Tuning Mie Scattering Resonances in Soft Materials with Magnetic Fields

An original approach is proposed here to reversibly tune Mie scattering resonances occurring in random media by means of external low induction magnetic fields. This approach is valid for both electromagnetic and acoustic waves. The experimental demonstration is supported by ultrasound experiments performed on emulsions made of fluorinated ferrofluid spherical droplets dispersed in a Bingham fluid. We show that the electromagnet-induced change of droplet shape into prolate spheroids, with a moderate aspect ratio of 2.5, drastically affects the effective properties of the disordered medium. Its effective acoustic attenuation coefficient is shown to vary by a factor of 5, by controlling both the flux density and orientation of the applied magnetic field.

Figure 1

Axial aspect ratio $a/b$ of a single fluorinated ferrofluid droplet embedded in a water-based gel matrix, submitted to a cycle of increasing and decreasing magnetic field inductions, with a 20 s delay between each step (a movie is available in the Supplemental Material [20]).

Figure 2

(a) Optical microscopy picture of fluorinated ferrofluid droplets embedded in a water-based gel matrix, achieved by means of robotics (${\mathrm{\Phi }}_V\sim 1\%$). (b) Corresponding histogram of the droplet-size distribution. Mean radius $⟨a⟩=105\mu \mathrm{m}$ and coefficient of variation $\mathrm{CV}=4\%$.

Figure 3

(a) Top and (b) side views of the experimental setup dedicated to acoustic measurements on fluorinated ferrofluid droplet emulsions under magnetic fields with various inductions (up to 43 mT) and orientations. The angle $\zeta$ between the direction of the magnetic field $B$ and the acoustic wave vector $k_0$ can be varied between 0° and 90°.

Figure 4

Evolution of the attenuation frequency spectra of fluorinated ferrofluid droplet emulsions submitted to a cycle of increasing (b),(e) and decreasing (c),(f) magnetic field inductions (from 0 to 43 mT). The direction of the magnetic field $B$ is parallel (a)–(c) or perpendicular (d)–(f) to the incident acoustic wave vector $k_0$. Thickest curves refer to the reference emulsion made of spherical droplets (no magnetic field). Panels (a) and (d) show the orientation of the fluorinated ferrofluid droplets along the direction of the magnetic field $B$ (movies are available in the Supplemental Material [20]).

Figure 5

Comparison between the measured attenuation coefficients (circles) and those predicted in the framework of the independent scattering approximation (solid lines) for emulsions made of prolate fluorinated ferrofluid droplets with an axial aspect ratio of 2. Various orientations between the direction of the magnetic field (of $B_0=25\mathrm{mT}$ induction) and the acoustic wave vector $k_0$ are investigated ($\zeta =0°$, 22.5°, 45°, 67.5°, and 90°). The top figure refers to the reference emulsion made of spherical droplets (no magnetic field).