Pressure-driven flow of suspensions: simulation and theory

Nott, Prabhu R.; Brady, John F.

doi:10.1017/s0022112094002326

Cited by 660 publications

(642 citation statements)

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“…On the other hand, normal stresses are crucial since they determine the migration of particles in suspensions subjected to an inhomogeneous shear field (Nott & Brady 1994;Mills & Snabre 1995;Morris & Boulay 1999;Nott et al 2011;Lhuillier 2009). This paper therefore intends to address this issue by considering numerical simulations of suspensions accounting for friction and roughness.…”

Section: Introductionmentioning

confidence: 99%

Rheology of sheared suspensions of rough frictional particles

et al. 2014

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This paper presents three-dimensional numerical simulations of non-Brownian concentrated suspensions in a Couette flow at zero Reynolds number using a fictitious domain method. Contacts between particles are modelled using a discrete element method (DEM)-like approach, which allows for a more physical description, including roughness and friction. This work emphasizes the effect of friction between particles and its role on rheological properties, especially on normal stress differences. Friction is shown to notably increase viscosity and second normal stress difference $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}|N_2|$ and decrease $|N_1|$, in better agreement with experiments. The hydrodynamic and contact contributions to the overall particle stress are particularly investigated. This shows that the effect of friction is mostly due to the additional contact stress since the hydrodynamic stress remains unaffected by friction. Simulation results are also compared with experiments, such as normal stresses or effective friction coefficient $\mu (I_v)$, and the agreement is improved when friction is accounted for. This suggests that friction is operative in actual suspensions.

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Section: Introductionmentioning

confidence: 99%

Rheology of sheared suspensions of rough frictional particles

et al. 2014

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“…Of the proposed theories, the most frequently used and quoted in the literature are the diffusive flux model proposed by Leighton and Acrivos, 1 and the suspension balance model proposed by Nott and Brady. 2 Both models supplement the equations of motion for the suspension with equations that describe the motion of the particles. The diffusive flux model is purely kinematic, in the sense that the flux of the particles in the suspension is described in terms of the gradients of the particle concentration and the strain rate.…”

Section: Introductionmentioning

confidence: 99%

“…The suspension balance model attempts to relate the rheology of the suspension with the migration flux of the particles. Nott and Brady 2 showed that the diffusive flux model can be recovered from the suspension balance model, thereby showing that the two models share the same physical origin. This paper addresses the suspension balance model ͑hereafter referred to as the SBM͒, but insofar as the two models are connected, its conclusions do have a bearing on the diffusive flux model.…”

Section: Introductionmentioning

confidence: 99%

“…We largely follow the approach of Jackson, 6 but deviate in some ways to make contact with the studies of Batchelor 3 and Nott and Brady. 2 Neglecting inertial effects, we arrive at momentum balances for the solid and fluid phases, and for the entire suspension-the complete balances, with the effects of particle and fluid inertia included, are given in Appendix A. In the momentum balance for the solid phase, we find that a part of the volume-averaged stress ͗ ͘ s cancels with a part of the traction at the particle-fluid interfaceswhat remains is the particle-averaged net force on the particles ͗f͘ p .…”

Section: Introductionmentioning

confidence: 99%

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The suspension balance model revisited

Nott¹,

Guazzelli²,

Pouliquen³

2011

Physics of Fluids

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122

119

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This paper addresses a fundamental discrepancy between the suspension balance model and other two-phase flow formulations. The former was proposed to capture the shear-induced migration of particles in Stokesian suspensions, and hinges on the presence of a particle phase stress to drive particle migration. This stress is taken to be the "particle stress," defined as the particle contribution to the suspension stress. On the other hand, the two-phase flow equations derived in several studies show only a force acting on the particle phase, but no stress. We show that the identification of the particle phase stress with the particle contribution to the suspension stress in the suspension balance model is incorrect, but there exists a well-defined particle phase stress. Following the rigorous method of volume averaging, we show that the force on the particle phase may be written as the sum of an interphase drag and the divergence of the particle phase stress. We derive exact micromechanical relations for these quantities. We also comment on the interpretations and results of previous studies that are based on the identification of the particle phase stress with the particle contribution to the suspension stress.

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“…Shear-induced migration occurs in a wide variety of flows other than viscometric ones, including the well-studied case of pressure-driven flows. These shearinduced migrations are argued to result from normal stress imbalances according to macroscopic, multiphase models (Nott & Brady 1994). Indeed, concentrated suspensions of spheres have measurable normal stress differences, a notable non-Newtonian characteristic (Hinch 2011).…”

Section: Introductionmentioning

confidence: 99%

Suspension dynamics: moving beyond steady

Butler

2014

J. Fluid Mech.

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The dynamics of flowing, concentrated suspensions of non-colloidal particles continues to surprise, despite decades of work and the widespread importance of suspension transport properties to industrial processes and natural phenomena. Blanc, Lemaire & Peters (J. Fluid Mech., 2014, vol. 746, R4) report a striking example. They probed the time-dependent dynamics of concentrated suspensions of rigid and neutrally buoyant spheres by simultaneously measuring the oscillatory rheology and the sedimentation rate of a falling ball. The sedimentation velocity of the ball through the suspension depends strongly on the frequency of oscillation, though the rheology was found to be independent of frequency. The results demonstrate the complexities of suspension flows and highlight opportunities for improving models by exploring suspension dynamics and rheology over a wide range of conditions, beyond steady and unidirectional ones.

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Pressure-driven flow of suspensions: simulation and theory

Cited by 660 publications

References 17 publications

Rheology of sheared suspensions of rough frictional particles

Rheology of sheared suspensions of rough frictional particles

The suspension balance model revisited

Suspension dynamics: moving beyond steady

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