Elastic-Like and Viscous-Like Components of the Shear Viscosity for Nearly Hard Sphere, Brownian Suspensions

Kaffashi, Babak; O’Brien, Vincent T.; Mackay, Michael E.; Underwood, S. M.

doi:10.1006/jcis.1996.4611

Cited by 42 publications

(31 citation statements)

References 6 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Computer simulations (Bossis & Brady 1989;Phung et al 1996;Foss & Brady 2000b) and recent, detailed experimental measurements (Bender & Wagner 1995;Kaffashi et al 1997;O'Brien & Mackay 2000) are all in firm agreement on this point.…”

Section: Resultssupporting

confidence: 66%

“…The simulation results, together with the present two-particle results on systems that intrinsically lack any structural order, provide conclusive evidence for shear thickening being triggered by the interplay between hydrodynamic lubrication interactions and boundary-layer formation. Finally, experimental techniques that can resolve the hydrodynamic and Brownian contributions to the viscosity also conclude that shear thickening is driven by hydrodynamic interactions (Bender & Wagner 1996;Kaffashi et al 1997;O'Brien & Mackay 2000). Barnes (1989) proposes that shear thickening -albeit perhaps not to a degree measurable mechanically -will occur in all suspensions.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

The non-Newtonian rheology of dilute colloidal suspensions

2002

View full text Add to dashboard Cite

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to P e 2 , where P e is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large P e limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large P e in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as P e is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions. IntroductionThe rheology of colloidal suspensions, consisting of submicrometre size particles dispersed in a Newtonian fluid, is an active field of research. This activity stems from the wide variety of colloidal systems and the many settings in which fluid flow plays a key role. Our understanding of the rheological behaviour of colloidal suspensions has benefited from access to exact results on model systems, such as those on dilute suspensions of particles with well-defined interactions in weak flows. As these weakflow theories for concentrated systems are continually being improved (Brady 1996;Lionberger & Russel 2000), it is important to focus attention on the effect of stronger flows. By strong flows we mean flows in which the non-dimensional shear rate or Péclet number (P e) is large.Because of a number of developments, the effect on the bulk rheology of particle

show abstract

Section: Resultssupporting

confidence: 66%

Section: Discussionmentioning

confidence: 99%

The non-Newtonian rheology of dilute colloidal suspensions

2002

View full text Add to dashboard Cite

show abstract

“…This scaling is generated because of the slow relaxation of rigid clusters, mediated by hydrodynamic interactions between clusters. We obtain a similar power-law correlation with the Brownian stress, G B ðt; γÞ, which we measure during stress relaxation after a nonlinear step strain deformation (31,36) (Fig. S7).…”

Section: Resultsmentioning

confidence: 53%

Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels

Hsiao¹,

Newman²,

Glotzer

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

146

144

View full text Add to dashboard Cite

We report a simple correlation between microstructure and straindependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology.colloids | confocal microscopy | suspensions | shear flow C olloidal gels form sample-spanning networks (1) and are used to generate solid-like properties in a broad range of materials such as direct-write inks (2), nanoemulsions (3), tissue scaffolds (4), and membranes (5). When gels undergo large deformations, their network ruptures into clusters via a complex process. The ability to connect structural changes to suspension rheology is critical in understanding the mechanism of yielding. The network of clusters that makes up colloidal gels arises due to percolation, dynamic arrest, and phase separation, where the volume fraction and pair potential play an important part in their structure and rheology (6-8). Interparticle bonds rupture under a sufficiently large stress; the result is a flow-induced fluidization transition accompanied by the formation of voids and aggregates that continuously break and reform along the principal axes of flow (9, 10). A complex two-step yielding process has been observed in gels at intermediate volume fractions (0.05 ≤ ϕ ≤ 0.30) (11,12). Within this regime, a small number of bonds are broken in gels undergoing steady shear yielding (9, 10). Methods that track the evolution of ensemble-averaged structure, such as mode coupling theory (6) and light scattering, lack sensitivity to these subpopulations. On the other hand, micromechanical treatments directly model the contributions of local microstructure to the macroscopic elasticity of the material (13-15). However, experiments to connect the yield stress to different interparticle potentials, volume fractions, and particle sizes show little agreement. Presently, these theories can only provide estimates of colloidal rheology under specific conditions.We demonstrate that a simple, general correlation between microstructure and strain-dependent rheology exists for colloidal depletion gels undergoing large deformations at high shear rates. Our experiments harness confocal laser scanning mi...

