Discontinuous shear thickening in Brownian suspensions

Discontinuous Shear Thickening in Biological Tissue Rheology

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕ_alumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τ_min). Increasing ϕ_alumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τ_min. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕ_PVP = 0.005-0.050) to suspensions with constant ϕ_alumina = 0.550. DST was observed in all cases and increasing ϕ_PVP increased the viscosity and yield stress. Interestingly, increasing ϕ_PVP also increased τ_min. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τ_min.

Fluid lubricated polishing based on shear thickening

With the development of short wavelength optics, high requirements are put forward for the full frequency errors of optical elements, while the processing efficiency and surface quality of traditional polishing methods are difficult to meet their requirements. In this paper, a fluid lubricated polishing method is proposed by combining non-Newtonian fluid with traditional polishing methods. According to Preston equation and shear thickening principle, the tool influence function of fluid lubricated polishing is established and verified by experiments. The results show that the fluid lubricated polishing has a very good convergence ability to the full frequency error of the workpiece. In addition, the convergence rate of fluid lubricated polishing on roughness is about twice that of chemical mechanical polishing. Finally, fluid lubricated polishing extends Preston from Newtonian fluid polishing to non-Newtonian fluid polishing.

Origin of nonlinear force distributions in a composite system

Composite materials have been actively developed in recent years because they are highly functional such as lightweight, high yield strength, and superior load response. In spite of importance of the composite materials, mechanisms of the mechanical responses of composites have been unrevealed. Here, in order to understand the mechanical responses of composites, we investigated the origin and nature of the force distribution in heterogeneous materials using a soft particle model. We arranged particles with different softness in a lamellar structure and then we applied homogeneous pressure to the top surface of the system. It is found that the density in each region differently changes and then the density difference induces a nonlinear force distribution. In addition, it is found that the attractive interaction suppresses the density difference and then the force distribution is close to the theoretical prediction. Those findings may lead material designs for functional composite materials.

Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear

In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divided by the strain amplitude and diameter of grains, at least for small values of the areas.

Rheology of two-dimensional crushable granular materials

The rheology of two-dimensional crushable granular materials under shear is numerically studied using the discrete element method. We find that the mean fragment size changes as the shear strain increases while the shear stress is almost independent of this mean size. The fragment size distribution is found to follow a power law. In particular, the exponent in the intermediate fragment size regime becomes approximately – 11/6, which is almost independent of the shear rate.

Dilatancy of frictional granular materials under oscillatory shear with constant pressure

We perform numerical simulations of a two-dimensional frictional granular system under oscillatory shear confined by constant pressure. We found that the system undergoes dilatancy as the strain increases. We confirmed that compaction also takes place at an intermediate strain amplitude for a small mutual friction coefficient between particles. We also found that compaction depends on the confinement pressure while dilatancy little depends on the pressure.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Frictional active Brownian particles

Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles and their motility-induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional systems become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility-induced phase diagram by tuning the roughness of the particles.

Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear

Herein we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.

Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear

We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus G^{'} and the loss modulus G^{''} in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying G^{'}>0) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed G^{'} after the reduction of the strain amplitude depends on the phase of the external shear strain. The loss modulus G^{''} exhibits a discontinuous jump corresponding to discontinuous shear thickening in the fragile state.

Discrete fluidization of dense monodisperse emulsions in neutral wetting microchannels

The rheology of pressure-driven flows of two-dimensional dense monodisperse emulsions in neutral wetting microchannels is investigated by means of mesoscopic lattice Boltzmann simulations, capable of handling large collections of droplets, in the order of several hundreds. The simulations reveal that the fluidization of the emulsion proceeds through a sequence of discrete steps, characterized by yielding events whereby layers of droplets start rolling over each other, thus leading to sudden drops of the relative effective viscosity. It is shown that such discrete fluidization is robust against loss of confinement, namely it persists also in the regime of small ratios of the droplet diameter over the microchannel width. We also develop a simple phenomenological model which predicts a linear relation between the relative effective viscosity of the emulsion and the product of the confinement parameter (global size of the device over droplet radius) and the viscosity ratio between the disperse and continuous phases. The model shows excellent agreement with the numerical simulations. The present work offers new insights to enable the design of microfluidic scaffolds for tissue engineering applications and paves the way to detailed rheological studies of soft-glassy materials in complex geometries.