scholarly journals Rheology of a suspension of elastic particles in a viscous shear flow

2011 ◽  
Vol 687 ◽  
pp. 209-237 ◽  
Author(s):  
Tong Gao ◽  
Howard H. Hu ◽  
Pedro Ponte Castañeda
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Effective Viscosity ◽  
Circular Cross Section ◽  
Solid Particles ◽  
Simple Shear Flow ◽  
Arbitrary Lagrangian Eulerian ◽  
Viscous Shear ◽  
Elastic Particles ◽  
Steady State Solutions

AbstractIn this paper we consider a suspension of elastic solid particles in a viscous liquid. The particles are assumed to be neo-Hookean and can undergo finite elastic deformations. A polarization technique, originally developed for analogous problems in linear elasticity, is used to establish a theory for describing the finite-strain, time-dependent response of an ellipsoidal elastic particle in a viscous fluid flow under Stokes flow conditions. A set of coupled, nonlinear, first-order ODEs is obtained for the evolution of the uniform stress fields in the particle, as well as for the shape and orientation of the particle, which can in turn be used to characterize the rheology of a dilute suspension of elastic particles in a shear flow. When applied to a suspension of cylindrical particles with initially circular cross-section, the theory confirms the existence of steady-state solutions, which can be given simple analytical expressions. The two-dimensional, steady-state solutions for the particle shape and orientation, as well as for the effective viscosity and normal stress differences in the suspension, are in excellent agreement with direct numerical simulations of multiple-particle dispersions in a shear flow obtained by using an arbitrary Lagrangian–Eulerian (ALE) finite element method (FEM) solver. The corresponding solutions for the evolution of the microstructure and the rheological properties of suspensions of initially spherical (three-dimensional) particles in a simple shear flow are also obtained, and compared with the results of Roscoe (J. Fluid Mech., vol. 28, 1967, pp. 273–293) in the steady-state regime. Interestingly, the results show that sufficiently soft elastic particles can be used to reduce the effective viscosity of the suspension (relative to that of the pure fluid).

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

scholarly journals A theoretical investigation of the frisbee motion of red blood cells in shear flow

2021 ◽  
Vol 16 ◽  
pp. 23
Author(s):  
Thierry Mignon ◽  
Simon Mendez
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Blood Cell ◽  
Red Blood Cells ◽  
Red Blood Cell ◽  
Blood Cells ◽  
Numerical Solutions ◽  
Shear Rates ◽  
Steady State Solutions ◽  
Low Shear

The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.

Effects of chain length and polydispersity on shear banding in simple shear flow of polymeric melts

Soft Matter ◽  
2020 ◽  
Vol 16 (28) ◽  
pp. 6468-6483 ◽  
Author(s):  
Mahdi Boudaghi-Khajehnobar ◽  
Brian J. Edwards ◽  
Bamin Khomami
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Shear Flow ◽  
Chain Length ◽  
Simple Shear ◽  
Polymer Melts ◽  
Shear Banding ◽  
Simple Shear Flow ◽  
Polydisperse Polymer ◽  
Transient And Steady State

Transient and steady-state shear banding are demonstrated for polydisperse polymer melts as functions of applied shear rate.

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

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