Index of content:
Volume 60, Issue 4, July 2016

Particle tracking microrheology of protein solutions
View Description Hide DescriptionVideobased particle tracking microrheology that requires ∼2 μl per sample is used to measure the viscosity of proteinsolutions of monoclonal antibodies. Direct imaging provides an immediate assessment of probe stability and the validity of the microrheology measurement. Precise measurements are made by choosing a displacement lag time that is a balance between minimizing tracking error while maximizing the number of sampled particle displacements. The excess kurtosis α2 of the probe displacement probability distribution and its test statistic are used to set the optimal lag time. The viscosity is calculated by fitting a Gaussian distribution to the sampled displacements. Microrheology viscosities for two monoclonal antibody solutions are in good agreement with bulk rheology. Using a similar comparison of the microrheology of sucrose solutions with a correlation relating viscosity and concentration, an analysis of covariance (p = 0.941) demonstrates the high accuracy of small volume microrheology measurements. Based on the relative error between measured and tabulated viscosities, the uncertainty of viscosities derived from particle tracking is less than 2% of the true value.

Universal aspects of hydrogel gelation kinetics, percolation and viscoelasticity from PAhydrogel rheology
View Description Hide DescriptionPolyacrylamide (PA) hydrogels have been studied extensively, but fundamental aspects of their gelation kinetics, percolation dynamics, and viscoelasticity are still not well understood. This paper focuses on the rheology of PA hydrogels having unusually low monomer concentrations (ca ≈ 3 w% equivalent to 0.42 mol l^{−1}). These furnish loss tangents that span 4 orders of magnitude when varying the crosslinker concentration. An optimum crosslinker concentration (cbis/ca ≈ 2.5 mol. % equivalent to 5.3 w%) is identified, below which the storage modulus increases almost linearly, and the loss modulus acquires a local maximum. Above the optimum crosslinker concentration, and both plateau, accompanied by a notable decrease in the maximum strain (increase in brittleness) before breaking. The dynamic shear moduli reveal universal dynamics at the gel point, as indicated by (i) scaling exponents (y = 3.1 ± 0.1, z = 2.1 ± 0.1 and Δ = 0.70 ± 0.02) that are consistent with the de Gennes [“On a relation between percolationtheory and the elasticity of gels,” J. Phys. Lett. 37, L1–L2 (1976)] electrical network analogy, and (ii) a critical relaxation exponent that is close to the Rouse limit Δ = 2/3 from the scaling theory of Martin. A close correspondence of the exponents with that of Adam and Delsanti [Macromolecules 18, 2285–2290 (1985)] for the radical copolymerization of a different material supports the longstanding hypothesis that dynamics at the gel point are universal for a prescribed gelation mechanism.

On the inseparability of slip and gaperror
View Description Hide DescriptionIn this paper, we demonstrate that it is principally not possible to separate a misalignment or gap error from an apparent slip length when employing a varying measuring gap analysis as the Kramer method or the Mooney analysis. Such error sources become important when utilizing parallel plates in rotational rheometry at low gap separation as for the determination of slip, for low sample volume availability, or for the study of confinement effects. While rheologists are generally aware that gap settings on the order of O(0.1 mm) and below can be affected by gap errors or nonparallelism, this is seldom discussed together with (or in comparison to) other error sources as slip, instabilities, compressibility, or normal stresses. However, other error sources such as slip lengths can easily be of the same order as the generally reported misalignment error of O(0.01 mm). We demonstrate with an experimental example that both error sources can be of similar order of magnitude, and can principally not be separated with a gap variation analysis. This should again raise awareness that, unless one of both effects can be ruled out or can be determined separately with an independent measurement technique, discussions of only slip velocities (or only gap error effects) should be taken with care if the results were obtained from a gap variation analysis.

Yielding in a strongly aggregated colloidal gel. Part I: 2D simulations
View Description Hide DescriptionWe investigate the microstructure details and the mechanical response under uniaxial compression of a strongly aggregating colloidal dispersion. The numerical simulations account for shortrange interparticle attraction, normal and tangential deformation at particle contacts, sliding and rolling resistance (RR), and preparation conditions. The compression rates are small so that hydrodynamic interactions are negligible. In the absence of RR, the average coordination number varies only slightly with compaction while the variation is significant in its presence. The particle contact distribution is isotropic throughout the consolidation process, irrespective of the magnitude of the parameters. In this limit of strong aggregation, the elastic modulus is a weak function of the magnitude of attraction. It is shown that the yield strain does not change significantly during the entire consolidation process, and the value in the presence of RR is marginally higher than in its absence. However, the yield stress increases with volume fraction which is a direct consequence of the increased elastic modulus. The yield stress, both in the presence and absence of RR, scales similarly with volume fraction. The overall power law exponent of 5.7 of the yield stress in the presence of RR as a function of volume fraction is in good agreement with previous simulation results.

