The Journal of Rheology^{®} formerly the Transactions of The Society of Rheology, is published six times per year by The Society of Rheology, a member society of the American Institute of Physics, through AIP Publishing LLC. It provides indepth interdisciplinary coverage of theoretical and experimental issues drawn from industry and academia. The Journal of Rheology is published for professionals and students in chemistry, physics, engineering, material science and mathematics.
Most Read This Month
Article
content/sor/journal/jor2
Journal
10
3
Latest Articles


View Description
Hide Description
We explore the effect of deliberately increased particle roughness on the rheology of noncolloidal suspensions of spheres, both in Newtonian (polydimethylsiloxane or silicone oil) and nonNewtonian (Boger fluid) matrices. The object of the experiment is to change only the roughness of the spheres, while leaving the density and the material of the particles unchanged, so as to isolate the effect of roughness on rheology. Two sphere materials, polystyrene (PS) and polymethylmethacrylate (PMMA) were used. The PS spheres were of 40 and 80 μm nominal diameters, and the PMMA spheres were 40 μm in diameter. Roughness ratios (average roughness/sphere radius) of 0.1%–5% were explored. With silicone matrices, there was up to 50% increase in viscosity with a 50% volume fraction suspension and an increase in the normal stress differences of a similar magnitude. Two polybutenebased Boger fluids were also used. The increases of viscosity with the polybutene matrices were somewhat larger than those with the Newtonian matrix; at 40% volume concentration, we saw approximately a 35% increase in viscosity with a roughness ratio of 5.3%. We compared the experimental results with computations for spheres in Newtonian matrices, and we found reasonable agreement with the computations of Mari et al. [J. Rheol. 58, 1693–1724 (2014)] if a friction coefficient of about 0.5 was assumed. We conclude that friction and roughness must be considered in computational work, or no agreement with experiment will be found. We suggest that the shearthinning seen with Newtonian matrices is due to a lessening of friction with shear rate. We also show that the unexpected success of the Maron–Pierce formula for Newtonian suspensions is due to the fact that it mimics well a frictional suspension with a friction coefficient of ∼0.5.


View Description
Hide Description
We investigate the phenomenon of delayed yield in reversible colloidal
gels via dynamic simulation, with a view toward revealing the microscopic particle dynamics and structural transformations that underlie the rheological behavior before, during, and after yield. Prior experimental studies reveal a pronounced delay period between application of a fixed shear stress and the onset of liquidlike flow, a socalled “delay time.” Catastrophic network failure—with sudden, cascading rupture of particle clusters or strands—is the primary model proposed for the structural evolution underlying rheological yield. However, no direct observation of such evolution has been made, owing to the difficulty of obtaining detailed microstructural information during the rapid yield event. Here, we utilize dynamic simulation to examine the microstructural mechanics and rheology of delayed yield. A moderately concentrated dispersion of Brownian hard spheres interacts via a shortrange attractive potential of O(kT) that leads to arrested phase separation and the formation of a bicontinuous network of reversibly bonded particles. The linearresponse rheology and coarsening dynamics of this system were characterized in our recent work. In the present study, a step shear stress is imposed on the gel, and its bulk deformation, as well as detailed positions and dynamics of all particles, are monitored over time. Immediately after the stress is imposed, the gel undergoes solidlike creep regardless of the strength of the applied stress. However, a minimum or “critical stress” is required to initiate yield: When the imposed stress is weak compared to the Brownian stress, the gel continues to undergo slow creeping deformation with no transition to liquidlike flow. Under stronger stress, creep is followed by a sudden increase in the strain rate, signaling yield, which then gives way to liquidlike viscous flow. The duration of the creep regime prior to yield is consistent with the delay time identified in prior experimental studies, decreasing monotonically with increasing applied stress. However, when the deformation rate is interrogated as a function of strain (rather than time), we find that a critical strain emerges: Yield occurs at the same extent of deformation regardless of the magnitude of the applied stress. Surprisingly, the gel network can remain fully connected throughout yield, with as few as 0.1% of particle bonds lost during yield, which relieve local glassy frustration and create localized liquidlike regions that enable yield. Brownian motion plays a central role in this behavior: When thermal motion is “frozen out,” both the delay time and the critical yield stress increase, showing that Brownian motion facilitates yield. Beyond yield, the longtime behavior depends qualitatively on the strength of the applied stress. In particular, at intermediate stresses, a “reentrant solid” regime emerges, whereupon a flowing gel resolidifies, owing to flowenhanced structural coarsening. A nonequilibrium phase diagram is presented that categorizes, and can be used to predict, the ultimate gel fate as a function of imposed stress. We make a connection between these behaviors and the process of ongoing phase separation in arrested colloidal
gels.


