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A microscale model of paste flow in piston-driven extrusion process
Published in Y. Kishino, Powders and Grains 2001, 2020
W.X. Yuan, A. S. Burbidge, K.A. Fisher, P.A. Langston, D.I. Wilson
plied to the high-energy collision-dominated flows, such as those in fluidised bed (Tsuji, et. al., 1992, Xu and Yu 1997), but have seldom (as far as the authors’ are aware) been used for low-energy, contact-dominated, paste flows. An alternative popular analysing approach for dense suspensions is the use of Stokesian dynamics (Brady and Bossis, 1985, Brady, 1993), wherein the effects of the fluid flow field surrounding the particles are included by solution of the stoke equation in a complex geometry. Actually the singular solutions to the Stokes equation are analytically integrated to give the forces acting between pairs of particles, which are then solved to evolve the microstructure of the suspension. It is not clear how easily such an approach could be scaled to deal with extremely large numbers of particles.
Simulation of Powders and Particles in Dry and Wet Phases
Published in Ko Higashitani, Hisao Makino, Shuji Matsusaka, Powder Technology Handbook, 2019
Junya Kano, Jusuke Hidaka, Mikio Sakai, Yutaka Tsuji, Mojtaba Ghadiri, Tina Bonakdar, Sadegh Nadimi, Kenji Iimura, Ko Higashitani, Ryoichi Yamamoto
Simulation methods for colloidal particle dispersions that do not explicitly solve the motions of fluid, such as Brownian dynamics (BD) and Stokesian dynamics (SD), have been extensively used because of their relatively low computational costs. However, such methods are mostly restricted to neutral particles in simple Newtonian host fluids, and extensions to complex fluids possessing complex internal degrees of freedom such as polymeric fluids or electrolyte solutions have proven extremely difficult. In addition, these approaches are applicable only in the low-Reynolds-number regime (Re ≪ 1), which is defined in terms of the size of the dispersed particles.
Dynamics of suspensions of rigid particles
Published in Annie Viallat, Manouk Abkarian, Dynamics of Blood Cell Suspensions in Microflows, 2019
Stany Gallier, Elisabeth Lemaire
The viscosity diverges at ϕ = ϕ* and the value of ϕ* is usually taken as a fitting parameter typically ranging between 0.53 and 0.74 for monodisperse spherical suspensions. It can significantly increase and possibly reach values close to 1 for polydisperse suspensions. Geometrical arguments are insufficient for predicting the value of ϕ* for a system of particles and a general theoretical framework is still lacking. In particular, as already mentioned in Sec. 2.2, ϕ* is different from the maximum volume fraction ϕmax that would be measured from sedimentation. Rather, the exact value of ϕ* seems to be controlled by the forces acting on the particles whether they are Brownian, colloidal or contact forces. Two results corroborating this idea are given hereafter. The first one is the influence of the particle friction coefficient on suspension viscosity. Recent numerical simulations [63, 78] have shown that for suspensions of non-Brownian and non-colloidal rough spheres, increasing the friction coefficient μ from 0 to 1 results in a decrease of the jamming fraction from 0.7 to 0.56 (Figure 2.7). The variation of ϕ* with the Péclet number is a second example showing how interactions at the particle scale affect the jamming fraction. It has been observed (see for instance [99] or [102]) that as Pe increases, ϕ* becomes larger and changes from ϕ* ≃ 0.63 in the zero Péclet number limit to ϕ* ≃ 0.7 in the high Péclet number limit. This dependence of ϕ* with Pe has been interpreted as a disorder-order transition that facilitates the flow through the sliding of particle layers over each other [99]. This hypothesis has been confirmed by scattering experiments [101] and discrete numerical simulations based on a molecular dynamics method that accounts for many-body hydrodynamic interactions, known as the Stokesian Dynamics [29, 82].
Hydrodynamic diffusive behavior of fine particle assemblage passing through nonuniform granular porous media
Published in Particulate Science and Technology, 2023
Ryoko Otomo, Yuki Nakano, Shusaku Harada
In this study, we numerically investigated how fine particle assemblages move through pore space of granular media filled with fluid on the assumption of micro-scale phenomena with extremely small Reynolds number and Stokes number. Similar to authors’ previous studies, the Stokesian dynamics method (Durlofsky, Brady, and Bossis 1987; Brady et al. 1988; Brady and Bossis 1988), which can take into account hydrodynamic interactions between particles, was applied to the calculation of particle behavior. Focusing on the hydrodynamic diffusion, the behavior of fine particles in the traveling direction and in the plane perpendicular to it was investigated in detail by setting an cylindrical calculation domain. The purpose of this study is to confirm the characteristics of hydrodynamic diffusion different from molecular diffusion, and to quantitatively clarify the effects of volume fraction and nonuniform structure of the granular media on it.
Effect of interparticle action on shear thickening behavior of cementitious composites: modeling and experimental validation
Published in Journal of Sustainable Cement-Based Materials, 2020
Xuhao Wang, Alan Lu, Kejin Wang
Stokesian dynamics is a molecular dynamics-like method for simulating the behavior of many particles suspended in a fluid. This method treats the suspended particles in a discrete sense, while the continuum approximation remains valid for the surrounding fluid, that is the suspended particles are generally assumed to be significantly larger than the molecules of the solvent. The particles then interact with hydrodynamic forces transmitted through the continuum fluid when the Reynolds number of the particles is small. These forces are determined by the linear Stokesian equations. In addition, the method can also resolve non-hydrodynamic forces, such as Brownian forces arising from the fluctuating motion of the fluid, and interparticle or external forces. Thus, Stokesian dynamics can be applied to a variety of problems, including sedimentation, diffusion, and rheology. It aims to provide the same level of understanding for multiphase particulate systems as molecular dynamics does for statistical properties of matter.
Numerical simulation of particle migration in suspension flow through heterogeneous porous media
Published in Particulate Science and Technology, 2021
Stokesian dynamics (SD) is a molecular dynamics type simulation method which accurately captures the multi-body hydrodynamic interactions. The main difficulty in dynamic simulation of dense suspension is the singular hydrodynamic interactions due to the lubrication interactions between the close particle pairs. SD method uses the local and pairwise additive nature of lubrication interactions to avoid this difficulty. It also captures many body hydrodynamic interaction by inverting the mobility matrix. However, the inversion of the mobility matrix for a system with a large number of particles is computationally expensive and this limits the application of the SD method to only a few hundred particles. The detailed formulation of SD was laid out in previous works (Bossis and Brady 1984; Brady and Bossis 1988). Primitively, SD method was formulated to simulate the dynamics of suspended particles in creeping flow regime with Re≪1, where interparticle, bulk, and hydrodynamic forces were taken into account (Bossis and Brady 1984). Thereafter, SD was implemented to study shear of suspension of particles bounded between two parallel plates by discretizing the particles into patches and assuming a uniform distribution of force density in each patch (Durlofsky, Brady, and Bossis 1987). Hydrodynamic interactions were calculated between suspended particles and patches. Nott and Brady (Nott and Brady 1994) considered the wall to be made up of spheres attached together, creating a bumpy wall. In progression, Singh and Nott (2000) suggested using exact sphere wall resistance for interactions of the suspended particles with wall particles instead of “bumpy” wall implementation (Nott and Brady 1994). Though SD method was upgraded to simulate suspension flow in the plane channel, yet its application is limited to small scale isotropic porous network.