Orientational Distributions of Ferromagnetic Spherocylinder Particles Influenced by External Magnetic Field

Abstract

We have analyzed the time-dependent behaviors of the orientational distributions of a dilute colloidal dispersion composed of the ferromagnetic spherocylinder particles influenced by the external magnetic field. A basic equation is derived for the orientational distributions of the particles in steady two dimensional flow by using the perturbation expansion method. An exact solution of the basic equation is obtained theoretically by considering the inverse matrix composed of the functions for the solvable condition. By using the solution, the relevant statistical quantities for an ensemble of the particles are calculated. It is shown that the steady flow causes a distortion of the orientational distribution and can not bring about the steady state of the distribution without the external magnetic field. However, we find the external magnetic field can not always create the steady state of the distribution. We have derived the condition that the steady state of the distribution is made by the external magnetic field and the steady flow. In order to estimate the response of the particles for the magnetic field, the reference time is obtained from the rate of the convergence to the steady state.