Yielding in a strongly aggregated colloidal gel. Part II: Theory
View Description Hide DescriptionWe derive a constitutive relation to describe the deformation of a twodimensional strongly aggregated colloidal system by incorporating the interparticle colloidal forces and contact dynamics. The theory accounts for the plastic events that occur in the form of rolling/sliding during the deformation along with elastic deformation. The theory predicts a yield stress that is a function of volume fraction of the colloidal packing, the coordination number, the interparticle potential, coefficient of friction, and the normal and the tangential stiffness coefficients. The predicted yield strain was independent of the particle volume fraction although the compressive yield stress exhibited a powerlaw relation with the volume fraction. The powerlaw exponent, however, was lower than that obtained from simulations reported in a paper by Roy and Tirumkudulu [“Yielding in a strongly aggregated colloidal gel. Part I: 2D simulations,” J. Rheol. 60(4), 559–574 (2016)]. The cause for the discrepancy was identified to be the nonaffine deformation of the network. To account for such effects, a constitutive relation based on a simple fractal model was developed that predicts yield stress profile close to those obtained from simulations.

Sedimentation of a sphere in wormlike micellar fluids
View Description Hide DescriptionIn this paper, we report a detailed experimental investigation of sedimentation of a sphere through wormlike micellar fluids by a combination of rheometry, particle tracking velocimetry, and particle image velocimetry techniques. Beyond a critical threshold, a sphere never reaches a terminal velocity and instead exhibits oscillatory motion in the axial direction similar to previous reports [Jayaraman and Belmonte, Phys. Rev. E 67, 065301R (2003); Chen and Rothstein, J. NonNewtonian Fluid Mech. 116, 205–234 (2004)]. Although this phenomenon has been reported in the past, there is little understanding of how various parameters affect sphere motion and whether it follows any scaling laws. In this work, we systematically varied parameters such as sphere density, sphere size, temperature, and concentration of surfactant and salt for the cetyltrimethylammonium bromide/sodium salicylate system over a wide range of inertia and elasticity. It is shown that a Deborah number, defined here as characteristic shear rate (, where is the average terminal velocity and d is the sphere diameter) multiplied by the relaxation time (λ), is insufficient to quantitatively characterize the onset of oscillatory motion. However, a locally determined extensional Deborah number based on the maximum strain rate multiplied by the relaxation time () presents a suitable criterion to separate different modes of sphere motion (i.e., unsteady and steady) in a phase diagram. Our results indicate the importance of the extensional flow in the wake of spheres as the main mechanism for the sphere instability in wormlike micellar solutions.

Startup shear of concentrated colloidal hard spheres: Stresses, dynamics, and structure
View Description Hide DescriptionThe transient response of model hard sphere glasses is examined during the application of steady rate startup shear using Brownian dynamics simulations, experimental rheology and confocal microscopy. With increasing strain, the glass initially exhibits an almost linear elastic stress increase, a stress peak at the yield point and then reaches a constant steady state. The stress overshoot has a nonmonotonic dependence with Peclet number, Pe, and volume fraction, φ, determined by the available free volume and a competition between structural relaxation and shear advection. Examination of the structural properties under shear revealed an increasing anisotropic radial distribution function, g(r), mostly in the velocitygradient (xy) plane, which decreases after the stress peak with considerable anisotropy remaining in the steadystate. Low rates minimally distort the structure, while high rates show distortion with signatures of transient elongation. As a mechanism of storing energy, particles are trapped within a cage distorted more than Brownian relaxation allows, while at larger strains, stresses are relaxed as particles are forced out of the cage due to advection. Even in the steady state, intermediate super diffusion is observed at high rates and is a signature of the continuous breaking and reformation of cages under shear.

