Brownian Dynamics simulation of hard-sphere colloidal dispersions

Foss, David R.; Brady, John F.

doi:10.1122/1.551104

Cited by 167 publications

(174 citation statements)

References 36 publications

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“…Furthermore, this limit has been surprisingly effective in reproducing experimental measurements of the shear viscosity of colloidal suspensions, for which all particles are equivalent ͑a = b͒. [30][31][32][33] Remarkably, the effective shear viscosity derived from the infinite limit does not differ appreciably from the results for as small as 1.1. ͑Khair and Brady find this also holds for the microviscosity when a = b.…”

Section: Model Systemmentioning

confidence: 65%

“…The expressions ͑10͒ and ͑14͒ for the viscosity increments clearly suggest a similarity, as does the force-thinning of the microviscosity; colloidal suspensions without hydrodynamic interactions also shear thin 31 and have a similar O͑1/ Pe͒ boundary layer at particle-particle contact at high Peclet number. 29 But exactly how good is the connection?…”

Section: Rheology a Comparison To Macrorheologymentioning

confidence: 97%

“…Although we have considered the simplest, ideal, case of a dilute suspension of hard spheres without hydrodynamic interactions, previous work on the macrorheology of colloidal dispersions 29,31,41 has shown that the results of such a model can be scaled up to accurately predict the behavior of concentrated dispersions both with and without hydrodynamic interactions. Here, we follow the same reasoning and offer suggestions as to how the present results may be extended to higher concentrations and to include hydrodynamic interactions.…”

Section: B Scale-up To Higher Concentrationsmentioning

confidence: 99%

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A simple paradigm for active and nonlinear microrheology

Squires¹,

Brady²

2005

Physics of Fluids

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240

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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: Model Systemmentioning

confidence: 65%

Section: Rheology a Comparison To Macrorheologymentioning

confidence: 97%

Section: B Scale-up To Higher Concentrationsmentioning

confidence: 99%

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A simple paradigm for active and nonlinear microrheology

Squires¹,

Brady²

2005

Physics of Fluids

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240

383

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“…In the Brownian dynamics simulations each swimmer is a sphere of radius a and the Langevin equation is integrated to track the dynamics. When a swimmer hits a boundary, it experiences a hard-particle force F P to prevent it from penetrating the boundary (following Foss & Brady (2000) a potential-free hard-particle force is implemented). By Newton's Third Law the boundary experiences an opposite force −F P , and then Π W is calculated from the definition of the pressure:…”

Section: Appendix a The Langevin Equation And Simulationmentioning

confidence: 99%

The force on a boundary in active matter

2015

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We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy k B T to the swimmer's activity k s T s = ζ U 2 0 τ R /6, where ζ is the Stokes drag coefficient, U 0 is the swim speed and τ R is the reorientation time of the active particles. The theory, which is valid on all length and time scales, has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behaviour when the boundary size is large compared to the swimmer's run length = U 0 τ R . The theory is used to predict the motion of bodies of all sizes immersed in active matter.

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“…Since the hard-core repulsion cannot be implemented in the interaction potential we employ a simple algorithm that detects collisions and computes the appropriate positions and velocities after the impact according to momentum and energy conservation (see Refs. [36,37] and references therein). The NESSs are prepared by initializing the particle positions on a regular lattice at low density.…”

Section: B Langevin Dynamics Simulationsmentioning

confidence: 99%

Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension

2012

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We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.

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Brownian Dynamics simulation of hard-sphere colloidal dispersions

Cited by 167 publications

References 36 publications

A simple paradigm for active and nonlinear microrheology

A simple paradigm for active and nonlinear microrheology

The force on a boundary in active matter

Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension

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