Effects of symmetry-breaking mechanisms on the flow field around magnetic-responsive material appendages that mimic swimming strokes

The flow field around bioinspired magnetic-responsive soft materials that mimic the symmetry-breaking mechanisms in swimming animals, such as pteropods and manta rays, is studied using the tomographic particle image velocimetry (tomo-PIV) technique. Magnetic-responsive material appendages are actuated by an oscillating external magnetic field. The fluid flow induced by two types of actuation is quantified. First, a single actuation mode involves alternating upward and downward bending motions. Second, an asymmetric multimodal actuation encompasses upward folding and downward bending motions by locating an asymmetric joint at the midpoint of the appendage. The formed vorticity field, vortex structure, and viscous energy dissipation rate in the surrounding fluid are observed to be weaker for the multimodal actuation case. The multimodal appendage moves with reduced flow resistance, leading to faster appendage velocity during the downward power stroke. Furthermore, the study examines the effect of an asymmetric magnetic field cycle on the flow field by extending the time interval of the applied positive voltage (upstroke motion) compared to the duration of the negative applied voltage (downstroke motion). The asymmetric cycle and extended stopping period provide time for greater dissipation of the formed vorticity field. Thus, the peak values of vorticity and viscous dissipation rate decrease to smaller magnitudes compared to the symmetric cycle case. These findings demonstrate that the utilization of symmetry-breaking morphology and an asymmetric cycle enhances stroke performance, offering promising avenues for achieving greater effectiveness in underwater propulsion.

Figure 1

Schematic of the experimental setup for the tomographic particle image velocimetry (tomo-PIV) measurements

Figure 2

Time record of the applied voltage to generate the magnetic field required for each upward (positive voltage) and downward (negative voltage) motion of the magnetic appendage for cases with (a) symmetric cycle and (b) asymmetric cycle. The green dashed line identifies the beginning of the stopping period preceding the up-to-downstroke and down-to-upstroke transitions. The light blue and orange regions correspond to the upstroke and downstroke of the appendage, respectively.

Figure 3

Schematic of the magnetic-responsive material appendage shape with (a) no joint and (b) asymmetric joint in the middle. The raw PIV images from one of the cameras in (c), (d) the upward position and (e), (f) the downward position for cases with (c), (e) no joint and (d), (f) asymmetric joint.

Figure 4

The maximum appendage flexion angle of (a) a shelled Antarctic pteropod (Limacina helicina antarctica) and (b) the magnetic-responsive material appendage (left: no joint, right: asymmetric joint) at the peak of the upward motion. (c) The swept area of the magnetic-responsive material appendage (left: no joint, right: asymmetric joint) at the peak of the upward motion. The pteropod image is directly extracted from the recording of a swimming specimen [58].

Figure 5

Time records of the magnetic-responsive material appendage tip velocity for cases with (a) no-joint and symmetric cycle, (b) no-joint and asymmetric cycle, (c) asymmetric joint and symmetric cycle, and (d) asymmetric joint and asymmetric cycle. The red and green ovals identify the time points of greatest appendage tip velocity while bending and folding, respectively. The black dashed line and the orange dash-dotted line identify the beginning and end of the stopping period of the second cycle, respectively. The stopping periods are also identified in Fig. 2. The light blue and orange regions correspond to the upstroke and downstroke of the appendage, respectively, as also shown in Fig. 2.

Figure 6

Velocity vector field in the volume surrounding the appendage for cases with (a), (b) no-joint and symmetric cycle and (c), (d) asymmetric joint and symmetric cycle at the beginning of the stopping period at the peak of (a), (c) the upward motion ($t$ = 0.285 s) and the peak of (b), (d) the downward motion ($t$ = 0.385 s). One-eighth of all vectors are shown for clarity.

