Continuum model of magnetic field induced viscoelasticity in magnetorheological fluids

Abstract

An effective macroscopic model of magnetorheological fluids in the viscoelastic regime is proposed. Under the application of an external magnetic field, columns of magnetizable particles are formed in these systems. The columns are responsible for solid-like properties, such as the existence of elastic shear modulus and yield stress, and are captured by the strain field, while magnetic properties are described by the magnetization. We investigate the interplay of these variables when static shear or normal pressure is imposed in the presence of the external magnetic field. By assuming a relaxing strain field, we calculate the flow curves, i.e. the shear stress as a function of the imposed shear rate, for different values of the applied magnetic field. Focusing on the small amplitude oscillatory shear we study the complex shear modulus, i.e. the storage and the loss moduli, as a function of the frequency. We demonstrate that already such a minimal model is capable of furnishing many of the key physical features of these systems, like yield stress, enhancement of the shear yield stress by pressure, threshold behavior in the spirit of the frequently employed Bingham law and several features in the frequency dependence of storage and loss moduli.

Macroscopic two-fluid effects in magnetorheological fluids

“…First we will discuss the variables necessary to generalize our MRF model [18] into a two-fluid system [17,19]. The basic notion is to have two intrinsically coupled subsystems, a Newtonian background fluid (index 1) and a (visco)elastic magnetic structure due to an applied magnetic field (index 2).…”

“…Similarly, Eqs. (17) and (18) lead to the desired form of the dynamics of g 1,2 [see Eqs. (B16) and (B17)].…”

“…It is instructive to compare the two-fluid model of magnetorheological fluids with the recently derived one-fluid model [18]. The one-fluid model is a special limiting case of the two-fluid one.…”

“…In Ref. [18] much emphasis was laid on the MRF behavior under external static strains and stationary and oscillatory shear flow in the presence of a magnetic field. Therefore, we discuss here the coupling of the specific two-fluid variables, w i andφ, to flow and to the elastic degrees of freedom.…”

“…It seems that macroscopic equations describing two-fluid effects with two velocities and two densities for magnetorheological fluids (MRFs) have not been considered before. Recently, a one-fluid description of MRFs in the framework of macroscopic dynamics (or generalized hydrodynamics) has been given [18]. Thus, for the purpose of this paper, the derivation of macroscopic two-fluid effects in MRFs, we have to generalize the macroscopic dynamics for isotropic viscoelastic two-fluid systems by including the magnetization as variable, or introduce a second velocity (and density) to the previous macroscopic dynamics of MRFs.…”