Fully Coupled Simulations of Non-Colloidal Monodisperse Sheared Suspensions

Chemical Engineering Research and Design (Impact Factor: 2.28). 06/2007; 8(6):778-791. DOI: 10.1205/cherd06114
Source: OAI


In this work we investigate numerically the dynamics of sheared suspensions in the limit of vanishingly small fluid and particle inertia. The numerical model we used is able to handle the multi-body hydrodynamic interactions between thousands of particles embedded in a linear shear flow. The presence of the particles is modeled by momentum source terms spread out on a spherical envelop forcing the Stokes equations of the creeping flow. Therefore all the velocity perturbations induced by the moving particles are simultaneously accounted for. The statistical properties of the sheared suspensions are related to the velocity fluctuation of the particles. We formed averages for the resulting velocity fluctuation and rotation rate tensors. We found that the latter are highly anisotropic and that all the velocity fluctuation terms grow linearly with particle volume fraction. Only one off-diagonal term is found to be non zero (clearly related to trajectory symmetry breaking induced by the non-hydrodynamic repulsion force). We also found a strong correlation of positive/negative velocities in the shear plane, on a time scale controlled by the shear rate (direct interaction of two particles). The time scale required to restore uncorrelated velocity fluctuations decreases continuously as the concentration increases. We calculated the shear induced self-diffusion coefficients using two different methods and the resulting diffusion tensor appears to be anisotropic too. The microstructure of the suspension is found to be drastically modified by particle interactions. First the probability density function of velocity fluctuations showed a transition from exponential to Gaussian behavior as particle concentration varies. Second the probability of finding close pairs while the particles move under shear flow is strongly enhanced by hydrodynamic interactions when the concentration increases.

Download full-text


Available from: Olivier Simonin
  • Source
    • "The numerical studies on the shear-induced microstructure started with the work of Bossis and Brady (1984) who used the Stokesian Dynamics method to study the particle arrangement in a monolayer. Later, 3D simulations were performed either using Stokesian Dynamics [Drazer et al. (2004); Sierou and Brady (2002)] or Force Coupling Method [Abbas et al. (2007); Yeo and Maxey (2010a,b)]. They all showed that the PDF of a concentrated non-Brownian suspension is anisotropic and fore-aft asymmetric with a larger number of pairs oriented on the approaching side of the reference particle than on the receding side. "
    [Show abstract] [Hide abstract]
    ABSTRACT: The shear-induced microstructure in non-Brownian suspensions is studied. The Pair Distribution Function in the shear plane is experimentally determined for particle volume fractions ranging from 0.05 to 0.56. Transparent suspensions made of PMMA particles (172µm in diameter) dispersed in a fluorescent index matched Newtonian liquid is sheared in a wide gap Couette rheometer. A thin laser sheet lights the shear plane. The particle positions are recorded and the pair distribution function (PDF) in the shear plane is computed. The PDF at contact is shown to be anisotropic, with a depleted area in the receding side of the reference particle. The angular position of the depleted zone, close to the velocity axis at low particle concentration, is tilted toward the dilatation axis as the volume fraction is increased. At high concentrations (larger than 0.45), the shape of the PDF changes qualitatively with a secondary depleted area in the compressional quadrant of the main flow and a probability peak in the velocity direction. These experimental results are in good agreement with numerical simulations in Stokesian Dynamics where the interaction force between particles has been tuned to reproduce the particle roughness effects.
    Full-text · Article · Nov 2012 · Journal of Rheology
  • Source
    • "The characterization of the microstructure has also motivated a lot of numerical studies based on various numerical techniques such as Stokesian Dynamics [Singh and Nott (2000), Sierou and Brady (2002), Drazer et al. (2004), Bricker and Butler (2007)] or Force Coupling Method [Yeo and Maxey (2010), Abbas et al. (2007)] which all conclude to the formation of an anisotropic shear-induced microstructure. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper reports experiments on the shear transient response of concentrated non-Brownian suspensions. The shear viscosity of the suspensions is measured using a wide-gap Couette rheometer equipped with a Particle Image Velocimetry (PIV) device that allows measuring the velocity field. The suspensions made of PMMA particles (31$\mu$m in diameter) suspended in a Newtonian index- and density-matched liquid are transparent enough to allow an accurate measurement of the local velocity for particle concentrations as high as 50%. In the wide-gap Couette cell, the shear induced particle migration is evidenced by the measurement of the time evolution of the flow profile. A peculiar radial zone in the gap is identified where the viscosity remains constant. At this special location, the local particle volume fraction is taken to be the mean particle concentration. The local shear transient response of the suspensions when the shear flow is reversed is measured at this point where the particle volume fraction is well defined. The local rheological measurements presented here confirm the macroscopic measurements of Gadala-Maria and Acrivos (1980). After shear reversal, the viscosity undergoes a step-like reduction, decreases slower and passes through a minimum before increasing again to reach a plateau. Upon varying the particle concentration, we have been able to show that the minimum and the plateau viscosities do not obey the same scaling law with respect to the particle volume fraction. These experimental results are consistent with the scaling predicted by Mills and Snabre (2009) and with the results of numerical simulation performed on random suspensions [Sierou and Brady (2001)]. The minimum seems to be associated with the viscosity of an isotropic suspension, or at least of a suspension whose particles do not interact through non-hydrodynamic forces, while the plateau value would correspond to the viscosity of a suspension structured by the shear where the non-hydrodynamic forces play a crucial role.
    Full-text · Article · Apr 2011 · Journal of Rheology
  • [Show abstract] [Hide abstract]
    ABSTRACT: Homogenous oil in water dispersion has been investigated in a horizontal pipe. The mean droplet size is 25 μm. Experiments were carried out in a 7.5-m-long transparent pipe of 50-mm internal diameter. The wall friction has been measured and modeled for a wide range of flow parameters, mixture velocities ranging from 0.28 to 1.2 m/s, and dispersed phase volume fractions up to 0.6, including turbulent, intermediate, and laminar regimes. Flow regimes have been identified from velocity profiles measured by particle image velocimetry in a matched refractive index medium. It is shown that the concept of effective viscosity is relevant to scale the friction at the wall of the dispersed flow. Based on mixture properties, the friction factor follows the Hagen-Poiseuille and the Blasius' law in laminar and turbulent regimes, respectively. Interestingly, the transition toward turbulence is delayed as the dispersed phase fraction is increased. © 2010 American Institute of Chemical Engineers AIChE J, 2011
    No preview · Article · May 2011 · AIChE Journal
Show more