Figure 7

The flow field (a), (b) at the peak of the upward motion ($t=0.285\mathrm{s}$) and (c), (d) at the peak of the downward motion ($t=0.385\mathrm{s}$) of the second cycle at the beginning of the stopping period for the case with no-joint and symmetric cycles. (a), (c) The isosurface of the $y$ component of vorticity (${\omega }_y=\pm 7$ (1/s)) and (b), (d) the isosurface of $Q=0.1$ ($1/{\mathrm{s}}^2$).

Figure 8

The midplane field of (a), (c) the $y$ component of vorticity overlaid with the velocity vectors and (b), (d) $Q>0$ for (a), (b) the peak of the upward motion ($t=0.285\mathrm{s}$) and (c), (d) the peak of the downward motion ($t=0.385\mathrm{s}$) of the second cycle at the beginning of the stopping period for the case with no-joint and symmetric cycles.

Figure 9

The flow field (a), (b) at the peak of the upward motion ($t=0.285\mathrm{s}$) and (c), (d) at the peak of the downward motion ($t=0.385\mathrm{s}$) of the second cycle at the beginning of the stopping period for the case with an asymmetric joint and symmetric cycle. (a), (c) The isosurface of the $y$ component of vorticity [${\omega }_y=\pm 7$ (1/s)] and (b), (d) the isosurface of $Q=0.1$ ($1/{\mathrm{s}}^2$).

Figure 10

The midplane field of (a), (c) the $y$ component of vorticity overlaid with the velocity vectors and (b), (d) $Q>0$ for (a), (b) the peak of the upward motion ($t=0.285\mathrm{s}$) and (c), (d) the peak of the downward motion ($t=0.385\mathrm{s}$) of the second cycle at the beginning of the stopping period for the case with an asymmetric joint and symmetric cycle.

Figure 11

(a)–(d) The isosurface of the absolute value of vorticity [$\left|\omega \right|=9$ (1/s)] at the peak of the upward motion of the second cycle at the beginning of the stopping period ($t=0.285\mathrm{s}$ and $t=0.32\mathrm{s}$ for the cases with symmetric and asymmetric cycles, respectively). (e)–(h) The isosurface of the absolute value of vorticity [$\left|\omega \right|=6$ (1/s)] at the peak of the upward motion of the second cycle at the end of the stopping period ($t=0.32\mathrm{s}$ and $t=0.39\mathrm{s}$ for the cases with symmetric and asymmetric cycles, respectively). The isosurfaces are for cases with (a), (e) no-joint and symmetric cycle; (b), (f) no-joint and asymmetric cycle; (c), (g) asymmetric joint and symmetric cycle; and (d), (h) the asymmetric joint and asymmetric cycle.

Figure 12

(a), (b) The isosurface of the absolute value of vorticity $\left[\right|\omega |=9$ (1/s)] at the peak of the downward motion of the second cycle at the beginning of the stopping period ($t=0.385\mathrm{s}$). (c), (d) The isosurface of the absolute value of vorticity [$\left|\omega \right|=6$ (1/s)] at the peak of the downward motion of the second cycle at the end of the stopping period ($t=0.42\mathrm{s}$). The isosurfaces are for cases with (a), (c) no-joint and symmetric cycle and (b), (d) asymmetric joint and symmetric cycle.

Figure 13

Time records of the volumetric average of the enstrophy for cases with (a) no-joint and symmetric cycle, (b) no-joint and asymmetric cycle, (c) asymmetric joint and symmetric cycle, and (d) asymmetric joint and asymmetric cycle. The red and green ovals identify the time-points of greatest appendage tip velocity while bending and folding, respectively (see Fig. 5). The light blue and orange regions correspond to the upstroke and downstroke of the appendage, respectively.

Figure 14

Time records of the total viscous energy dissipation rate for cases with (a) no-joint and symmetric cycle, (b) no-joint and asymmetric cycle, (c) asymmetric joint and symmetric cycle, and (d) asymmetric joint and asymmetric cycle. The red and green ovals identify the time points of greatest appendage tip velocity while bending and folding, respectively (see Fig. 5). The light blue and orange regions correspond to the upstroke and downstroke of the appendage, respectively.