2D foams above the jamming transition: Deformation matters

Rigidity transition of a highly compressible granular medium

A wide range of disordered materials, from biological to geological assemblies, feature discrete elements undergoing large shape changes. How significant geometrical variations at the microscopic scale affect the response of the assembly, in particular rigidity transitions, is an ongoing challenge in soft matter physics. However, the lack of a model granular-like experimental system featuring large and versatile particle deformability impedes advances. Here, we explore the oscillatory shear response of a sponge-like granular assembly composed of highly compressible elastic rings. We highlight a progressive rigidity transition, switching from a yielded phase to a solid one by increasing density or decreasing shear amplitude. The rearranging yielded state consists of crystal clusters separated by melted regions; in contrast, the solid state remains amorphous and absorbs all imposed shear elastically. We rationalize this transition by uncovering an effective, attractive shear force between rings that emerges from a friction-geometry interplay. If friction is sufficiently high, the extent of the contacts between rings, captured analytically by elementary geometry, controls the rigidity transition.

Colony-like Protocell Superstructures

We report the formation, growth, and dynamics of model protocell superstructures on solid surfaces, resembling single cell colonies. These structures, consisting of several layers of lipidic compartments enveloped in a dome-shaped outer lipid bilayer, emerged as a result of spontaneous shape transformation of lipid agglomerates deposited on thin film aluminum surfaces. Collective protocell structures were observed to be mechanically more stable compared to isolated spherical compartments. We show that the model colonies encapsulate DNA and accommodate nonenzymatic, strand displacement DNA reactions. The membrane envelope is able to disassemble and expose individual daughter protocells, which can migrate and attach via nanotethers to distant surface locations, while maintaining their encapsulated contents. Some colonies feature "exocompartments", which spontaneously extend out of the enveloping bilayer, internalize DNA, and merge again with the superstructure. A continuum elastohydrodynamic theory that we developed suggests that a plausible driving force behind subcompartment formation is attractive van der Waals (vdW) interactions between the membrane and surface. The balance between membrane bending and vdW interactions yields a critical length scale of 236 nm, above which the membrane invaginations can form subcompartments. The findings support our hypotheses that in extension of the "lipid world hypothesis", protocells may have existed in the form of colonies, potentially benefiting from the increased mechanical stability provided by a superstructure.

Soft-grain compression: Beyond the jamming point

We present the experimental studies of highly strained soft bidisperse granular systems made of hyperelastic and plastic particles. We explore the behavior of granular matter deep in the jammed state from local field measurement from the grain scale to the global scale. By means of a dedicated digital image correlation code and an accurate image recording method, we measure for each compression step the evolution of the particle geometries and their right Cauchy-Green strain tensor fields. We analyze the evolution of the usual macroscopic observables (stress, packing fraction, coordination, fraction of nonrattlers, etc.) along the compression process through the jamming point and far beyond. Analyzing the evolution of the local strain statistics, we evidence a crossover in the material behavior deep in the jammed state for both sorts of particles. We show that this crossover is due to a competition between material compression, dilation, and shear, so its position depends on the particle material. We argue that the strain field is a reliable observable to describe the evolution of a granular system through the jamming transition and deep in the dense packing state whatever the material behavior.

The role of deformability in determining the structural and mechanical properties of bubbles and emulsions

We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and deformable particle (DP) model that we developed for bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We compare the structural and mechanical properties of jammed packings generated using the SP and DP models as a function of the packing fraction ρ, instead of the reduced number density φ. We show that near jamming onset the excess contact number Δz = z - zJ and shear modulus G scale as Δρ0.5 in the large system limit for both models, where Δρ = ρ - ρJ and zJ ≈ 4 and ρJ ≈ 0.842 are the values at jamming onset. Δz and G for the SP and DP models begin to differ for ρ ⪆ 0.88. In this regime, Δz ∼ G can be described by a sum of two power-laws in Δρ, i.e. Δz ∼ G ∼ C0Δρ0.5 + C1Δρ1.0 to lowest order. We show that the ratio C1/C0 is much larger for the DP model compared to that for the SP model. We also characterize the void space in jammed packings as a function of ρ. We find that the DP model can describe the formation of Plateau borders as ρ → 1. We further show that the results for z and the shape factor A versus ρ for the DP model agree with recent experimental studies of foams and emulsions.

Viscous forces and bulk viscoelasticity near jamming

When weakly jammed packings of soft, viscous, non-Brownian spheres are probed mechanically, they respond with a complex admixture of elastic and viscous effects. While many of these effects are understood for specific, approximate models of the particles' interactions, there are a number of proposed force laws in the literature, especially for viscous interactions. We numerically measure the complex shear modulus G* of jammed packings for various viscous force laws that damp relative velocities between pairs of contacting particles or between a particle and the continuous fluid phase. We find a surprising sensitive dependence of G* on the viscous force law: the system may or may not display dynamic critical scaling, and the exponents describing how G* scales with frequency can change. We show that this sensitivity is closely linked to manner in which viscous damping couples to floppy-like, non-affine motion, which is prominent near jamming.

Bubble-bubble interactions in a 2d foam, close to the wet limit

Following the general approach of Morse and Witten for the deformation of a bubble in contact with neighbouring bubbles, we develop a model for contacting bubbles in two dimensions which can be solved analytically. The force-displacement relations are derived by elementary methods; unlike the case of 3d, no logarithmic factors arise in two dimensions. We also discuss the case of a uniform compression of a symmetric foam structure; the (osmotic) compressibility depends on the number of contacts, as was shown in earlier work by Lacasse et al. Our model, which is based on first principles, without any free parameters, may be extended to simulate 2d foams.