show abstract

“…Nonequilibrium transient behavior has also been studied experimentally for sheared dispersions, where it has been shown that multiple mechanisms play a role in suspension stress and viscosity-e.g., hydrodynamic, interparticle, and Brownian forces-and give rise to distinct relaxation processes. For example Mackay and Kaffashi (1995) and Kaffashi et al (1997) studied the decay of stress immediately after the cessation of imposed strain-rate on a sheared suspension; they found that the hydrodynamic stress decays instantaneously, as it must-the hydrodynamic stress is proportional to the imposed strain-rate, and thus must vanish in the absence of flow. Watanabe et al (1996b) and Watanabe et al (1996a) analyzed stress development and relaxation in sudden startup and cessation of shearing flow and found both short-and long-time relaxation modes.…”

Section: Introductionmentioning

confidence: 99%

Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology

Zia¹,

Brady²

2013

Journal of Rheology

View full text Add to dashboard Cite

Performance of mesoscale modeling methods for predicting rheological properties of charged polystyrene/water suspensions J. Rheol. 56, 353 (2012) Three-dimensional flow of colloidal glasses J. Rheol. 56, 259 (2012) Emergence of turbid region in startup flow of CTAB/NaSal aqueous solutions between parallel plates J. Rheol. 56, 245 (2012) Nonlinear rheology and yielding in dense suspensions of hard anisotropic colloids J. Rheol. 55, 1069Rheol. 55, (2011 Additional information on J. Rheol. SynopsisThe motion of a single Brownian particle in a complex fluid can reveal material behavior both at and away from equilibrium. In active microrheology, a probe particle is driven by an external force through a complex medium and its motion studied in order to infer properties of the embedding material. Most work in microrheology has focused on steady behavior and established the relationship between the motion of the probe, the microstructure, and the effective microviscosity of the medium. Transient behavior in the near-equilibrium, linear-response regime has also been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation in a medium is captured by startup and cessation of the imposed deformation in the nonlinear regime, where the structure is driven far from equilibrium. Here, we study theoretically and by dynamic simulation the transient behavior of a colloidal dispersion undergoing nonlinear microrheological forcing. The strength with which the probe is forced, F ext , compared to thermal forces, kT/b, governs the dynamics and defines a P eclet number, Pe ¼ F ext =ðkT=bÞ, where kT is the thermal energy and b is the colloidal bath particle size. For large Pe, a boundary layer (in which unsteady advection balances diffusion) forms at particle contact on the time scale of the flow, a/U, where a is the probe size and U its speed, whereas the wake forms over O(Pe) diffusive time steps. Similarly, relaxation following cessation occurs over several time scales corresponding to distinct physical processes. For very short times, the time scale for relaxation is set by a boundary layer of thickness d $ ða þ bÞ=Pe, and so s $ d 2 =D r , where D r is the relative diffusivity between the probe of size a and a bath particle. Nearly all stress relaxation occurs during this time. At longer times, the Brownian diffusion of the bath particles acts to close the wake on a time scale set by how long it takes a bath particle to diffuse laterally across it, s $ ða þ bÞ 2 =D r . Although the majority of the microstructural relaxation occurs during this wakehealing process, it does so with little change in the stress. Also during relaxation, the probe travels backward in the suspension; this recovered strain is proportional to the free energy stored in the a) Author to who...

show abstract

Elastic-Like and Viscous-Like Components of the Shear Viscosity for Nearly Hard Sphere, Brownian Suspensions

Cited by 42 publications

References 6 publications

The non-Newtonian rheology of dilute colloidal suspensions

The non-Newtonian rheology of dilute colloidal suspensions

Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels

Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology

Contact Info

Product

Resources

About