biological tissues or textiles. This work proposes and experimentally tests a prediction for the local wavelength of wrinkles in nonuniform curved topographies. Wrinkle patterns in compressed thin sheets are ubiquitous in nature and technology, from the furrows on our foreheads to crinkly plant leaves, from ripples on plastic-wrapped objects to the protein film on milk. The current understanding of an elementary descriptor of wrinkles—their wavelength—is restricted to deformations that are parallel, spatially uniform, and nearly planar. However, most naturally occurring wrinkles do not satisfy these stipulations. Here we present a scheme that quantitatively explains the wrinkle wavelength beyond such idealized situations. We propose a local law that incorporates both mechanical and geometrical effects on the spatial variation of wrinkle wavelength. Our experiments on thin polymer films provide strong evidence for its validity. Understanding how wavelength depends on the properties of the sheet and the underlying liquid or elastic subphase is crucial for applications where wrinkles are used to sculpt surface topography, to measure properties of the sheet, or to infer forces applied to a film.

The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering, and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a cross-over region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram.

Coalescence of bubbles and drops in an outer fluid

When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence in a dense surrounding fluid, such as oil coalescence in brine. Here we study the merging of gas bubbles and liquid drops in an external fluid. Our data indicate that the flows occur over much larger length scales in the outer fluid than inside the drops themselves. Thus, we find that the asymptotic early regime is always dominated by the viscosity of the drops, independent of the external fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies a dimensionless number that signifies when the external viscosity can be important.

Multiple transient memories in experiments on sheared non-Brownian suspensions.

A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been predicted for cyclically sheared non-Brownian suspensions. Here we present experiments on such suspensions, finding behavior consistent with multiple transient memories and showing how memories can be stabilized by noise.

Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticity.

Multiple transient memories, originally discovered in charge-density-wave conductors, are a remarkable and initially counterintuitive example of how a system can store information about its driving. In this class of memories, a system can learn multiple driving inputs, nearly all of which are eventually forgotten despite their continual input. If sufficient noise is present, the system regains plasticity so that it can continue to learn new memories indefinitely. Recently, Keim and Nagel [Phys. Rev. Lett. 107, 010603 (2011)] showed how multiple transient memories could be generalized to a generic driven disordered system with noise, giving as an example simulations of a simple model of a sheared non-Brownian suspension. Here, we further explore simulation models of suspensions under cyclic shear, focusing on three main themes: robustness, structure, and overdriving. We show that multiple transient memories are a robust feature independent of many details of the model. The steady-state spatial distribution of the particles is sensitive to the driving algorithm; nonetheless, the memory formation is independent of such a change in particle correlations. Finally, we demonstrate that overdriving provides another means for controlling memory formation and retention.

Geometry-Driven Folding of a Floating Annular Sheet

Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.

Wrapping with a splash: High-speed encapsulation with ultrathin sheets

Its a wrap Whether an object has a regular or irregular shape, wrapping it with a thin film can be challenging. Kumar et al. released droplets of oil above thin polymer sheets floating on water (see the Perspective by Amstad). With sufficient impact force, the polymer wrapped around the droplet with near perfect seams. The shape of the resulting enclosed drop depended on the shape of the sheet initially placed at the air-liquid interphase. Science, this issue p. 775; see also p. 743 Oil droplets are rapidly wrapped with a thin polymer sheet on impact. Many complex fluids rely on surfactants to contain, protect, or isolate liquid drops in an immiscible continuous phase. Thin elastic sheets can wrap liquid drops in a spontaneous process driven by capillary forces. For encapsulation by sheets to be practically viable, a rapid, continuous, and scalable process is essential. We exploit the fast dynamics of droplet impact to achieve wrapping of oil droplets by ultrathin polymer films in a water phase. Despite the violence of splashing events, the process robustly yields wrappings that are optimally shaped to maximize the enclosed fluid volume and have near-perfect seams. We achieve wrappings of targeted three-dimensional (3D) shapes by tailoring the 2D boundary of the films and show the generality of the technique by producing both oil-in-water and water-in-oil wrappings.

A Model for Approximately Stretched-Exponential Relaxation with Continuously Varying Stretching Exponents

Relaxation in glasses is often approximated by a stretched-exponential form:

Optimal wrapping of liquid droplets with ultrathin sheets

f(t) = A \exp [-(t/\tau )^{\beta }]