Controlled flow of smart powders

The flow properties of powders are mainly due to the interplay of cohesive forces and intergrain frictional forces. We have experimentally investigated a “smart granular system” for which the interparticle cohesion can be tuned by a magnetic field $\vec{B}$. We show that the rheological features of such a system can be controlled. Indeed, the granular flow can be controlled or even stopped by the magnetic field. Depending on the orientation of $\vec{B}$, different dynamical regimes can be obtained like a “dry liquid state” forming conical droplets as well as a “layered soft state.” Scaling laws are given for the flow rate outside a funnel as a function of $B$ and for the stopping threshold of the flow as a function of the funnel output diameter $D$. From this analysis, it appears that the flowing properties are related to the dimensionality of the magnetic aggregates.

Figure 1

(Color online) (a) Interactions between two ferromagnetic particles in a magnetic field $\vec{B}$. The $\vec{\mu }$ vector denotes the magnetic dipole induced by the magnetic field $\vec{B}$, and $\overrightarrow{r_{ij}}$ denotes the vector between the dipoles. (b) The magnetization of two ferromagnetic particles in a vertical magnetic field induces repulsive interaction when $\overrightarrow{r_{ij}}$ is perpendicular to $\vec{B}$ and attractive interaction when $\overrightarrow{r_{ij}}$ is parallel to $\vec{B}$.

Figure 2

(Color online) Sketch of the experimental setup in two different configurations. (Left) The powder flow driven by gravity is perpendicular to the magnetic field produced by vertical Helmholtz coils. (Right) The powder flow driven by gravity is parallel to the magnetic field produced by horizontal Helmholtz coils. In both configurations, the intermittency of the flow is observed with a laser beam and a photodiode.

Figure 3

(Color online) (Left) Normalized flow rate $T_0∕T$ as a function of the applied magnetic field. Both configurations are illustrated (dots for $B_{\parallel }$ and squares for $B_{\perp }$). Data represent averages over five experiments. The output diameter is fixed to $D=8\mathrm{mm}$. Error bars (not shown) have roughly the size of the symbols used in the figure. Below the critical point, data are fitted using a parabolic curve $T_0∕T=1-(B∕B^{c,\mathrm{fit}})$ with $B_{\parallel }^{c,\mathrm{fit}}=39.9\pm 0.6\mathrm{G}$ and $B_{\perp }^{c,\mathrm{fit}}=88.4\pm 0.9\mathrm{G}$. (Right) The intermittency $I$ as a function of the magnetic field, using the same code. When the magnetic field is parallel to the gravity, a strong intermittency of the flow is observed near the critical point. The lines linking the experimental points are a guide for the eyes.

Figure 4

(Color online) Critical values of the magnetic field $B_{\parallel }^c$ and $B_{\perp }^c$ for different values of the funnel output diameter $D$. Error bars are indicated. A linear behavior is fitted.

Figure 5

Three pictures of the granular flow for different situations. (Left) The cohesiveless case $(B=0)$. (Center) The magnetic field $(B_{\parallel }=18\mathrm{G})$ is parallel to gravity and the clusters are seen to be vertical and needlelike. A dry droplet, having a nearly conical shape, is observed to fall free. (Right) The magnetic field $(B_{\perp }=43\mathrm{G})$ is perpendicular to the gravity and the clusters are organized such that a horizontal layered structure is seen in the flow.

Figure 6

Distribution of the ratio between the volume $V$ of the detected droplets and the average volume $⟨V⟩$ for an output diameter $D=8\mathrm{mm}$. The magnetic field $B=18\mathrm{G}$ is parallel to the gravity and is slightly inferior to $B_{\parallel }^c$.