In this paper I present a simple and self-consistent framework based on microrheology that allows one to obtain the mechanical response of viscoelastic fluids and gels from the motion of probe particles immersed on it. By considering a non-markovian Langevin equation, I obtain general expressions for the mean-squared displacement and the time-dependent diffusion coefficient that are directly related to the memory kernels and the response function, and which allow one to obtain estimates for the complex shear modulus and the complex viscosity of the material. The usefulness of such approach is demonstrated by applying it to describe experimental data on chemically cross-linked polyacrylamide through its sol-gel transition.
Using analytical calculations, we characterize the rotational behavior of a rigid spherical particle when subject to a net external torque in a continuous viscoelastic environment. On long time scales, the embedding medium can either feature a net terminal flow, like a fluid, or damped reversible dynamics, like an elastic solid. The coupling of the sphere to its environment together with the therein induced deformations and flows are taken into account explicitly. In reality, using magnetically anisotropic particles, the torque can, for instance, be applied via magnetic fields. We calculate co…
Polymer gels have been shown to behave as viscoelastic materials but only a small amount of data is usually provided in the glassy transition. In this paper, the dynamic moduli G' and G" of polyacrylamide hydrogels are investigated using both an AFM in contact force modulation mode and a classical rheometer. The validity is shown by perfect matching of the two techniques. Measurements are carried out on gels of increasing polymer concentration in a wide frequency range. A model based on fractional derivatives is proposed, covering the whole frequency range. G_0^N, the plateau modulus, as well …
We investigate the linear viscoelasticity of polymer gels produced by the dispersion of gluten proteins in water:ethanol binary mixtures with various ethanol contents, from pure water to 60% v/v ethanol. We show that the complex viscoelasticity of the gels exhibits a time/solvent composition superposition principle, demonstrating the self-similarity of the gels produced in different binary solvents. All gels can be regarded as near critical gels with characteristic rheological parameters, elastic plateau and characteristic relaxation time, which are related one to another, as a consequence of …
We present a simulation study of colloidal particles having very short range attractions. In particular, we investigate the interplay between the effective attractive range and the viscoelastic properties of the gels that form when the temperature of the system is sufficiently low. Using Brownian dynamics simulations we study particles with different size and interaction range, and characterize the mechanical properties of the gels by performing small amplitude oscillatory and transient starts-up shear simulations. We found that the effective attractive range is a key parameter affecting the g…
Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon ($i$) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and ($ii$) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical resp…
Readily synthesizable nano-graphene and poly ethylene glycol based stable gels have been synthesized employing an easy refluxing method and exhaustive rheological and viscoelastic characterizations have been performed to understand the nature of such complex gel systems. The gels exhibit shear thinning response with pronounced yield stress values which is indicative of a microstructure where the graphene nanoflakes intercalate with the polymer chains and form a pseudo spring damper network. Experimentations on the thixotropic behavior of the gels indicate that the presence of the G nanoflakes …
Through a combination of rheological characterization and temperature-variable imaging methods, a novel gelation pathway in dilute solutions of a semiconducting polymer to achieve interconnected, crystalline networks with hierarchical porosity is reported. Upon rapid cooling, solutions of regioregular poly(3-hexylthiophene) (RR-P3HT) in ortho-dichlorobenzene formed thermoreversible gels. Temperature-variable confocal microscopy revealed cooling-induced structural rearrangement to progress through viscoelastic phase separation. The phase separation process arrested prematurely during the format…
We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus $G^{*}(ω)$ over a very wide range of frequencies (1 Hz- 100 kHz). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels - the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5 micrometer. Despite this characteristic dif…
