Numerical simulation of electrorheological fluids based on an extended Bingham model

Abstract

In the framework of the macroscopic simulation of electrorheological fluids, we present an extension of the classical Bingham model which goes beyond pure shear flows and thus enables the simulation of settings in more complex geometries. Emphasis is on the numerical solution of the resulting nonsmooth minimization problem. We propose the method of augmented Lagrangians combined with an operator-splitting technique which allows to confine the nonlinearity to local, low-dimensional problems. Numerical results are given that illustrate the electrorheological effects for various shear rates and electric field strengths in case of an electrorheological suspension rotating between two revolving cylinders.

Modelling and Simulation of Electro- and Magnetorheological Fluid Dampers

“…The simulation is able to predict the apparent viscosity in accordance with the experimental data. Recently, Engelmann et al [16] proposed an extension of the classical Bingham model which goes beyond pure shear flows and enables the simulation of electrorheological fluids in complex geometries [23]. Except for small shear rates (expressed in terms of the so-called Mason number) the results of the simulation match with the Bingham plastic model described in the next section (Bonnecaze and Brady [6]).…”

Modeling, Simulation and Optimization of Electrorheological Fluids

“…has been used in ENGELMANN et al [2000], HOPPE and MAZURKEVICH [2001], HOPPE et al [2000] in combination with a potential equation for the electric potential ψ (E = −∇ψ) to provide numerical simulations of steady electrorheological fluid flows. In the spirit of RAJAGOPAL and WINEMAN [1992,1995], RUZICKA [2000] has developed a model that takes into account the interaction between the electric field and the fluid flow (see also RUZICKA [1996, 2001]).…”

“…Hence, appropriate numerical methods for such variational inequalities have to be provided (cf., e.g., GLOWINSKI et al [1981]). We present here an augmented Lagrangian approach relying on a mixed formulation of the problem that has been used in ENGELMANN et al [2000] for the computation of electrorheological fluid flows obeying the constitutive law (2.13).…”

“…Since electrorheological fluids exhibit a Non-Newtonian flow behavior, significant efforts have been devoted to the derivation of appropriate constitutive equations relating the stress tensor to the rate of deformation tensor by taking into account the influence of the electric field. We mention the pioneering work by RAJAGOPAL and WINEMAN [1992,1995] (see also ENGELMANN et al [2000]) and the systematic treatment by RUZICKA [2000] providing a constitutive equation of power law type (see also BUSUIOC and CIO-RANESCU [2003], ECKART [2000], RAJAGOPAL and RUZICKA [2001]). Other continuum-based approaches try to incorporate micro-and mesoscale effects by using internal variables (DROUOT et al [2002]), transverse isotropy ABU-JDAYIL [1998, 2004]), polar theory (ECKART and SADIKI [2001]), and more general rate-type models (SADIKI and BALAN [2003]).…”

Electro-osmosis of electrorheological fluids

“…Later on, continuum-based models that describe the influence of the orientation of the electric field on ER flow were developed [31]. Several other mathematical formulations were developed in parallel to mathematically model the experimental results for ER flows [32][33][34].…”