We analyze transient dynamics during shear start-up in viscoelastic flows between two parallel plates, with a specific focus on the signatures for the onset of transient shear banding using the Johnson-Segalman, non-stretching Rolie-Poly and Giesekus
models. We explore the dynamics of shear start-up in monotonic regions of the constitutive curves using two different methodologies: (i) the oft-used `frozen-time linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed on instantaneous stress components (treated as quasi steady states) exhibit exponential growth, and (ii) the more mathematically rigorous fundamental-matrix approach that characterizes the transient growth via a numerical solution of the time-dependent linearized governing equations, wherein the linearized perturbations co-evolve with the start-up shear flow. Our results reinforce the hitherto understated point that there is no universal connection between the overshoot and subsequent decay of shear stress in the base state and the unstable eigenvalues obtained from the frozen-time stability analysis. It may therefore be difficult to subsume the occurrence of transient shear banding during shear start-up within the ambit of a single model-independent criterion. Our work also suggests that the strong transients during shear start-up seen in earlier work could well be a consequence of consideration of the limit of small solvent viscosity in the absence of otherwise negligible terms such as fluid inertia.
The evolution of viscoelastic properties near the sol-gel transition is studied by performing oscillatory rheological measurements on two different types of systems: a colloidal dispersion and a thermo-responsive polymer solution under isothermal and
non-isothermal conditions. While undergoing sol-gel transition, both the systems pass through a critical point. An approach to the critical point is characterized in terms of divergence of zero shear viscosity and the subsequent appearance of the low frequency modulus. In the vicinity of the critical gel state, both the viscosity and the modulus show a power-law dependence on relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both the sides of the critical point and also shows a power-law dependence on relative distance from the critical point. The critical (power-law) exponents of the zero-shear viscosity and modulus are observed to be related to the exponents of the longest relaxation time by the hyper scaling laws. The dynamic critical exponent has also been calculated from the growth of the dynamic moduli. Remarkably, the critical relaxation exponent and dynamic critical exponent predicted from the scaling laws precisely agree with the experimental values from the isothermal as well as non-isothermal experiments. The associated critical exponents show remarkable internal consistency and universality for different kinds of systems undergoing the sol-gel transition.
Yielding transition in isotropic soft materials under superposition of orthogonal deformation fields is known to follow von Mises criterion. However, in anisotropic soft materials von Mises criterion fails owing to preferred directions associated wit
h the system. In this work we study a model anisotropic yield stress system: electrorheological (ER) fluids that show structure formation in the direction of electric field. We subject the ER fluids to superposition of orthogonal stress fields that leads to different yield stress values. We obtain a yielding state diagram by plotting normalized rotational shear stress against normalized radial shear stress corresponding to yield point for a given electric field. Remarkably, the state diagram validates the Hill yielding criterion, which is a general yielding criterion for materials having anisotropy along three orthogonal directions, originally developed for metallic systems. Validation of Hill criterion suggests the universality of its application to anisotropic systems including conventional anisotropic soft materials having yield stress.
In this work, we investigate signatures of physical aging in an aqueous dispersion of Carbopol that shows yield stress and weak enhancement in elastic modulus as a function of time. We observe that the creep curves, as well as strain recovery, show a
significant dependence on waiting time elapsed since shear melting. The corrected strain, which is the strain in excess of the recovered strain, has been observed to show time waiting time superposition in the effective time domain, wherein time is normalized by time-dependent relaxation time that shows a power-law dependence. The corresponding power law exponent, which is close to unity in a limit of small stresses, decreases with stress and tends to zero as stress approaches the yield stress. For a range of stresses, the material shows time stress superposition suggesting the shape of the evolving relaxation time spectrum to be independent of the time as well as the stress. This work, therefore, suggests the presence of physical aging in an aqueous dispersion of Carbopol even though the elastic modulus shows only a weak enhancement. We also discuss Andrade type of creep behavior in aqueous Carbopol dispersion.
In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the
relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.
Aqueous dispersion of Laponite, when exposed to carbon dioxide environment leads to in situ inducement of magnesium and lithium ions, which is, however absent when dispersion is exposed to air. Consequently, in the rheological experiments, Laponite d
ispersion preserved under carbon dioxide shows more spectacular enhancement in the elastic and viscous moduli as a function of time compared to that exposed to air. By measuring concentration of all the ions present in a dispersion as well as change in pH, the evolving inter-particle interactions among the Laponite particles is estimated. DLVO analysis of a limiting case is performed, wherein two particles approach each other in a parallel fashion a situation with maximum repulsive interactions. Interestingly it is observed that DLVO analysis explains the qualitative details of an evolution of elastic and viscous moduli remarkably well thereby successfully relating the macroscopic phenomena to the microscopic interactions.
