Fluid–particle shear flows

Bertrand Maury

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 4, page 699-708
  • ISSN: 0764-583X

Abstract

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Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction, we assume periodicity of the flow in the shear direction. Direct simulations are based on the so–called Arbitrary Lagrangian Eulerian approach, which we adapted to make it suitable to periodic domains. As a first step toward modelling of interacting red cells in the blood, we propose a simple model of circular particles submitted to an attractive force which tends to form aggregates.

How to cite

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Maury, Bertrand. "Fluid–particle shear flows." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 699-708. <http://eudml.org/doc/194186>.

@article{Maury2010,
abstract = { Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction, we assume periodicity of the flow in the shear direction. Direct simulations are based on the so–called Arbitrary Lagrangian Eulerian approach, which we adapted to make it suitable to periodic domains. As a first step toward modelling of interacting red cells in the blood, we propose a simple model of circular particles submitted to an attractive force which tends to form aggregates. },
author = {Maury, Bertrand},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fluid–particle; ALE; Finite Element; Shear Flow.; Fluid-particle; Shear Flow},
language = {eng},
month = {3},
number = {4},
pages = {699-708},
publisher = {EDP Sciences},
title = {Fluid–particle shear flows},
url = {http://eudml.org/doc/194186},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Maury, Bertrand
TI - Fluid–particle shear flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 699
EP - 708
AB - Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction, we assume periodicity of the flow in the shear direction. Direct simulations are based on the so–called Arbitrary Lagrangian Eulerian approach, which we adapted to make it suitable to periodic domains. As a first step toward modelling of interacting red cells in the blood, we propose a simple model of circular particles submitted to an attractive force which tends to form aggregates.
LA - eng
KW - Fluid–particle; ALE; Finite Element; Shear Flow.; Fluid-particle; Shear Flow
UR - http://eudml.org/doc/194186
ER -

References

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  1. R. Folkersma, A.J.G. vanDiemen, J. Laven and H.N. Stein, Steady shear rheology of dilute polystyrene particle gels. Rheol. Acta 38 (1999) 257-267.  
  2. R. Glowinski, T.-W. Pan, T.I. Hesla and D.D. Joseph, A Distributed Lagrange Multiplier/Fictitious Domain Method for Particulate Flows. Int. J. Multiphas. Flow25 (1999) 755.  Zbl1137.76592
  3. H.H. Hu, Direct Simulation of Flows of Solid-Liquid Mixtures. Int. J. Multiphas. Flow 22 (1996) 335-352.  Zbl1135.76442
  4. A.A. Johnson and T.E. Tezduyar, Simulation of Multiple Spheres Falling in a Liquid-Filled Tube. Comput. Methods Appl. M.134 (1996) 351-373.  Zbl0895.76046
  5. B. Maury, Direct Simulation of 2D Fluid-Particle Flows in Biperiodic Domains. J. Comp. Phys.156 (1999) 325-351.  Zbl0958.76045
  6. O. Pironneau, J. Liou, T. Tezduyar, Characteristic-Galerkin and Galerkin Least Squares Space-Time Formulations for the Advection-Diffusion Equation with Time-Dependent Domains. Comput. Meth. Appl. M.100 (1922) 117-141.  Zbl0761.76073

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