View Description
Hide Description
A single Brownian “probe” particle is driven by an external force through a colloidal
suspension and its motion studied to elucidate the relative impacts of external, Brownian, and interparticle forces on the suspension stress. As the probe moves through the suspension, distortions to and relaxation of the particle arrangement give rise to nonequilibrium stress. The shape of the distorted microstructure is set by the strength of the external force, F
0, relative to the entropic restoring force, kT/ath, of the suspension, and by the balance of microscopic forces between the constituent particles. The former is given by the Péclet number, , where kT is the thermal energy and ath is the thermodynamic size of the particles. The latter comprise external, Brownian, and interparticle forces, and the sensitivity of each to flow strength Pe is set by the dimensionless repulsion range, , where a is the hydrodynamic size of the particles. The total stress comprises hydrodynamic and entropic contributions which manifest as Brownian, interparticle, and external forceinduced stress. To analyze the influence of these forces on structure and suspension stress as they evolve with flow strength, we formulate and solve a Smoluchowski equation analytically in the dual limits of weak and strong external force and hydrodynamic
interactions, and numerically for arbitrary values of Pe and κ. Nonequilibrium statistical mechanics are then utilized to compute elements of the stress tensor. Owing to the axisymmetric geometry of the microstructure about the line of the external force, only the diagonal elements are nonzero. When hydrodynamic
interactions are negligibly weak, only the hardsphere interparticle force matters regardless of the flow strength, and the results of Zia and Brady [J. Rheol. 56(5), 1175–1208 (2012)] are recovered whereby normal stresses scale as Pe
^{2} and Pe in the limits of weak and strong forcing, respectively. That is, entropic forces dominate suspension stress regardless of the value of Pe when hydrodynamic
interactions are weak. As the repulsion range κ shrinks, hydrodynamic
interactions begin to play a role: When forcing is weak, Brownian disturbance flows provide the dominant contribution to suspension stress, but as Pe increases, the external forceinduced stress takes over to dominate the total stress. Interestingly, the total suspension stress decreases as the strength of hydrodynamic
interactions increases, regardless of the value of Pe. That is, hydrodynamic
interactions suppress suspension stress. Owing to the dependence of hydrodynamic
interactions on particle configuration, this stress suppression varies with flow strength: At low Pe, the stress scales as Pe
^{2} and the suppression is quantitative, whereas at high Pe, the stress scales as Pe^{δ}, where 1 ≥ δ ≥ 0.799 for hydrodynamic
interactions spanning from weak to strong. We identify the origin of such suppression via an analysis of pair trajectories: While entropic forces—interparticle repulsion and Brownian motion—destroy reversible trajectories, hydrodynamic
interactions suppress structural asymmetry and this underlies the suppression of the nonequilibrium stress. We relate the stress to the energy density: Hydrodynamic
interactions shield particles from direct collisions and promote foreaft and structural symmetry, resulting in reduced entropic energy storage.


View Description
Hide Description
Discrete 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.


View Description
Hide Description
We 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.


View Description
Hide Description
Large 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.