The process of phase separation in elastic solids and viscous fluids is of fundamental importance to the stability and function of soft materials. We explore the dynamics of phase separation and domain growth in a viscoelastic material such as a polymer gel. Using analytical theory and Monte Carlo simulations we report a new domain growth regime, in which the domain size increases algebraically with a ripening exponent $α$ that depends on the viscoelastic properties of the material. For a prototypical Maxwell material, we obtain $α=1$, which is markedly different from the well-known Ostwald ripening process with $α=1/3$. We generalize our theory to systems with arbitrary power-law relaxation behavior and discuss our findings in the context of the long-term stability of materials as well as recent experimental results on phase separation in cross-linked networks and cytoskeleton.
Liquid-liquid phase separation is an important mechanism for compartmentalizing the cell's cytoplasm, allowing the dynamic organization of the components necessary for survival. However, it is not clear how phase separation is affected by the complex viscoelastic environment inside the cell. Here, we study theoretically how stiffness gradients influence droplet growth and arrangement. We show that stiffness gradients imply concentration gradients in the dilute phase, which transport droplet material from stiff to soft regions. Consequently, droplets dissolve in the stiff region, creating a dis…
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…
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…
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…
Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization fo…
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 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 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…
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…
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…
Employing X-ray photon correlation spectroscopy we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The $g_2$-functions display a two-step decay with a gradually increasing non-ergodicity parameter typical for gelation. We observe fast superdiffusive ($γ\geq 3/2$) and slow subdiffusive ($γ< 0.6$) motion associ…
Histotripsy relies on cavitation to mechanically homogenize soft tissue. There is strong evidence that the high stresses, strains, and strain rates developed as bubbles grow and collapse contribute to this tissue homogenization. While such stresses and strains have been examined computationally in model systems with assumed constitutive models (e.g., finite-deformation Neo-Hookean model) and viscoelastic properties determined under quasi-static conditions, recent studies proposed that the Quadratic Law Kelvin-Voigt (QLKV) constitutive model, which additionally accounts for strain stiffening, m…
Relations between static and dynamic viscoelastic responses in gels can be very elucidating and may provide useful tools to study the behavior of bio-materials such as protein hydrogels. An important example comes from the viscoelasticity of semisolid gel-like materials, which is characterized by two regimes: a low-frequency regime where the storage modulus $G^{\prime}(ω)$ displays a constant value $G_{\text{eq}}$, and a high-frequency power-law stiffening regime, where $G^{\prime}(ω) \sim ω^{n}$. Recently, by considering Monte Carlo simulations to study the formation of peptides networks, we …
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…
The formation and destabilisation of viscoelastic filaments are of importance in many industrial and biological processes. Filament instabilities have been observed for viscoelastic fluids but recently also for soft elastic solids. In this work, we address the central question how to connect the dynamical behavior of viscoelastic liquids to that of soft elastic solids. We take advantage of a biopolymer material whose viscoelastic properties can be tuned over a very large range by its pH, and study the destabilization and ensuing instabilities in uniaxial extensional deformation. In agreement w…
Externally driven condensates show translation-induced polarization, directed coalescence, and anomalous diffusion in viscoelastic media
Institute for Medical Engineering and Science, Massachusetts Institute of Technology（麻省理工学院医学工程与科学研究所）；Department of Systems Immunology, Helmholtz Centre for Infection Research（亥姆霍兹感染研究中心系统免疫学部）；Institute for Biochemistry, Biotechnology and Bioinformatics, Technische Universität Braunschweig（布伦瑞克工业大学生物化学、生物技术及生物信息学研究所）；Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed)（下萨克森州医学人工智能与因果方法中心（CAIMed））
Processing of concentrated lignocellulosic biomass suspensions typically involves the conversion of the cellulose into sugars and sugars into ethanol. Biomass is usually pre-processed (i.e. via comminution, steam explosion, etc.) to form fine cellulosic fibers to be dispersed into an aqueous phase for further treatment. The resulting cellulose suspensions need to be pressurized and pumped into and out of various processing vessels without allowing the development of flow instabilities that are typically associated with the demixing, i.e., the segregation of the cellulosic biomass from the aque…
Hydrogels behave as viscoelastic soft solids and display a porous microstructure filled with water with typical amounts of 90\%~w/w or more. As such, these materials are highly sensitive to water loss through evaporation, which impacts their mechanical properties. Yet, aside from scattered empirical observations, little is known about the gel drying kinetics for which there is a lack of temporally and spatially resolved measurements. Here we report a benchmark study of the slow drying of agarose gels cast in cylindrical Petri dishes. The weak adhesion of the gel to the lateral wall of the dish…
We investigate by time-resolved Synchrotron ultra-small X-ray scattering the dynamics of liquid-liquid phase-separation (LLPS) of gluten protein suspensions following a temperature quench. Samples at a fixed concentration (237 mg/ml) but with different protein compositions are investigated. In our experimental conditions, we show that fluid viscoelastic samples depleted in polymeric glutenin phase-separate following a spinodal decomposition process. We quantitatively probe the late stage coarsening that results from a competition between thermodynamics that speeds up the coarsening rate as the…
Hydrogels are widespread soft materials, which can serve a wide range of applications. The control over the viscoelastic properties of the gel is of paramount importance. Ongoing environmental issues have raised the consumer's concern towards the use of more sustainable materials, including hydrogels. However, are greener materials compatible with high functionality? In a safe-by-design approach, this work demonstrates that functional hydrogels with in situ responsivity of their elastic properties by external stimuli can be developed from entirely ``sustainable'' components, a biobased amphiph…