A hierarchical multimode molecular stress function model for linear polymer melts in extensional flows
View Description Hide DescriptionA novel hierarchical multimode molecular stress function (HMMSF) model for linear polymer melts is proposed, which implements the basic ideas of (i) hierarchical relaxation, (ii) dynamic dilution, and (iii) interchain tube pressure. The capability of this approach is demonstrated in modeling the extensional viscosity data of monodisperse, bidisperse, and polydisperse linear polymer melts. Predictions of the HMMSF model, which are solely based on the linearviscoelastic relaxation modulus and a single free model parameter, the segmental equilibration time, are compared to elongational viscosity data of monodisperse polystyrene melts and solutions as well as to the elongational viscosity data of a bidisperse blend of two monodisperse polystyrenes, and good agreement between model and experimental data is observed. By using a simplified relation between the Rouse stretchrelaxation times and the relaxation times of the melts, the modeling is extended to the uniaxial, equibiaxial, and planar extensional viscosity data of a highdensity polyethylene, the uniaxial and equibiaxial extensional viscosity data of a polydisperse polystyrene, the elongational viscosity data of three highdensity polyethylenes, and a linear lowdensity polyethylene. For polydisperse melts, the modeling is again based exclusively on the linearviscoelastic relaxation modulus with only one material parameter, the dilution modulus, which quantifies the onset of dynamic dilution.

Coalescence in PLAPBAT blends under shear flow: Effects of blend preparation and PLA molecular weight
View Description Hide DescriptionBlends containing 75 wt. % of an amorphous polylactide (PLA) with two different molecular weights and 25 wt. % of a poly[(butylene adipate)coterephthalate] (PBAT) were prepared using either a Brabender batch mixer or a twinscrew extruder. These compounds were selected because blending PLA with PBAT can overcome various drawbacks of PLA such as its brittleness and processability limitations. In this study, we investigated the effects of varying the molecular weight of the PLA matrix and of two different mixing processes on the blend morphology and, further, on droplet coalescence during shearing. The rheological properties of these blends were investigated and the interfacial properties were analyzed using the Palierne emulsion model. Droplet coalescence was investigated by applying shear flows of 0.05 and 0.20 s^{−1} at a fixed strain of 60. Subsequently, small amplitude oscillatory shear tests were conducted to investigate changes in the viscoelastic properties. The morphology of the blends was also examined using scanning electron microscope (SEM) micrographs. It was observed that the PBAT droplets were much smaller when twinscrew extrusion was used for the blend preparation. Shearing at 0.05 s^{−1} induced significant droplet coalescence in all blends, but coalescence and changes in the viscoelastic properties were much more pronounced for the PLAPBAT blend based on a lower molecular weight PLA. The viscoelastic responses were also somehow affected by the thermal degradation of the PLA matrix during the experiments.

iRheo: Measuring the materials' linear viscoelastic properties “in a step”!
View Description Hide DescriptionWe present a simple new analytical method for educing the materials' linear viscoelastic properties, over the widest range of experimentally accessible frequencies, from a simple stepstrain measurement, without the need of preconceived models nor the idealization of real measurements. This is achieved by evaluating the Fourier transforms of raw experimental data describing both the timedependent stress and strain functions. The novel method has been implemented into an open access executable “iRheo,” enabling its use to a broad scientific community. The effectiveness of the new rheological tool has been corroborated by direct comparison with conventional linear oscillatory measurements for a series of complex materials as diverse as a monodisperse linear polymer melt, a bimodal blend of linear polymer melts, an industrial styrenebutadiene rubber, an aqueous gelatin solution at the gel point and a highly concentrated suspension of colloidal particles. The broadband nature of the new method and its general validity open the route to a deeper understanding of the material's rheological behavior in a variety of systems.

Normal stress differences in nonBrownian fiber suspensions
View Description Hide DescriptionIn this paper, we present an experimental study of the normal stress differences that arise in nonBrownian rigid fiber suspensions subject to a shear flow. While early measurements of the normal stress in fiber suspensions in Newtonian fluids measured only N 1 − N 2, the recent work of Snook et al. [J. Fluid Mech. 758, 486–507 (2014)] and the present paper provide the first measurements of N 1 and N 2 separately. Snook et al. [J. Fluid Mech. 758, 486–507 (2014)] perform such measurements with a gap that is very wide compared with the fiber length, whereas the present paper explores the effects of confinement when the gap is 4–10 times the fiber length. The first and the second normal stress differences are measured using a single experiment which consists of determining the radial profile of the second normal stress, along the velocity gradient direction, Σ22, in a torsional flow between two parallel disks. Suspensions are made of monodisperse fibers immersed in a neutrally buoyant Newtonian fluid. Two fiber lengths and three aspect ratios ar = L/d, and a wide range of concentrations have been tested. N 1 is found to be positive while N 2 is negative and the magnitude of both normal stress differences increases when nL ^{2} d increases, n being the number fraction of fibers. The magnitude of N 2 is found to be much smaller than N 1 only for high aspect ratios and low fiber concentrations. Otherwise, N 1 and N 2 are of the same order of magnitude. This is in contradiction with what is often assumed (i.e., ) but consistent with the recent numerical work of Snook et al. [J. Fluid Mech. 758, 486–507 (2014)] that includes contact interactions. The effect of confinement on N 1 and N 2 is studied and it is shown that the more confined the suspension, the greater the magnitude of the normal stress differences. At last, the surface properties of the fibers are changed and the impact on the normal stress differences is discussed.

