Research ArticleMATERIALS SCIENCE

Undulatory topographical waves for flow-induced foulant sweeping

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Science Advances  29 Nov 2019:
Vol. 5, no. 11, eaax8935
DOI: 10.1126/sciadv.aax8935
  • Fig. 1 Design of the Batoidea-inspired dynamic undulatory composite.

    (A) Conceptual illustration showing the undulatory gait of the Batoidea’s pectoral fin together with the histological cross section of the pectoral fin (red, muscle; blue, collagen and bone). Nanoscale bumps are observed on the surface of the pectoral fin (scanning electron microscopy image). (B) Schematic illustrations showing vortices around the pectoral fin induced by the undulatory gait. (C) (i) A schematic structure of the multilayered dynamic undulatory composite and (ii) image of the fabricated composite. (D) A cross-sectional stereo zoom microscope image of the fabricated multilayered undulatory composite. (E) Schematic illustrations showing (i) the propagating undulatory topographical wave along with the translation of the magnet and (ii) the topographical wave–induced sweeping of foulants.

  • Fig. 2 Magnetic field–responsive deformations of the dynamic undulatory composite.

    (A to C) Quantitative FEA results of the magnetic field density, Maxwell stress tensor, strain tensor, and displacement of the composites with three different thicknesses of the RDL (tRDL) along (A) plane 1 (the cross-sectional plane parallel to the magnet movement), (B) line 1 (top horizontal line of plane 1), and (C) line 2 (vertical center line of plane 1). Detailed descriptions of the plane and the lines of interests are available in fig. S1. (D) (i) Cross-sectional views and (ii) simulation results of the deformations of the composite with different values of tRDL (2.1, 1.4, and 0.7 mm). (E) Comparisons of the experimental deformation behaviors of the composite with the FEA results.

  • Fig. 3 Undulatory topographical waves of the dynamic composite modulated by the controlled magnetic field.

    (A) Time-lapse monochromic cross-sectional images of the undulatory surface waves of the composite generated by the translation of a permanent magnet. (B) Time-lapse fluorescence cross-sectional images of the undulatory surface waves of the composite. The skin layer of the composite was dyed with rhodamine B.

  • Fig. 4 Analysis of fluid flow on the dynamic undulatory composite.

    (A) Schematic diagram of the experimental setup and the planes of interest for the PIV experiment. (B) PIV measurement results for a flow on the dynamic undulatory surface observed along plane 1 and plane 2 as a function of the periodic time (t/T) of the topographical wave with T = 3 s and H = 0.394 mm. (C) (i) Variations of three velocity components of the flow in the x (Vx), y (Vy), and z (Vz) directions at the center (x = 0, y = 0, z = 0) of the undulatory surface during the repeating five T cycles, evaluated from the PIV results, and (ii) mean velocity components averaged from the experimental data during 10 reciprocating cycles. (D) (i and ii) Photographs showing the path lines of tracer particles and (iii) analyzed trajectories of single tracer particle on the undulatory surface along plane 1 (left) and plane 2 (right), which were obtained through PIV velocity field measurements with T = 3 s and H = 0.394 mm.

  • Fig. 5 Analysis of trajectories of bacterial cells on the dynamic undulatory composite.

    (A) Trajectories of E. coli on the (i) static surface and (ii) dynamic undulatory surface. Axes for the two-dimensional observation plane and time legends are noted. (B) X and Y displacements of E. coli cells on the (i and ii) static and (iii and iv) dynamic surfaces. (C) Velocity histogram of E. coli cells on the (i and ii) static and (iii and iv) dynamic surfaces. (D) Moment scaling spectrum (MSS) of representative bacterial trajectories on the static and dynamic surfaces. (E) SMSS/D2 scatter of E. coli trajectories on the static and dynamic surfaces.

  • Fig. 6 Anti-biofilm assay.

    (A) Confocal microscopy images of the stained E. coli cultured (18 hours at 37°C) on the static control and dynamic undulatory composite surfaces with different operation conditions (T and H) of topographical waves: (i) T = ∞ and H = 0, (ii) T = 60 s and H = 0.394 mm, (iii) T = 20 s and H = 0.394 mm, (iv) T = 3 s and H = 0.394 mm, (v) T = 3 s and H = 0.312 mm, and (vi) T = 3 s and H = 0.176 mm. (B) Phase diagram showing different regimes of the CFU counting according to the actuation period (T) and dimple depth (H) of topographical waves. (C) Areal coverages of the live E. coli cultured on the different static and dynamic surfaces. (D) CFUs of the E. coli cultured on the different static and dynamic surfaces (n = 5; ***P < 0.001; data were analyzed by Kruskal-Wallis’ H test).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaax8935/DC1

    Note S1. Theory for magnetic field–induced structural deformations of the magnetoresponsive material

    Note S2. Theory for structure deformation–induced fluid field (fluid-structure interactions)

    Note S3. Characterization of the flow over the undulatory surface

    Fig. S1. A schematic showing the experiment setup together with geometries of the dynamic undulatory composite.

    Fig. S2. FEA for the dynamic undulatory wave under a controlled magnetic field.

    Fig. S3. A schematic illustration describing the terms of depth (H) and period (T) of the topographical wave.

    Fig. S4. FEA of the fluid velocity field and the path lines on the dynamic undulatory composite.

    Fig. S5. Quantitative analysis of bacterial trajectories on the dynamic undulatory composite.

    Fig. S6. FEA of the fluid flow on the dynamic undulatory composite with different wave depth (H) and period (T).

    Fig. S7. Anti-biofilm assays for four different types of surfaces under various static and dynamic conditions.

    Movie S1. Real-time monochromic video recording of undulatory surface waves of the composite generated by the translation of a permanent magnet.

    Movie S2. Real-time fluorescence video recording of undulatory surface waves of the composite generated by the translation of a permanent magnet.

    Movie S3. Real-time video recording of traced E. coli on the static control surface.

    Movie S4. Real-time video recording of traced E. coli on the dynamic undulatory surface.

  • Supplementary Materials

    The PDFset includes:

    • Note S1. Theory for magnetic field–induced structural deformations of the magnetoresponsive material
    • Note S2. Theory for structure deformation–induced fluid field (fluid-structure interactions)
    • Note S3. Characterization of the flow over the undulatory surface
    • Fig. S1. A schematic showing the experiment setup together with geometries of the dynamic undulatory composite.
    • Fig. S2. FEA for the dynamic undulatory wave under a controlled magnetic field.
    • Fig. S3. A schematic illustration describing the terms of depth (H) and period (T) of the topographical wave.
    • Fig. S4. FEA of the fluid velocity field and the path lines on the dynamic undulatory composite.
    • Fig. S5. Quantitative analysis of bacterial trajectories on the dynamic undulatory composite.
    • Fig. S6. FEA of the fluid flow on the dynamic undulatory composite with different wave depth (H) and period (T).
    • Fig. S7. Anti-biofilm assays for four different types of surfaces under various static and dynamic conditions.
    • Legends for movies S1 to S4

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Real-time monochromic video recording of undulatory surface waves of the composite generated by the translation of a permanent magnet.
    • Movie S2 (.avi format). Real-time fluorescence video recording of undulatory surface waves of the composite generated by the translation of a permanent magnet.
    • Movie S3 (.avi format). Real-time video recording of traced E. coli on the static control surface.
    • Movie S4 (.avi format). Real-time video recording of traced E. coli on the dynamic undulatory surface.

    Files in this Data Supplement:

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