From Yielding to Shear Jamming in a Cohesive Frictional Suspension

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, with an intermediate region of stress in which the material is flowable.

Shear thickening in concentrated suspensions of smooth spheres in Newtonian suspending fluids

Shear thickening is a phenomenon in which the viscosity of a suspension increases with increasing stress or shear rate, sometimes in a discontinuous fashion. While the phenomenon, when observed in suspensions of corn starch in water, or Oobleck, is popular as a science experiment for children, shear thickening is actually of considerable importance for technological applications and exhibited by far simpler systems. Concentrated suspensions of smooth hard spheres will exhibit shear thickening, and understanding this behavior has required a fundamental change in the paradigm of describing low-Reynolds-number solid-fluid flows, in which contact forces have traditionally been absent. Here, we provide an overview of our understanding of shear thickening and the methods that have been developed to describe it, as well as outstanding questions.

Nonmonotonic flow curves of shear thickening suspensions

The discontinuous shear thickening (DST) of dense suspensions is a remarkable phenomenon in which the viscosity can increase by several orders of magnitude at a critical shear rate. It has the appearance of a first-order phase transition between two hypothetical "states" that we have recently identified as Stokes flows with lubricated or frictional contacts, respectively. Here we extend the analogy further by means of stress-controlled simulations and show the existence of a nonmonotonic steady-state flow curve analogous to a nonmonotonic equation of state. While we associate DST with an S-shaped flow curve, at volume fractions above the shear jamming transition the frictional state loses flowability and the flow curve reduces to an arch, permitting the system to flow only at small stresses. Whereas a thermodynamic transition leads to phase separation in the coexistence region, we observe a uniform shear flow all along the thickening transition. A stability analysis suggests that uniform shear may be mechanically stable for the small Reynolds numbers and system sizes in a rheometer.

Discontinuous shear thickening of frictional hard-sphere suspensions

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.

Surface-induced morphology and free-energy pathways in breakup of a nematic liquid crystalline cylinder

We compute the surface-induced morphology and the free-energy pathways as a cylindrical liquid crystalline filament with preferred homeotropic (orthogonal) interface orientation passes through a sequence of growing sinusoidal perturbations and breaks up into droplets. Liquid crystalline morphology is determined using a simulated annealing algorithm [R. K. Goyal and M. M. Denn, Phys. Rev. E, 75, 021704 (2007)] to minimize the Oseen-Frank free energy. A first-order morphological transition with a finite energy barrier is required when the perturbation amplitude exceeds a critical value, and it is possible that progress towards breakup will be kinetically trapped in a varicose cylindrical shape. This result may be related to the apparent kinetic trapping of dispersed nematic 4'-octyl-4-biphenylcarbonitrile in a gel state reported by Inn and Denn [J. Rheol., 49, 887 (2005)].

Orientational multiplicity and transitions in liquid crystalline droplets

Orientation distributions in droplets of liquid crystals with homeotropic anchoring are computed with a simulated annealing algorithm that minimizes the free energy of the Oseen-Frank continuum theory. The droplets exhibit multiple orientational steady states that are separated by finite energy barriers over the entire range of the dimensionless ratio of surface to elastic forces, with maximum transition energy densities of the order of 2000 J/m3 (Pa) for a typical liquid crystalline droplet with a spherical radius of 1 microm. The transition energy densities decrease with elongation to spheroidal droplets with aspect ratios of four or more, indicating that droplet elongation is favored to drive surface-induced transitions.

Dielectric spectroscopy of liquid crystalline dispersions

We describe dielectric spectroscopy measurements on dispersions of two thermotropic liquid crystals (5CB and 8CB) in a poly(dimethylsiloxane) matrix. 5CB exhibits nematic and isotropic phases, while 8CB exhibits smectic, nematic, and isotropic phases. The spectra of the dispersions exhibit a temperature-dependent dielectric relaxation in the interval from 100 to 1000 Hz, with relaxation times that depend strongly on whether the dispersed phase is isotropic, nematic, or smectic. The dielectric relaxation times also depend on the viscosity of the matrix fluid. These results suggest a coupling between the electric field and the mechanics of the interface that affects the spectrum of the dispersed phase and shifts the Maxwell-Wagner interfacial polarization peak.

Influence of bulk nematic orientation on the interface between a liquid crystalline polymer and a flexible polymer

The structure of the interface between a liquid crystalline polymer (LCP) and a flexible polymer was studied using the three-dimensional bond fluctuation model in Monte Carlo simulations. Orientation in both phases in the neighborhood of the interface is sensitive to the far-field nematic orientation. The more diffuse interface caused by a homeotropic far-field orientation in the LCP results in a substantial reduction in the calculated interfacial tension relative to that for a planar far-field orientation.

Molecular motion and orientation distributions in melt-processed, fully aromatic liquid crystalline polyesters from 1H NMR

Fully-aromatic thermotropic liquid crystalline polymers (LCP) containing 4-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid (HNA) were studied with 1H NMR. A two- or three-parameter nematic director distribution in molten or nearly molten samples was obtained via rigorous simulation of wideline spectral lineshapes. This methodology was further employed to yield the chain director distribution in macroscopic sections derived from a frozen contraction flow. In addition, the dynamic conformation of polymer chains through the melting transition was monitored via lineshape analysis of samples having (bulk) isotropic director distributions. Extension of rigorous 1H NMR spectral deconvolution to recently developed solid-state NMR imaging sequences is discussed.

Comparison of medical-grade ultrahigh molecular weight polyethylene microstructure by atomic force microscopy and transmission electron microscopy

Atomic force microscopy is used to image the topography of surfaces of bulk medical-grade ultrahigh molecular weight polyethylene (UHMWPE). Comparison with transmission electron microscopy images demonstrates that the AFM can resolve the plate-like stacks of crystalline lamellae characteristic of UHMWPE without aggressive surface treatment. Surface preparation for the AFM must be carried out by cryomicrotomy at extremely low temperatures to prevent smearing of surface features. Chemically-etched surfaces of UHMWPE require substantially less surface preparation for AFM imaging.