Analytical calculation of chain length in ferrofluids

The response of a typical ferrofluid (FF) lies in its explicit property of chain formation of magnetic nanoparticles. The most significant magneto-optic (MO) and magneto-viscous (MV) effects of FF are attributed to chaining effect. In the present research, an effort was made to analytically justify the dependence of the structure evolution of FFs on different measurable parameters involved in MO and MV effects. The problem is treated with the help of dimensional analysis and an empirical relation is formulated relating the equilibrium chain length with Verdet coefficient (constant), particle diameter, viscosity of the carrier fluid, particle density, magnetization and shear rate. The formulated relation of chain length is supported by error analysis to yield the uncertainty in the result. The maximum uncertainty in four sets of data is found as ∼0.75.