Anisotropy of the magnetoviscous effect in ferrofluids

The anisotropy of the magnetoviscous effect in ferrofluids subjected to weak planar Couette flow is investigated by extensive molecular simulations. The field and concentration dependence of the viscosity coefficients are found to depend on the relative orientation of the magnetic field with respect to the flow geometry. Comparison with dynamical mean-field models shows satisfactory agreement for moderate interaction strengths. In the semidilute regime it is found that the anisotropy contains valuable information on particle interaction.

Figure 1

The nonequilibrium magnetization $M_y∕M_{\mathrm{sat}}$ is shown as a function of the Langevin parameter $h$. The magnetic field was oriented in the flow direction. Circles and squares correspond to volume fractions of $\varphi =0.05$ and $\varphi =0.1$, respectively. Solid, shaded, and open symbols correspond to ${\chi }_{\mathrm{L}}=0.2,0.4$, and 0.8, respectively. Also shown are the predictions of the DMF model, cf. Eq. (13).

Figure 2

The nonequilibrium magnetization components $M_x∕M_{\mathrm{sat}}$ (circles) and $M_y∕M_{\mathrm{sat}}$ (squares) are shown as a function of the Langevin parameter $h$. The magnetic field was oriented parallel to the bisector between the flow and the gradient direction. Again, solid, shaded, and open symbols correspond to ${\chi }_{\mathrm{L}}=0.2,0.4$, and 0.8, respectively. Also shown are the predictions of the DMF model; cf. Eq. (13).

Figure 3

The relative change of shear viscosity $\Delta {\eta }_{yx}∕{\eta }_0$ is shown as a function of the Langevin parameter $h$. Circles, squares, and diamonds correspond to orientations of the magnetic field in the flow, gradient, and vorticity direction of the flow, respectively. The volume fraction was chosen as $\varphi =0.1$. Solid, shaded, and open symbols correspond to $\lambda =0.25,0.5$, and 1.0, respectively. Also shown are the predictions of the DMF model; cf. Eq. (15).

Figure 4

The relative change of shear viscosity as a function of the volume fraction $\varphi$ for dipolar interaction strengths $\lambda =0.5$ (full symbols) and 1.0 (open symbols). The value of the Langevin parameter was chosen as $h=20.0$. Circles, squares, and diamonds show the simulation results for magnetic fields oriented in the flow, gradient, and vorticity direction, respectively. Solid and dashed lines are the result of the DMF model for $\lambda =0.5$; dotted line the NI model.