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Using our open-source programming environment Morpho, an energy-optimization method is developed to compute equilibrium shapes of an arbitrarily confined swollen hydrogel. The internal strains and contact forces are measured, probing its mechanics.

 

We examine the regime between crystalline and amorphous packings of anisotropic objects on surfaces of different genus by continuously varying their size distribution or shape from monodispersed spheres to bidispersed mixtures or monodispersed ellipsoidal particles; we also consider an anisotropic variant of the Thomson problem with a mixture of charges. With increasing anisotropy, we first observe the disruption of translational order with an intermediate orientationally ordered hexatic phase as proposed by Nelson, Rubinstein and Spaepen, and then a transition to amorphous state. By analyzing the structure of the disclination motifs induced, we show that the hexatic-amorphous transition is caused by the growth and connection of disclination grain boundaries, suggesting this transition lies in the percolation universality class in the scenarios considered. 

Arrested, or partial, coalescence of viscoelastic emulsion droplets can occur when elastic resistance to deformation offsets droplet surface area minimization. Arrest is a critical element of food and consumer product microstructure and performance, but direct studies of structural arrest and rearrangement have been carried out using only two or three droplets at a time. The question remains whether the behavior of small numbers of droplets also occurs in larger, more realistic many-droplet systems. Here we study two-dimensional aggregation and arrested coalescence of emulsions containing ∼1000 droplets and find that the restructuring mechanisms observed for smaller systems have a large effect on local packing in multidroplet aggregates, but surprisingly do not significantly alter overall mass scaling in the aggregates. Specifically, increased regions of hexagonal packing are observed as the droplet solids level, and thus elasticity, is decreased because greater degrees of capillary force-driven restructuring are possible. Diffusion-limited droplet aggregation simulations that account for the restructuring mechanisms agree with the experimental results and suggest a basis for prediction of larger-scale network properties and bulk emulsion behavior. 

Arrested coalescence occurs in Pickering emulsions where colloidal particles adsorbed on the surface of the droplets become crowded and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution of curvature and, depending on the initial coverage, may incorporate a region with negative Gaussian curvature around the neck that bridges the two droplets. Here, we resolve the relative influence of the curvature and the kinetic process of arrest on the microstructure of the final state. In the quasistatic case, defects are induced and distributed to screen the Gaussian curvature. Conversely, if the rate of area change per particle exceeds the diffusion constant of the particles, the evolving surface induces local solidification reminiscent of jamming fronts observed in other colloidal systems. In this regime, the final structure is shown to be strongly affected by the compressive history just prior to arrest, which can be predicted from the extrinsic geometry of the sequence of surfaces in contrast to the intrinsic geometry that governs the static regime.