Colloidal stability influence on rheology of magnetic fluids

Abstract

Rheology of suspensions [1] is a complex hydrodynamic question. If the very dilute regime is now well understood from a theoretical point of view, the concentrated regime still raises many questions. In his pioneering works Einstein [2] proposed a powerful model, derived from the flow field of pure strain perturbed by the presence of a sphere, which correctly accounts for viscosity of suspensions in file limit of low concentrations of suspended particles, taking in account hydrodynamic interactions, Batchelor [3] then calculated the second order in concentration contribution to viscosity. Many other laws, semiphenomenological [4], are proposed to describe the whole viscosity dependence on concentration. Viscosity of colloids [5] is an even more difficult problem, because thermodynamical interactions between particles such as van der Waals or electrostatic interactions, have to be encountered together with Brownian motion and hydrodynamic interactions. In magnetic colloids [6,7,8], in addition to dipolar-magnetic interactions, an external parameter enriches the system. If a magnetic field is applied to the flowing system, it introduces an anisotropy inside the fluid, which is different of the anisotropy of the shear flow, leading then to specific effects [9]. Rheological properties of magnetic fluids (also called ferrofluids) are fundamental in regards to their technical applications[7]. To use such a fluid in a seal, a damper, a clutch, a car-springing or an accelerometer sensor, a well defined rheological behaviour is oftenly required from the magnetic fluid, at least during the life-time and in the working conditions of the mechanical device. The viscosity of magnetic fluids is discussed as a function of different parameters such as temperature or volume fraction of particles, in absence or in presence of an applied magnetic field,. We are here concerned with colloidal solutions containing magnetic particles of typical mean diameter 10 nm. Rheological behaviour, as most of physical properties of ferrofluids is related to a major problem : the colloidal stability of the magnetic fluid. Lowering the temperature or applying a large magnetic field, a phase separation [10] may be induced in the ferrofluid which may become diphasic. Macroscopic structurations [ 11] then appear inside the fluid leading to large apparent viscosities, usually going with nonNewtonian behaviours [ 12,13,14]. To some extents, rheology of such diphasic solutions may be compared to that of "magnetorheological fluids" which are non-colloidal suspensions of a few pm-sized magnetic grains [15]. First section deals with colloidal stability of ferrofluids. In the second section, viscosity of monophasic ferrofluids is described as a function of various experimental parameters. The third section shows how these rhcological properties are modified with ferrofluids undergoing a phase separation.