Phenomenological model for yield stress based on the distribution of chain lengths in a dilute magnetorheological fluid under an oscillatory magnetic field.

We study the distribution of chain lengths in a magnetorheological fluid based on mineral magnetite particles dispersed in a dexrontype oil exposed simultaneously to a static magnetic field and a sinusoidal field of low amplitude, the fields are transverse to each other. We experimentally determined the general behavior of the distributions under several conditions of intensities of the fields, particle concentration, liquid viscosity, and frequency of the sinusoidal field. We found that in all cases exponential fits describe well these distributions. Based on this result we propose a simple yield stress model for a magnetorheological fluid which differs from other models that posit all chains are of the same length. We compare this model with experimental results and found that there is a well qualitative agreement with them and in some cases also there is a quantitative agreement. In the case of using only static field, the model is in accord with the existence of a magnetic field threshold above which the yield stress increases faster than below it.