Hydrodynamic theory of polydisperse chain-forming ferrofluids

The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the chain-forming particles, while accounting for the free magnetic particles by dissipative terms in the Maxwell equations.

Figure 1

Particle density versus the logarithms of relaxation time. The large curve shows the distribution at zero field. Particles of the shaded area form chains at finite fields. The associated magnetization relaxes much more slowly, because it is dominated by the transport of particles through the liquid.

Figure 2

The two orientations of the external field.

Figure 3

Shear thinning (and thickening) of a monodisperse ferrofluid obeying linear constitutive relation, for parallel and perpendicular fields. $({\eta }^{\parallel }-{\eta }_0)∕\left[\tau H_0^2\right]$ and $({\eta }^{\perp }-{\eta }_0)∕\left[\tau H_0^2\right]$, calculated using Eqs. (9), with $\chi =0.1/0.3/0.5/1/2.5/4$ and ${\lambda }_2=0.2$, are plotted against $\xi \equiv \dot{\gamma }\tau$. Note that increasing $\chi$ may actually reduce the magnetoviscous effect.

Figure 4

Shear thinning calculated employing the given theory (lines), and compared to two sets of experimental data [4] from APG 513A (diamonds).

Figure 5

Same data as Fig. 4, zoomed into two shear regions.

Figure 6

Shear thinning for the parallel field orientation, $({\eta }^{\parallel }-{\eta }_0)∕{\eta }_0$ versus $\dot{\gamma }[1∕s]$, using the same parameters as in Fig. 3.