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Register a new userSize-dependent rheology of type-I collagen networks
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We investigate the system size dependent rheological response of branched type I collagen gels. When subjected to a shear strain, the highly interconnected mesh dynamically reorients, resulting in overall stiffening of the network. When a continuous shear strain is applied to a collagen network, we observe that the local apparent modulus, in the strain-stiffening regime, is strongly dependent on the gel thickness. In addition, we demonstrate that the overall network failure is determined by the ratio of the gel thickness to the mesh size. These findings have broad implications for cell-matrix interactions, the interpretation of rheological tissue data, and the engineering of biomimetic scaffolds.
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We study the micromechanics of collagen-I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Three-dimensional images of fluorescently labeled collagen are obtained by confocal microscopy and the network geometry is extracted using a 3d network skeletonization algorithm. Each fiber is modeled as a worm-like-chain that resists stretching and bending, and each cross-link is modeled as torsional spring. The stress-strain curves of networks at three different densities are compared to rheology measurements. The model shows good agreement with experiment, confirming that strain stiffening of collagen can be explained entirely by geometric realignment of the network, as opposed to entropic stiffening of individual fibers. The model also suggests that at small strains, cross-link deformation is the main contributer to network stiffness whereas at large strains, fiber stretching dominates. Since this modeling effort uses networks with realistic geometries, this analysis can ultimately serve as a tool for understanding how the mechanics of fibers and cross-links at the microscopic level produce the macroscopic properties of the network. While the focus of this paper is on the mechanics of collagen, we demonstrate a framework that can be applied to many biopolymer networks.
We present contactless atomic-force microscopy measurements of the hydrodynamic interactions between a rigid sphere and an air bubble in water at the micro-scale. The size of the bubble is found to have a significant effect on the response due to the long-range capillary deformation of the air-water interface. To rationalize the experimental data, we develop a viscocapillary lubrication model accounting for the finite-size effect. The comparison between experiments and theory allows us to measure the air-water surface tension, without contact, paving the way towards robust contactless tensiometry of polluted air-water interfaces.
We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.
This article deals with the Hadamard instability of the so-called $mu(I)$ model of dense rapidly-sheared granular flow, as reported recently by Barker et al. (2015,this journal, ${bf 779}$, 794-818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wave-vector stretching by the base flow. We provide a closed form solution for the linear stability problem and show that wave-vector stretching leads to asymptotic stabilization of the non-convective instability found by Barker et al. We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analog of the van der Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyper-stress, as the analog of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced continuum model, we also present a model of steady shear bands and their non-linear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barker et al. and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the $mu(I)$ rheology and variants thereof.
Observations of flowing granular matter have suggested that same-material tribocharging de- pends on particle size, rendering large grains positive and small ones negative. Models assuming the transfer of trapped electrons can explain this, but so far have not been validated. Tracking individual grains in an electric field, we show quantitatively that charge is transferred based on size between materially identical grains. However, the surface density of trapped electrons, measured independently by thermoluminescence techniques, is orders of magnitude too small to account for the scale of charge transferred. This suggests that another negatively charged species, such as ions, is responsible.
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