Shear Banded Flows and Nematic-to-Isotropic Transition in ER and MR Fluids

Abstract

Above a critical shear rate we observe in suspensions polarized by an external field an abrupt jump of stress and the onset of a layered stripe pattern. This novel shear-induced transition can be systematically found by using appropriated geometry. We show that it can be explained by the transition from a nematiclike order induced by the field to an isotropic state which is obtained when the shearing hydrodynamic forces on a pair of particles overcome the magnetic or electrostatic forces. The critical shear stress predicted on this basis is in good agreement with the experimental results.[S0031-9007(98)08119-8] PACS numbers: 82.70.Kj, 83.80.Gv Electrorheological (ER) and magnetorheological (MR) fluids are suspensions of highly polarizable particles in a nonconducting oil. In the presence of an electric or of a magnetic field the attractive dipolar interaction in the direction of the field induces the formation of a solid network of particles which can sustain a stress without flowing. This fundamental change of rheology being electronically controlled, these fluids are very attractive for applications in active damping and many others fields [1][2][3]. For the sake of simplicity, the rheology of these fluids is very often characterized by a Bingham law: t t s 1 h ᠨ g; although a Casson law or other power laws can often better describe their rheological behavior [4,5].Actually, a good model should take into account the shear rate dependence of the average length of the transient aggregates by using a balance between the hydrodynamic and dipolar forces and some attempts have been done in this direction at low volume fractions [6,7].In order to obtain accurate rheological measurements on magnetic fluids, we have used a cone-plate geometry which has the advantage-relative to the more usual plate-plate geometry-of a constant shear rate inside the cell. In this geometry we have found a jump of stress at a critical shear rate, and we have observed that this jump of stress was related to the onset of a layered structure. To account for these unexpected results we propose a novel mechanism of phase separation which couples the disappearance of oriented chains of particles to the onset of attractive forces in the plane defined by the velocity and the field.Samples.-We have prepared fluids which are made of spherical particles with a rather good monodispersity. For MR fluids the magnetic particles are made of polystyrene containing magnetite inclusions. These particles are manufactured by Rhone-Poulenc for protein separation. They have an average diameter of 0.5 mm and a standard deviation of 10% measured by light scattering and are suspended in a mixture of water and glycerol in order to increase the zero field viscosity of the suspension. The permeability of the particles as a function of the magnetic field has been obtained from a measurement of the magnetization at a volume fraction of 4.7% and by using the Maxwell-Garnett theory [8], which is well adapted for low volume fraction. The ER fluid we have used is made fr...

Fluid dynamics of dilatant fluids

“…Although in the different physical context, the clear oscillatory flows [35] along with a discontinuous transition and hysteresis [36,37] have been observed in the liquid crystal system that shows the shear thinning due to the state dependent viscosity. Such behavior could be also described using the phenomenological model like the present one.…”

Structure evolution in electrorheological and magnetorheological suspensions from a continuum perspective

“…In experiments, shear flow appears to rapidly produce a concentration profile that is uniform in the flow (x) and electric field (z) directions. [7][8][9][10][11] Analysis of the linearized model in the previous section also suggests that the suspension evolves to a structure that only varies in the vorticity (y) direction. Finally, a full description of structure evolution with arbitrary, finite amplitude fluctuations re- quires the simultaneous solution of four nonlinear partial differential equations: the particle conservation equation, the bulk suspension momentum balance, the bulk suspension mass balance, and Gauss' law.…”

“…Within this region, the most unstable fluctuations will be those with k x ϭ0 and nonzero k y -that is, the dominant structure is predicted to be stripes of particle-rich regions oriented in the flow direction, as commonly observed experimentally. [7][8][9][10][11] Equation ͑30͒ has also been solved by the finite difference method to illustrate the stripe formation process. A no flux boundary condition was applied at the electrodes ( j z ϭ0 at zϭ0,L); periodic boundary conditions were applied at x,yϭ0,L.…”

“…2,4 In shear flow, applied fields cause the formation of concentrated particulate stripes oriented in the flow direction. [7][8][9][10][11] These patterns are intimately connected to the rheological phenomena.…”

Nonlocal electrostatics in heterogeneous suspensions using a point-dipole model

“…These stripes consist of bands of high particle concentration separated by bands of low particle concentration. [8][9][10][11][12] Stripe formation is illustrated in Fig. 1 where photographs of a shear flow experiment with an ER suspension in a concentric cylinder geometry are presented.…”