Stress Jumps of Charged Colloidal Suspensions, Measurement of the Elastic-like and Viscous-like Stress Components

Mackay, Michael E.; Kaffashi, Babak

doi:10.1006/jcis.1995.1372

Cited by 30 publications

(17 citation statements)

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“…5 As in macrorheology, these would allow experiments to differentiate between the hydrodynamic and Brownian contributions to the viscosity increment. In such experiments, a probe would be moved steadily ͑where it is subject to hydrodynamic and Brownian forces͒ and suddenly allowed to stop.…”

Section: Discussionmentioning

confidence: 99%

“…1 Nonlinear rheological measurements can also be performed by significantly straining the material, which enables additional information to be obtained, such as shear thinning and shear thickening, 2,3 normal stress differences, 4 and relaxation processes. [5][6][7][8][9] However, some materials of interest ͑particularly biomaterials͒ are difficult to procure in the large quantities required for traditional rheometers. To address such issues, techniques encompassing "microrheology" are being developed using small colloidal beads as tracers.…”

Section: Introductionmentioning

confidence: 99%

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A simple paradigm for active and nonlinear microrheology

Squires¹,

Brady²

2005

Physics of Fluids

238

383

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In microrheology, elastic and viscous moduli are obtained from measurements of the fluctuating thermal motion of embedded colloidal probes. In such experiments, the probe motion is passive and reflects the near-equilibrium ͑linear response͒ properties of the surrounding medium. By actively pulling the probe through the material, further information about material properties can be obtained, analogous to large-amplitude measurements in ͑macro-͒ rheology. We consider a simple model of such systems: a colloidal probe pulled through a suspension of neutrally buoyant bath colloids. We choose a system with hard-sphere interactions but neglect hydrodynamic interactions, which is simple enough to permit analytic solutions, but nontrivial enough to raise issues important for the interpretation of experiments in active and nonlinear microrheology. We calculate the microstructural deformation for arbitrary probe size and pulling rate ͑expressed as a dimensionless Péclet number Pe͒. From this, we determine the average retarding effect on the probe due to the microstructure, as well as fluctuations about this average. The high-Pe limit is singular, giving a finite Brownian contribution even in the limit of negligible diffusion. Significantly, different results are obtained for probes driven at constant velocity and constant force. Furthermore, we demonstrate that a probe pulled with an optical tweezer ͑roughly a harmonic well͒ can behave as fixed-force, fixed-velocity, or as a mixture of those modes, depending on the strength of the trap and on the pulling speed. More generally, we discuss how these results relate to previous work on the rheology of colloidal suspensions. Not surprisingly, the present theory ͑which ignores hydrodynamic interactions͒ gives shear thinning but no shear thickening; we expect that the incorporation of hydrodynamics would result in shear thickening as well. The effective micro-and macro-viscosities, when appropriately scaled, are in semi-quantitative agreement. This seems remarkable, given the rather significant difference in the two methods of measurement. However, for more complicated or unknown materials, where such scaling relations may not be known in advance, the comparison between micro-and macro may not be so favorable, which raises important questions about the relation between micro-and macrorheology. Finally, by analogy with previous work on macrorheology, we propose methods to scale up the present ͑dilute͒ theory to account for more concentrated suspensions, and suggest new active microrheological experiments to probe different aspects of suspension behavior.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A simple paradigm for active and nonlinear microrheology

Squires¹,

Brady²

2005

Physics of Fluids

238

383

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“…A thorough review of traditional rheology techniques may be found in the work of Barnes et al (1989). Transient flows also give insight into the micromechanics of rate-dependent processes in steady-state flow behavior: Sudden removal of external forcing demonstrates that the microstructure relaxes over multiple time scales, each associated with distinct physical processes [Mackay and Kaffashi (1995); Watanabe et al (1996aWatanabe et al ( , 1996b; Kaffashi et al (1997); Foss (1999); Zia and Brady (2013)]. Such temporal response reveals the underlying connection between structure and rheology.…”

Section: Introductionmentioning

confidence: 99%

Large amplitude oscillatory microrheology

Swan¹,

Zia²,

Brady³

2014

Journal of Rheology

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SynopsisWe study the motion of a colloidal particle as it is driven by an oscillating external force of arbitrary amplitude and frequency through a colloidal dispersion. Large amplitude oscillatory flows (LAOFs) are examined predominantly from a phenomenological perspective in which experimental measurements inform constitutive models. Here, we investigate a LAOF from a microstructural perspective by connecting motion of the probe particle to the material response while making no assumptions a priori about how stress relaxes in the material. The suspension exerts nonconservative, hydrodynamic forces on the probe, while distortions in the particle configuration exert conservative forces: Brownian and interparticle forces, for example. The relative importance of each of these contributions to particle motion evolves with the degree of displacement from equilibrium. When the force on the probe is weak, the linear microviscoelasticity of the suspension is probed [see, e.g., Khair and Brady, J. Rheol. 49, 1449-1481]. When oscillation rate is slow, the steady microrheology is probed [see, e.g., Squires and Brady, Phys. Fluids 17, 073101 (2005); Khair and Brady, J. Fluid Mech. 557, 73-117 (2006)]. This article develops a micromechanical model that recovers these limiting cases and then uses the same model to reveal the microrheology of colloidal dispersions deformed by a probe driven with arbitrary force amplitude and frequency. A chief result of this work is the discovery of a regime in which the resistance to motion of the probe particle is on average weaker than the resistance the probe experiences when deformed by high frequency oscillation. This hypoviscous effect arises when the reciprocating motion of the probe particle opens a a)

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“…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

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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...

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Stress Jumps of Charged Colloidal Suspensions, Measurement of the Elastic-like and Viscous-like Stress Components

Cited by 30 publications

References 0 publications

A simple paradigm for active and nonlinear microrheology

A simple paradigm for active and nonlinear microrheology

Large amplitude oscillatory microrheology

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

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