Synthetic hectorite clay Laponite RD/XLG is composed of disk-shaped nanoparticles that acquire dissimilar charges when suspended in an aqueous media. Owing to their property to spontaneously self-assemble, Laponite is used as a rheology modifier in a
variety of commercial water-based products. Particularly, aqueous dispersion of Laponite undergoes liquid - to - solid transition at about 1 volume % concentration. The evolution of the physical properties as dispersion transforms to solid state is reminiscent of physical aging in molecular as well as colloidal glasses. The corresponding soft glassy dynamics of an aqueous Laponite dispersion, including the rheological behavior, has been extensively studied in the literature. In this feature article we take an overview of recent advances in understanding soft glassy dynamics and various efforts taken to understand the peculiar rheological behaviors. Furthermore, the continuously developing microstructure that is responsible for eventual formation of soft solid state that supports its own weight against gravity has also been a topic of intense debate and discussion. Particularly extensive experimental and theoretical studies lead to two types of microstructures for this system: an attractive gel-like or repulsive glass like. We carefully examine and critically analyze the literature and propose a state diagram that suggests aqueous Laponite dispersion to be present in an attractive gel state.
Microscopic relaxation timescales are estimated from the autocorrelation functions obtained by dynamic light scattering experiments for Laponite suspensions with different concentrations ($C_{L}$), added salt concentrations ($C_{S}$) and temperatures
($T$). It has been shown in an earlier work [Soft Matter, 10, 3292-3300 (2014)] that the evolutions of relaxation timescales of colloidal glasses can be compared with molecular glass formers by mapping the waiting time ($t_{w}$) of the former with the inverse of thermodynamic temperature ($1/T$) of the latter. In this work, the fragility parameter $D$, which signifies the deviation from Arrhenius behavior, is obtained from fits to the time evolutions of the structural relaxation timescales. For the Laponite suspensions studied in this work, $D$ is seen to be independent of $C_{L}$ and $C_{S}$, but is weakly dependent on $T$. Interestingly, the behavior of $D$ corroborates the behavior of fragility in molecular glass formers with respect to equivalent variables. Furthermore, the stretching exponent $beta$, which quantifies the width $w$ of the spectrum of structural relaxation timescales is seen to depend on $t_{w}$. A hypothetical Kauzmann time $t_{k}$, analogous to the Kauzmann temperature for molecular glasses, is defined as the timescale at which $w$ diverges. Corresponding to the Vogel temperature defined for molecular glasses, a hypothetical Vogel time $t^{infty}_{alpha}$ is also defined as the time at which the structural relaxation time diverges. Interestingly, a correlation is observed between $t_{k}$ and $t^{infty}_{alpha}$, which is remarkably similar to that known for fragile molecular glass formers. A coupling model that accounts for the $t_{w}$-dependence of the stretching exponent is used to analyse and explain the observed correlation between $t_{k}$ and $t^{infty}_{alpha}$.
A model is proposed that considers aging and rejuvenation in a soft glassy material as respectively a decrease and an increase in free energy. The aging term is weighted by inverse of characteristic relaxation time suggesting greater mobility of the
constituents induce faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions, leads to power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases namely, a constant modulus when aging is entropy controlled and a time dependent modulus. In the former and the latter cases the model has respectively two and three experimentally measurable parameters that are physically meaningful. Overall the model predicts how material undergoes aging and approaches rejuvenated state under application of deformation field. Particularly model proposes distinction between various kinds of rheological effects for different combinations of parameters. Interestingly, when relaxation time evolves stronger than linear, the model predicts various features observed in soft glassy materials such as thixotropic and constant yield stress, thixotropic shear banding, and presence of residual stress and strain.
The primary and secondary relaxation timescales of aging colloidal suspensions of Laponite are estimated from intensity autocorrelation functions obtained in dynamic light scattering (DLS) experiments. The dynamical slowing down of these relaxation p
rocesses are compared with observations in fragile supercooled liquids by establishing a one-to-one mapping between the waiting time since filtration of a Laponite suspension and the inverse of the temperature of a supercooled liquid that is rapidly quenched towards its glass transition temperature. New timescales, such as the Vogel time and the Kauzmann time, are extracted to describe the phenomenon of dynamical arrest in Laponite suspensions. In results that are strongly reminiscent of those extracted from supercooled liquids approaching their glass transitions, it is demonstrated that the Vogel time calculated for each Laponite concentration is approximately equal to the Kauzmann time, and that a strong coupling exists between the primary and secondary relaxation processes of aging Laponite suspensions. Furthermore, the experimental data presented here clearly demonstrates the self-similar nature of the aging dynamics of Laponite suspensions within a range of sample concentrations.
