A single-chain model for quasi-static shear stress-strain properties of magnetorheological fluids

The quasi-static shear stress-strain property of magnetorheological fluids is analyzed, based on the calculation of the interaction energy of chains of equi-spaced magnetic spheres with the applied uniform magnetic field. First, the dipole moment of a chain of equi-spaced magnetic spheres imposed to a uniform magnetic field is determined, and simple expressions are given. Then, the interaction energy of a chain with the forcing field is determined, and the restoring force is calculated when the chain is slanted and elongated. In our analysis, only the contributions from the mutual interaction of the particles in chains are considered. Comparison with experimental results is made, and good agreement is obtained.