Jammed elastic shells – a 3D experimental soft frictionless granular system

Abstract

We present a new experimental system of monodisperse, soft, frictionless, fluorescent labeled elastic shells for the characterization of structure, universal scaling laws and force networks in 3D jammed matter. The elastic shells in a jammed packing are deformed in such a way that at each contact one of the shells buckles with a dimple and the other remain spherical, closely resembling overlapping spheres. Using confocal microscopy, we obtained 3D stacks of images of shells at different volume fractions which were subsequently processed in ImageJ software to find their coordinates. The determination of 3D coordinates involved three steps: locating the edges of shells in all 2D slices, analyzing their shape and subsequently finding their 2D coordinates, and finally determining their 3D centers by grouping the corresponding 2D coordinates. From this analysis routine we obtained particle coordinates with subpixel accuracy. In a contact pair we also identified the shell that underwent buckling forming a dimple by analyzing the intensity profile of a line that connects the centers of particle pairs. The amorphous structure of the packing was analyzed as a function of distance to the jamming threshold by investigating the radial distribution function, bond order parameters, contact numbers and the number of dimples per particle (buckling number), which is a unique property of this system. We find that the power law scaling of the contact number with excess volume fraction deviated from theoretical and computer simulation predictions. In addition, the buckling number also showed a similar scaling as that of the contact number with distance to the jamming transition.

Fluid flow through packings of elastic shells

“…N → ∞. From Equation 25, we can see that for finite system sizes, where C I L −1/ν δφ, the tortuosity is finite and reaches a maximum value at δφ = 0. This maximum tortuosity scales with the system size as τ max H (N |δφ = 0) ∼ N −(1−D)/d ≈ N 0.14 (D = 1.43, d = 3, and recall that N ∼ L d ; see Section VI E for details).…”

Random three-dimensional jammed packings of elastic shells acting as force sensors

“…Monodisperse, several micron-sized elastic shells of tetraethoxysilane crosslinked polydimethylsiloxane used were prepared by an emulsion templating technique. The template polydimethylsiloxane (PDMS) oil droplets were obtained by using a Turrax homogenizer for the efficient mixing of reactants followed by droplet growth without external agitation [29,30]. The system used for this study is same as that of Ref.…”

“…Because we feel it is important that there are more granular model systems available with different properties from those already studied to be able to check generality of the findings so far, we recently introduced a granular model system. This system is suitable to study forces in packings, and it comprises fluorescently labeled elastic shells that interact through shortranged repulsive forces [29]. These charged spherical particles (with a size around 5 μm, although we recently were successful in also creating monodisperse droplets with larger size even further into the granular regime [30]) contain a solid membrane with a liquid interior [30].…”

“…The membrane is a cross-linked network formed from a mixture of silicone and silica forming monomers and with a Young's modulus of 200 MPa [31]. A key feature of these particles is the membrane elasticity, which facilitates reversible deformations, as shown in our recent articles [29,32]. Therefore they can serve as a sensor of local force.…”

“…This we checked by releasing the stress acting on individual particles in a respective strongly compressed packing and reported in detail in Ref. [29]. It only took less than 2 min for a completely emptied or buckled shell to relax back to its uncompressed original spherical shape.…”