Nonequilibrium molecular dynamics study of ring polymer melts under shear and elongation flows: A comparison with their linear analogs
View Description Hide DescriptionWe present detailed results for the structural and rheological properties of unknotted and unconcatenated ring polyethylene (PE) melts under shear and elongation flows via direct atomistic nonequilibrium molecular dynamics simulations. Short (C78H156) and long (C400H800) ring PE melts were subjected to planar Couette flow (PCF) and planar elongational flow (PEF) across a wide range of strain rates from linear to highly nonlinear flow regimes. The results are analyzed in detail through a direct comparison with those of the corresponding linear polymers. We found that, in comparison to their linear analogs, ring melts possess rather compact chain structures at or near the equilibrium state and exhibit a considerably lesser degree of structural deformation with respect to the applied flow strength under both PCF and PEF. The large structural resistance of ring polymers against an external flow field is attributed to the intrinsic closedloop configuration of the ring and the topological constraint of nonconcatenation between ring chains in the melt. As a result, there appears to be a substantial discrepancy between ring and linear systems in terms of their structural and rheological properties such as chain orientation, the distribution of chain dimensions, viscosity, flow birefringence, hydrostatic pressure, the pair correlation function, and potential interaction energies. The findings and conclusions drawn in this work would be a useful guide in future exploration of the characteristic dynamical and relaxation mechanisms of ring polymers in bulk or confined systems under flowing conditions.

A rheological evaluation of steady shear magnetorheological flow behavior using threeparameter viscoplastic models
View Description Hide DescriptionKnowledge of the complicated flow characteristics of magnetorheological (MR) suspensions is necessary for simulations, calculations in engineering processes, or designing new devices utilizing these systems. In this study, we employed three constitutive equations (threeparameter models) for an evaluation of steady shear behavior of MR suspensions. The predictive/fitting capabilities of the Robertson–Stiff (R–S) model were compared with the commonly used Herschel–Bulkley (as a reference) and the Mizrahi–Berk models. The appropriateness of the models was examined using rheological data for diluted as well as concentrated MR systems. The effect of magnetic field strength on model fitting capabilities was also investigated. The suitability of the individual models was evaluated by observing correlation coefficient, sum of square errors, and root mean square errors. A statistical analysis demonstrated that the best fitting capabilities were exhibited by the R–S model, while others provided less accurate fits with the experimental data. Therefore, shear stresses and the yield stress predicted according to the R–S equation can be considered as the most accurate under defined conditions in comparison with the Herschel–Bulkley and the Mizrahi–Berk model predictions. We also showed that the consistency index obtained from the R–S model increased with increasing magnetic field and particle concentration, which physically reflected more rigid internal structures generated in MR suspensions upon an external magnetic field. This behavior was indistinguishable when other models were applied.

In situ measurement of the rheological properties and agglomeration on cementitious pastes
View Description Hide DescriptionVarious factors influence the rheology of cementitious pastes, with the most important being the mixing protocol, mixture proportions, and mixture composition. This study investigated the influence of groundgranulated blastfurnace slag, on the rheological behavior of cementitious pastes. In tandem with the rheological measurements, fresh state microstructural measurements were conducted using three different techniques: A coupled stroboscoperheometer, a coupled laser backscatteringrheometer, and a conventional laser diffraction technique. Laser diffraction and the coupled stroboscoperheometer were not good measures of the in situ state of flocculation of a sample. Rather, only the laser backscattering technique allowed for in situ measurement on a highly concentrated suspension (cementitious paste). Using the coupled laser backscatteringrheometer technique, a link between the particle system and rheological behavior was determined through a modeling approach that takes into account agglomeration properties. A higher degree of agglomeration was seen in the ordinary Portland cement paste than pastes containing the slag and this was related to the degree of capillary pressure in the paste systems.

