Origin of the slow wave in a magnetorheological slurry.

In Ref. [ 1 ] the propagation of a longitudinal slow mode parallel to an applied magnetic field has been observed in a magneto-rheological slurry. This mode has been discussed in terms of a Biot slow compressional wave as it is found in porous fluid-saturated media [ 1-3 ]. The slow mode described in ref. 1 is only observed in the presence of an external magnetic field. This feature all by itself renders a description in terms of a Biot slow wave [ 4 ] impossible, since the latter is also expected to occur in any fluid-saturated porous medium in the absence of an external magnetic field. The previous Comment [ 2 ] missed this crucial point. Here we propose a completely different physical mechanism for the origin of this slow mode, namely a wave propagating along the chains or columnar structures formed by the suspended particles that was analyzed previously by the present authors in the context of ferrofluids [ 5 ]. As it is clear from Ref. [ 3 ] no shear wave component was involved in the experiments in Ref. 1; the formation of separate columns in a field [ 1,3 ] is also unfavorable for the presence of a Biot slow wave. Thus what one is looking for is a mechanism specific for materials consisting of magnetic particles suspended in a carrier fluid. The particles used for the experiments described in Refs. [ 1,3 ] are large (∼ 10μm) and thus a magnetorheological fluid results. If smaller magnetic monodomain particles (∼ 10nm) are suspended in a carrier fluid, a ‘ferrofluid’ results [ 6 ]. Triggered by the observation of an anisotropy in the velocity of ultrasound in ferrofluids [ 7 ], we analyzed the influence of non-hydrodynamic degrees of freedom on sound propagation in ‘ferrofluids’ [ 5 ]. This extension appeared to be necessary since in the strictly hydrodynamic limit the sound velocity must be isotropic in the long wavelength limit. As it turns out [ 5 ], the relevant additional macroscopic variables (that is, variables slowly relaxing in the long wavelength limit) are the magnitude of the magnetization density m and the average velocity w of the ferrofluid particles relative to the carrier fluid. These two variables characterize macroscopically the internal chain motion in an external magnetic field in such a system. Their influence gives rise to two important physical consequences. The first is the anisotropy of the ultrasound velocity. And the second one is the occurrence of a slow mode with a dispersion relation of the type