Flow-induced anisotropy in the susceptibility of a particle suspension

The initial susceptibility, or low-field high-frequency permeability, of a rod-like particle suspension or polymer solution can become anisotropic when the particles or molecules interact with a magnetic field in a directional manner and are nonrandomly oriented by certain types of flow field. This is the alignment that leads to thixotropy and deviatoric stresses during rheological measurements on these fluids. A general expression for the particle order parameter and the fluid permeability in terms of Legendre polynomials is derived by calculating the ensemble average over all possible orientation angles. This is an integral containing the orientation angle-dependent orientation probability function. The example case of single-domain magnetic particles suspended in extensional flow of a newtonian fluid is examined by using the following well-known models: chain-of-spheres model for the magnetic properties of a particle and the Kirkwood-Auer theory for the orientation probability function. From this, the particle orientation in the flow direction downstream from a sharp circular convergence is predicted to dramatically increase with an increase in the ratio of the extension rate to the particle rotary diffusion coefficient. Consequently, the measured permeability of the fluid is predicted to decrease parallel to, and to increase perpendicular to, the flow direction.