Static yield stresses and shear moduli in electrorheological fluids

Abstract

A previously introduced method to study many-body electrostatic interactions among spherical particles ͓H. J. H. Clercx and G. Bossis, Phys. Rev. E 48, 2721 ͑1993͔͒ has been used to study yield stresses and shear moduli for simple cubic ͑SC͒, simple hexagonal ͑SH͒, and body-centered tetragonal ͑BCT͒ structures, with polarizable spheres on the lattice sites, to gain insight in the electrostatic response of these structures to externally applied stresses. The shear modulus G and the static yield stress s have been calculated for several ratios of particle to fluid dielectric constant. It turned out that interchain interactions are very weak in SC and SH structures which is confirmed by the nearly linear dependence of G and s ͑even no weak maximum appears in these curves͒. The results reported for the BCT structure are rather unexpected, because both G and s suddenly decrease to zero at large volume fractions. We discuss the data for G and s and compare some of these results with data obtained by employing the dipolar approximation and the Laplacian relaxation technique to calculate the electrostatics. This comparison shows that in general a multipolar approach is indispensable in obtaining correct values for G and ; especially the dipolar approximation underestimates these quantities. As an example the strength of single vs double chains has been compared for both the dipolar approach and a multipolar calculation. In the dipolar approximation the double chain structure seems strongest. However, multipolar calculations show that the single chain structure is stronger than the double chain structure.

A slender-body micromechanical model for viscoelasticity of magnetic colloids: Comparison with preliminary experimental data

“…As an example, accounting for higher order multipoles (125 multipoles) in carbonyl iron suspensions under the presence of an external magnetic field of 29.7 kA/m, gives G = 119 kPa. In this calculation we have used the multipolar model between magnetizable spheres of Clercx and Bossis [31]-particularly, we have taken α = 50 in Table 1 of the cited paper. This G value is higher than the one predicted by mechanical models (see Fig.…”

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

“…On the other hand, the magnetic (or electrostatic) force on a particle in the presence of a second one has been calculated from a multipolar development [15,16]:…”

Dielectric electrorheological fluids: Theory and experiment

“…Such a shear distortion is characterized by an angle , and involves a change in unit cell volume given by different approximations [56][57][58]. Theories based on the finite element method [32] and multipole expansion method [59,60] have also been developed. The starting point of the work by Clercx and Bossis [59] is the same as ours [35], by expanding the electrostatic field in vector spherical harmonic functions.…”

“…Theories based on the finite element method [32] and multipole expansion method [59,60] have also been developed. The starting point of the work by Clercx and Bossis [59] is the same as ours [35], by expanding the electrostatic field in vector spherical harmonic functions. They succeeded in obtaining an exact representation of the electrostatic energy as a function of structure and component dielectric constants.…”