Networklike Propagation of Cell-Level Stress in Sheared Random Foams

Abstract

Quasistatic simple shearing flow of random monodisperse soap froth is investigated by analyzing Surface Evolver simulations of spatially periodic foams. Elastic-plastic behavior is caused by irreversible topological rearrangements (T1s) that occur when Plateau's laws are violated; the first T1s occur at the elastic limit and at large strains frequent cascades of T1s, composed of one or more individual T1s, sustain the yield-stress plateau. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell's contribution to the global stress. During each T1 cascade, the connected set of cells with decreasing Q, called the stress release domain, is network-like and highly non-local. Geometrically, the network-like nature of the stress release domains is corroborated through morphological analysis using the Euler characteristic. The stress release domain is distinctly different from the set of cells that change topology during a T1 cascade. Our results highlight the unique rheological behavior of foams, where complex large-scale cooperative rearrangements of foam cells are observed as a consequence of distinctly local events.

Normal stress measurement in foams and emulsions in the presence of slip

“…6a, the basic assumption regarding the relation between the shear stress flow curve and the slip velocity dependence on stress that is required for the Mooney method to be rigorously valid, namely that shear stress data show no obvious confinement effect, but we cannot be certain that confinement will be the same for the shear and normal stresses.) With that caveat in mind, the N 1 data for the foam show a power law exponent of 0.48 with shear rate, and we find that N 1 is of the order of -N 2 , which is consistent with the prior report for foams [25,26,49]. The power-law slope for N 1 for the mobile emulsion is 0.51, which is a bit larger than 0.38.…”

“…9 do show a power law relation with a slope of about 2 for the normal stress difference as a function of the shear stress; the best fit slope to the full set of data is 2.07, while the best quadratic fit to all the data points, which is shown on the plot, is . If N 2 ~ -N 1 for foams [49], then ( ) and we obtain an estimate of the modulus of the foam before yielding of about 435 Pa. Cohen-Addad and coworkers [54] give an equation for the modulus of a disordered polydisperse foam as …”

Foam rheology at large deformation

“…As suggested by these authors, an individual stress relaxation process would be a T 1 cascade, which produces different cell neighbors, reduces the surface energy of the foam, and provides mechanism for its plastic yield behavior [25]. More recently, Evans and co-workers [26] corroborated numerically that, in a 3d foam, the first T 1 event is responsible for the elastic limit whereas "frequent T 1 avalanches sustain the yield-stress plateau at large scale. "…”

Beyond the percolation universality class: the vertex split model for tetravalent lattices

“…(vi) In analogy to standard percolation, one may expect the critical behaviour to be independent of the type of underlying network; this expectation should be verified by an analysis of node severing of other fourcoordinated networks, such as the crystalline nbo network [9] or the network of plateau edges in random isotropic or sheared foams [19,20].…”