The recent experiments of Crocker et al. suggest that microrheological measurements obtained from the correlated fluctuations of widely-separatedprobe particles determine the rheological properties of soft, complex materials more accurately than do the more traditional particle autocorrelations. This presents an interesting problem in viscoelastic dynamics. We develop an important, simplifing analogy between the present viscoelastic problem and classical electrostatics. Using this analogy and direct calculation we analyze both the one and two particle correlations in a viscoelastic medium in o…
Bulk rheological properties of viscoelastic fluids have been extensively studied in macroscopic shearing geometries. However, little is known when an active microscopic probe is used to locally perturb them far from the linear-response regime. Using a colloidal particle dragged periodically by scanning optical tweezers through a viscoelastic fluid, we investigate both, its linear and nonlinear microrheological response. With increasing particle velocity, we observe a transition from constant viscosity to a thinning regime, where the drag force on the probe becomes a nonlinear function of the p…
We study colloidal gels formed by competing electrostatic repulsion and short-range attraction by means of extensive numerical simulations under external shear. We show that, upon varying the repulsion strength, the gel structure and its viscoelastic properties can be largely tuned. In particular, the gel fractal dimension can be either increased or decreased with respect to mechanical equilibrium conditions. Unexpectedly, gels with stronger repulsion, despite being mechanically stiffer, are found to be less viscous with respect to purely attractive ones. We provide a microscopic explanation o…
We use molecular dynamics simulations of a model three-dimensional particulate gel, to investigate the linear viscoelastic response. The numerical simulations are combined with a novel test protocol (the optimally- windowed chirp or OWCh), in which a continuous exponentially-varying frequency sweep windowed by a tapered cosine function is applied. The mechanical response of the gel is then analyzed in the Fourier domain. We show that i) OWCh leads to an accurate computation of the full frequency spectrum at a rate significantly faster than with the traditional discrete frequency sweeps, and wi…
We report contactless measurements of the viscoelastic rheological properties of soft gels. The experiments are performed using a colloidal-probe Atomic Force Microscope (AFM) in a liquid environment and in dynamic mode. The mechanical response is measured as a function of the liquid gap thickness for different oscillation frequencies. Our measurements reveal an elastohydrodynamic (EHD) coupling between the flow induced by the probe oscillation and the viscoelastic deformation of the gels. The data are quantitatively described by a viscoelastic lubrication model. The frequency-dependent storag…
The effects of the addition of sub-micrometer sized colloidal silica spheres on the linear and nonlinear rheology of semi-dilute solutions of a viscoelastic gel are studied. For a 1.4 wt.% solution of the surfactant CTAT, a peak in the zero shear rate viscosity $η_{\circ}$ is observed at approximately equal weight percents of silica and CTAT. This peak shifts to lower silica concentrations on increasing either the CTAT concentration or the surface charge on silica and disappears when the CTAT concentration is increased to 2.6wt%. The increases in $η_{\circ}$ and the high frequency plateau modu…
We investigated the viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples ranged from fluids to gels. Already in the liquid phase the viscoelastic properties significantly changed when approaching the gelation boundary, indicating the formation of clusters and transient networks. This is supported by an increasing correlation length of the density fluctuations, observed by static light scattering and microscopy. A…
Mucus is a biological gel covering the surface of several tissues and insuring key biological functions, including as a protective barrier against dehydration, pathogens penetration, or gastric acids. Mucus biological functioning requires a finely tuned balance between solid-like and fluid-like mechanical response, insured by reversible bonds between mucins, the glycoproteins that form the gel. In living organisms, mucus is subject to various kinds of mechanical stresses, e.g. due to osmosis, bacterial penetration, coughing and gastric peristalsis. However, our knowledge of the effects of stre…
We propose an analytical model for the force-indentation relationship in viscoelastic materials exhibiting a power law relaxation described by an exponent n, where n = 1 represents the standard viscoelastic solid (SLS) model, and n < 1 represents a fractional SLS model. To validate the model, we perform nanoindentation measurements of poylacrylamide gels with atomic force microscopy (AFM) force curves. We found exponents n < 1 that depends on the bysacrylamide concentration. We also demonstrate that the fitting of AFM force curves for varying load speeds can reproduce the dynamic viscoelastic …
We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel generates a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.
