Many experiments show that protein condensates formed by liquid-liquid phase separation exhibit aging rheological properties. Quantitatively, recent experiments by Jawerth et al. (Science 370, 1317, 2020) show that protein condensates behave as aging Maxwell fluids with an increasing relaxation time as the condensates age. Despite the universality of this aging phenomenon, a theoretical understanding of this aging behavior is lacking. In this work, we propose a mesoscopic model of protein condensates in which a phase transition from aging phase to non-aging phase occurs as the control parameter changes, such as temperature. The model predicts that protein condensates behave as viscoelastic Maxwell fluids at all ages, with the macroscopic viscosity increasing over time. The model also predicts that protein condensates are non-Newtonian fluids under a constant shear rate with the shear stress increasing over time. Our model successfully explains multiple existing experimental observations and also makes general predictions that are experimentally testable.
We use state-of-the-art molecular dynamics simulations to study hydrodynamic effects on aging during kinetics of phase separation in a fluid mixture. The domain growth law shows a crossover from a diffusive regime to a viscous hydrodynamic regime. There is a corresponding crossover in the autocorrelation function from a power-law behavior to an exponential decay. While the former is consistent with theories for diffusive domain growth, the latter results as a consequence of faster advective transport in fluids for which an analytical justification has been provided.
Intricate fluid displacement patterns, arising from the unstable growth of interfacial perturbations, can be driven by fluid viscoelasticity and surface tension. A soft glassy suspension ages, $i.e.$ its mechanical moduli evolve with time, due to the spontaneous formation of suspension microstructures. The shear and time-dependent rheology of an aging suspension can be exploited to generate a wide variety of interfacial patterns during its displacement by a Newtonian fluid. Using video imaging, we report a rich array of interfacial pattern morphologies: dense viscous, dendritic, viscoelastic f…
We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power-law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that th…
The adsorption dynamics of a colloidal particle at a fluid interface is studied theoretically and numerically, documenting distinctly different relaxation regimes. The adsorption of a perfectly smooth particle is characterized by a fast exponential relaxation to thermodynamic equilibrium where the interfacial free energy has a minimum. The short relaxation time is given by the ratio of viscous damping to capillary forces. Physical and/or chemical heterogeneities in a colloidal system, however, can result in multiple minima of the free energy giving rise to metastability. In the presence of met…
We examine the structure of Maxwell stress in binary fluid mixtures under an external electric field and discuss its consequence. In particular, we show that, in immiscible blends, it is intimately related to the statistics of domain structure. This leads to a compact formula, which may be useful in the investigation of electro-rheological effects in such systems. The stress tensor calculated in a phase separated fluid under a steady electric field is in a good agreement with recent experiments.
We study a two-dimensional system of dipolar hard disks in the presence of a uniform external electric field $\boldsymbol{\mathcal{E}} $ by Monte Carlo simulations in a square with periodic boundary conditions. The study is performed in both the fluid at high temperature and the phase of living polymers at low temperature. In the considered geometry the macroscopic Maxwell field $ \mathbf{E}$ is computed and found to be equal to the external field $\boldsymbol{\mathcal{E}} $ in both phases. The dielectric properties of the system in the liquid phase as well as in the polymeric phase are invest…
The rheological properties of capillary suspensions, suspensions with small amounts of an added immiscible fluid, are dramatically altered with the addition of the secondary fluid. We investigate a capillary suspension to determine how the network ages and restructures at rest and under applied external shear deformation. The present work uses calcium carbonate suspended in silicone oil (11 % solids) with added water as a model system. Aging of capillary suspensions and their response to applied oscillatory shear is distinctly different from particulate gels dominated by the van der Waals forc…
When a soft glassy colloidal suspension is displaced by a Newtonian fluid in a radial Hele-Shaw geometry, the pattern morphology that develops at the interface is determined by the complex rheology of the former. We had reported in an earlier work [Palak, V. R. S. Parmar, D. Saha and R. Bandyopadhyay, JCIS Open, 6 (2022) 100047] that a range of interfacial patterns can be formed by controlling the elasticity of the displaced suspension, the flow rate of the displacing fluid and the interfacial tension of the fluid pair. Interestingly, all the different morphological features can be distinguish…
The phenomenon of aging in soft matter systems is an intriguing and interesting. In his study we investigate the microstructure and aging dynamics of fluorescent nanoclay gels formed from the mixture of small (~25) and large (~250) aspect ratio nanodiscs using various experimental techniques. We examine how the presence of one kind of clay in other clay of different nature affect the aging dynamics, microstructure and the final resulting phase. Viscosity of the dispersions grows as a power-law with waiting time of the system and the dispersions initially show Maxwellian behaviour but deviated …
In this paper we study deformation, failure and breakage of visco-elastic thin films of aging laponite suspension under tensile deformation field. Aqueous suspension of laponite is known to undergo waiting time dependent evolution of its micro-structure, also known as aging, which is accompanied by an increase in the elastic modulus and relaxation time. In the velocity controlled tensile deformation experiments, we observed that the dependence of force and dissipated energy on velocity and initial thickness of the film is intermediate to a Newtonian fluid and a yield stress fluid. For a fixed …
We employ the state-of-the-art molecular dynamics simulations to study the kinetics of phase separation and aging phenomena of segregating binary fluid mixtures imbibed in porous materials. Different random porous structures are considered to understand the effect of pore morphology on coarsening dynamics. We find the effect of complex geometrical confinement resulting in the dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with an exponent dependent on the porous host structure. After the transient period, a crossover to a slower domain growth is…
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…
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected that those physics in a viscoelastic fluid is much more interesting due to the presence of the additional frequency dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive aspects. In…
Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a non-equilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process like CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and deceler…
We introduce a nonlinear generalized tensorial Maxwell-type constitutive equation to describe shear-thinning glass-forming fluids, motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions. The model captures a nonvanishing dynamical yield stress at the glass transition and incorporates normal-stress differences. A modified lattice-Boltzmann (LB) simulation scheme is presented that includes non-Newtonian contributions to the stress tensor and deals with flow-induced pressure differences. We test this scheme in pressure-driven 2D Poiseuille flow of the nonlin…
A thermal colloid suspended in a liquid will transition from a short time ballistic motion to a long time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a …
The applicability of theories describing the kinetic evolution of fluid mixtures depends on the underlying physical assumptions. The Maxwell-Stefan equations, widely used for miscible fluids, express forces depending on coupled fluxes. They need to be inverted to recover a Fickian form which is generally impossible analytically. Moreover, the concentration dependence of the diffusivities has to be modelled, e.g. by the multicomponent Darken equation. Cahn-Hilliard type equations are preferred for immiscible mixtures, whereby different assumptions on the coupling of fluxes lead to the slow-mode…
We investigate the spontaneous evolution of various self-assembled phase states from a homogeneous aqueous dispersion of high-aspect ratio Montmorillonite (Na Cloisite) nanoclay platelets grounded on the observations made over a period of 3.5 years. We have established the tw-c phase diagram for this system for the first time in salt-free suspensions under normal pH conditions using rheology experiments and have detected that these suspensions do undergo nontrivial phase evolution and aging dynamics. Distinctive phase separation, equilibrium fluid and equilibrium gels in the tw-c phase space a…
We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are driven by power-law distributed mechanical noise from yield events throughout the material, in contrast to the well-studied Hébraud-Lequeux model where the noise is Gaussian. We first use a mapping to a mean first passage time problem to study the phase diagram in the absence of shear, which shows a transition between an arrested and a fluid state. We then …
