Magnetic control of metafluids for fluid-like applications of metamaterials

TL;DR

The paper tackles the challenge of imparting fluid-like behavior to metamaterials by introducing mechanical metafluids—suspensions of multistable capsules in a liquid. It leverages time-varying magnetic fields to externally actuate both the motion and the state of these capsules, enabling programmable flow and local compressibility. A theoretical model based on coupled momentum and mass balances is developed and validated against experiments in a 1D closed tube, showing excellent agreement in capsule trajectories and velocity scaling with actuation frequency. The work broadens metamaterial applications to fluid-like domains such as heat engines, cooling cycles, energy harvesting, and robotics, by offering a controllable, magnetically actuated metafluid platform.

Abstract

Metamaterials are structures composed of repeating unit-cells which enable macro-scale properties not found in nature. Since metamaterials are typically solid structures with predetermined interconnections, it is challenging to leverage their unique properties for many critical applications that require fluid-like behavior, such as heat engines or cooling cycles. Recent research suggested overcoming this limitation by creating a mechanical metafluid', which is a lubricated suspension of multistable unit-cells. However, realization of this concept necessitates the ability to control both velocity and state of the metafluid. Here, we propose the use of time-varying magnetic fields as a mechanism to manipulate metafluids. We focus on a lattice of magnetic multistable capsules enclosing gas and suspended within a liquid-filled tube. We derive the governing equations and examine one-dimensional fluid mechanics of the metafluid, both theoretically and experimentally, at the viscous limit under magnetic actuation. By applying time-varying magnetic fields, we control both the local compression and expansion of the capsules, as well as the entire flow field. Our theoretical results are compared with experimental data, showing good agreement. This work paves the way for the utilization of mechanical metamaterials to applications that require fluid-like behavior, thus extending the scope of metamaterial applications.

Figures (4)

• Figure 1: Liquifying metamaterial for a fluid-like applications. (A) Metamaterial in a standard lattice structure (left) and metamaterial unit cells submerged in a liquid (right). (B) An example of an application of metafluid in a thermodynamic cycle, where motion, compression, and expansion of the unit cells are needed. (C) Our proposed concept for metafluid based on time-varying magnetic fields to manipulate the unit cells including motion, compression and expansion.
• Figure 2: System configuration. (A) The image of the experimental setup, which comprises from a long closed tube filled with metafluid. The metafluid is obtained by suspending a 1D array of multistable elastic capsules in water. The capsules are equipped with magnets, which are attached to the capsules' ends and actuated by a magnetic field induced by six solenoids. The solenoids are installed over the tube at predefined locations, each connected to a power supply. The power supplies are connected to the drivers and all of the drivers are connected to Arduino, which gets signals from a computer according to our code (for more information see Section 4). In panel (A1), we show an increased view of the tube in the vicinity of the solenoid. (B) The sketch of our system, where our notations are indicated. In panel (B1), we show an increased view of our system (rotated). The scale bar corresponds to 10 [cm].
• Figure 3: Controlling the metafluid velocity. (A) A sequence of frames from a video (see Movie S1) in our experiment, where we track the location of the green capsule at times $t=0,\,2.5,\,5.5$, and 8.5 seconds. Panels A1 and A4 look the same, which visualizes the fact that the capsules completed one cycle. The operation of the solenoids is with stepwise function with delay between the solenoids, as detailed in Experimental Section, where the current of the solenoids is $I_{\text{curr}}=16$ A, the number of capsules is $N_{\text{cap}}=30$, and the frequency of the actuated solenoids is $\omega=3.57$ Hz. The scale bar in panel (A1) corrsponds to 30 [cm]. (B)-(C) A comparison between theory (dashed lines) and experiment (solid lines) for (B) the location of capsules versus time for different frequencies and various numbers of capsules within the tube and for (C) the mean velocity of the capsules versus frequency, for different numbers of the capsules within the tube.
• Figure 4: Controlling compression and expansion. (A)-(C) Average length map of the capsules, where initially they are assumed to be in an expanded state at permutation of $\overrightarrow{per}=(7,0,11)$, as a function of their location within the tube obtained by simulation, in three different cases of the current intensity, (A) $I_{\text{curr}}=2$ [A], (B) $I_{\text{curr}}=8$ [A], and (C) $I_{\text{curr}}=16$ [A]. The solenoids are marked with black rectangles and their numbering is indicated. (D) A frame from an experiment with the current of $I_{\text{curr}}=16$ [A] and frequency of $\omega=3.57$ Hz, with capsules' compression starting from the expanded state of the capsules. (D1) An increased view of the region marked by a black rectangle in (D), in three different states captured at different times: expanded, at rest, and compressed. (E) The actuation functions of the solenoids 1-3 with a general amplitude of $\tilde{A}$, which changes between the panels (A)-(C) as indicated. The solenoids 4-6 are actuated similarly to solenoids 1-3, in panel (C) and with opposite signs in panels (A)-(B). Both, in theory (panels (A)-(C)) and experiment, there 30 capsules in the system. The colorbar refers to panels (A)-(C), where below the colorbar we show for example two sketches of expanded and compressed capsules. The scale bars correspond to 30 [cm] in panels (A)-(D), and to 9.1, 7.9, and 7 [cm] in panel (D1).