Soft particulate gels include materials we can eat, squeeze, or 3D print. From foods to bio-inks to cement hydrates, these gels are composed of a small amount of particulate matter (proteins, polymers, colloidal particles, or agglomerates of various origins) embedded in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction $ϕ$: however, the diverse range of different functio…
Spinodal demixing of systems into two phases having very different viscosities leads to viscoelastic networks, i.e. gels. Here we consider demixing in a colloidal system where one phase is a nematic liquid crystal with a strongly anisotropic viscosity. We combine real space analysis of a sepiolite clay system with molecular dynamics computer simulation. We find a long-lived network with many of the characteristics of a colloidal gel. Remarkably the anisotropic viscosity means that flow is possible within the nematic network, but only along the network, which thus preserves its structure, leadi…
Long-chained surfactant solutions have found widespread use in the oil and gas industry due to a host of attractive properties. In this paper, we characterize one such commercially used viscoelastic surfactant that forms a wormlike micellar gel at room temperature and a viscoelastic solution at higher temperatures. We probe both states by conducting linear and nonlinear rheological tests and analyze their behaviour under the framework of micellar rheology. Our study outlines departure from behaviour exhibited by more conventional micellar systems and uncovers interesting dynamics like shear-in…
The mechanical response of active media ranging from biological gels to living tissues is governed by a subtle interplay between viscosity and elasticity. In this Letter, we generalize the canonical Kelvin-Voigt and Maxwell models to active viscoelastic media that break both parity and time-reversal symmetries. The resulting continuum theories exhibit viscous and elastic tensors that are both antisymmetric, or odd, under exchange of pairs of indices. We analyze how these parity violating viscoelastic coefficients determine the relaxation mechanisms and wave-propagation properties of odd materi…
Understanding surface mechanics of soft solids, such as soft polymeric gels, is crucial in many engineering processes, such as dynamic wetting and adhesive failure. In these situations, a combination of capillary and elastic forces drives the motion, which is balanced by dissipative mechanisms to determine the rate. While shear rheology (i.e. viscoelasticity) has long been assumed to dominate the dissipation, recent works have suggested that compressibility effects (i.e. poroelasticity) could play roles in swollen networks. We use fast interferometric imaging to quantify the relaxation of surf…
We present a continuum model of the coupling between cells and substrate that accounts for some of the observed substrate-stiffness dependence of cell properties. The cell is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoelastic fluids. The coupling to the substrate enters as a boundary condition that relates the cell's deformation field to local stress gradients. In the presence of activity, the coupling to the substrate yields spatially inhomogeneous contractile stresses and deformations in the cell and can enhance polarization, breaking the …
Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we introduce a numerical methodology to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shea…
We study the nonlinear rheology of a novel class of transient networks, made of surfactant micelles of tunable morphology reversibly linked by block copolymers. We couple rheology and time-resolved structural measurements, using synchrotron radiation, to characterize the highly nonlinear viscoelastic regime. We propose the fluctuations of the degree of alignment of the micelles under shear as a probe to identify a fracture process. We show a clear signature of a brittle-to-ductile transition in transient gels, as the morphology of the micelles varies, and provide a parallel between the fractur…
Complex fluids, such as polymer solutions and blends, colloids and gels, are of growing interest in fundamental and applied soft-condensed-matter science. A common feature of all such systems is the presence of a mesoscopic structural length scale intermediate between atomic and macroscopic scales. This mesoscopic structure of complex fluids is often fragile and sensitive to external perturbations. Complex fluids are frequently viscoelastic (showing a combination of viscous and elastic behaviour) with their dynamic response depending on the time and length scales. Recently, non-invasive method…
We demonstrate a simple method for rotational microrheology in complex fluids, using micrometric wires. The three-dimensional rotational Brownian motion of the wires suspended in Maxwell fluids is measured from their projection on the focal plane of a microscope. We analyze the mean-squared angular displacement of the wires of length between 1 and 40 microns. The viscoelastic properties of the suspending fluids are extracted from this analysis and found to be in good agreement with macrorheology data. Viscosities of simple and complex fluids between 0.01 and 30 Pa.s could be measured. As for t…