Constitutive issues associated with LAOS experimental techniques
View Description Hide DescriptionLarge amplitude oscillatory shear (LAOS) is a rheological test method for the characterization of viscoelastic nonlinear materials. The correlation between the characteristic parameters obtained from measurements and theoretical models is a complex issue, one that requires the extraction of significant data from the measurements in order to identify corresponding models. Alternatively, a process of deductive logic may be useful in predicting typical behaviors of the materials through modeling which can then be verified by the analysis of measured data. The aim of this work is to highlight the potential of this logical deductive approach regarding LAOS testing. For this purpose, a LAOS is analytically simulated for an isotropic viscoelastic material of a differential type, with cubic nonlinearities and a correspondence of the Fourier coefficients. This is how nonlinearity parameters of the model are obtained. It can be seen that each nonlinearity parameter depends on Fourier coefficients through one of the new measures introduced by Ewoldt et al. [J. Rheol. 52, 1427–1458 (2008)] in 2008. Analysis of the function which represents shear stress suggests new interpretations of the experimental results and highlights how characteristics of the model can be compared with typical behaviors of the Lissajous–Bowditch plots.

Rheology of nonBrownian suspensions of rough frictional particles under shear reversal: A numerical study
View Description Hide DescriptionWe perform particle scale simulations of suspensions submitted to shear reversal. The simulations are based on the Force Coupling method, adapted to account for short range lubrication interactions together with direct contact forces between particles, including surface roughness, contact elasticity, and solid friction. After shear reversal, three consecutive steps are identified in the viscosity transient: An instantaneous variation, followed by a rapid contact force relaxation, and finally a long time evolution. The separated contributions of hydrodynamics and contact forces to the viscosity are investigated during the transient, allowing a qualitative understanding of each step. In addition, the influence of the contact law parameters (surface roughness height and friction coefficient) on the transient is evaluated. Concerning the long time transient, the difference between the steady viscosity and minimum viscosity is shown to be proportional to the contact contribution to the steady viscosity, allowing in principle easy determination of the latter in experiments. The short time evolution is studied as well. After the shear reversal, the contact forces vanish over a strain that is very short compared to the typical strain of the long time transient, allowing to define an apparent step between the viscosity before shear reversal and after contact force relaxation. This step is shown to be an increasing function of the friction coefficient between particles. Two regimes are identified as a function of the volume fraction. At low volume fraction, the step is small compared to the steady contact viscosity, in agreement with a particle pair model. As the volume fraction increases, the value of the viscosity step increases faster than the steady contact viscosity, and, depending on the friction coefficient, may approach it.

Active microrheology of colloidal suspensions: Simulation and microstructural theory
View Description Hide DescriptionDiscrete particle simulations by accelerated Stokesian dynamics (ASD) and a microstructural theory are applied to study the structure and viscosity of hardsphere Brownian suspensions in active microrheology (MR). The work considers moderate to dense suspensions, from near to far from equilibrium conditions. The microscopic theory explicitly considers manybody hydrodynamic interactions in active MR and is compared with the results of ASD simulations, which include detailed near and farfield hydrodynamic interactions. We consider probe and bath particles which are spherical and of the same radius a. Two conditions of moving the probe sphere are considered: These apply constant force (CF) and constant velocity (CV), which approximately model magnetic bead and optical tweezer experiments, respectively. The structure is quantified using the probability distribution of colloidal particles around the probe, , giving the probability of finding a bath particle centered at a vector position r relative to a moving probe particle instantaneously centered at the origin; n is the bath particles number density, and is related to the suspension solid volume fraction, , by . The pair distribution function for the bath particles relative to the probe, , is computed as a solution to the pair Smoluchowski equation (SE) for , and a range of Péclet numbers, describing the ratio of external force on the probe to thermal forces and defined as and for CF and CV conditions, respectively. Results of simulation and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large Péclet numbers, while a boundarylayer accumulation develops upstream and near the probe. The wake length saturates at for CF, while it continuously grows with PeU in CV. This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion; the dispersion is a direct result of manybody nonthermal interactions. This effect is incorporated in the theory as a forceinduced diffusion flux in pair SE. We also demonstrate that, despite this difference of structure in the two methods of moving the probe, the probability distribution of particles near the probe is primarily set by the Péclet number, for both CF and CV conditions, in agreement with dilute theories; as a consequence, similar values for apparent viscosity are found for the CF and CV conditions. Using the microscopic theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predicts larger distortions and Brownian viscosities in CV, by a factor of two relative to CF MR. This difference relative to dilute theory arises due to the determining role of manybody interactions associated with the underlying equilibrium structure in the semidilute to concentrated regime.