Research ArticlePHYSICS

Topological liquid diode

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Science Advances  27 Oct 2017:
Vol. 3, no. 10, eaao3530
DOI: 10.1126/sciadv.aao3530
  • Fig. 1 Design and characterization of liquid diode.

    (A) SEM image of the as-designed liquid diode. (B) Magnified SEM image of U-shaped island arrays with the reentrant cavity on one end. L and D are the length and width of the island, l and d are the length and width of the cavity, and s is the opening width of divergent side-channel. Here, L ~ 150 μm, D ~ 50 μm, l ~ 100 μm, d ~ 30 μm, and s ~ 5 μm. (C) Magnified cross-sectional view of the reentrant structure at the inner wall of the cavity. α is the apex angle of the diverging side-channel, and here, α ~ 2.2°. (D) Optical images of time-dependent directional liquid spreading on liquid diode. A water droplet (~5 μl) deposited on the surface propagates preferentially in the direction toward the opening of the cavities and gets pinned in the reverse direction. The rectification coefficient is 5.76. (E) The normalized plot of time-dependent liquid spreading on liquid diode. (F) Rescaled plot of the data summarized in (E). The droplet in the later stage exhibits a logarithmic slowing-down kinetics as evidenced in the semi-log plot of 1 − Ls/Lsm versus t/τ (inset), where Lsm is the maximum spreading length.

  • Fig. 2 Microscopic spreading dynamics.

    (A) Schematic depiction of the corner flow induced by the side-channels and eventual filling-up of the cavities with reentrant structure. (B) To demonstrate the corner flow, we created two diverging channels using two nonparallel glass slides. As a water droplet containing 0.1-μm fluorescent particles is placed in the mouth of a channel (0 s), the liquid flows fast along all the available corners (indicated by the red arrow) and fills partially the entrance region of the channel. However, as flow continues along the corners, this accumulated liquid is depleted, indicating the role of the corner flow on the liquid transport. (C) Visualization of the time-dependent flow behavior of a water droplet on liquid diode. As the precursor film continues to flow ahead of the primary droplet, the spreading liquid accumulates to form a nearly straight wetting front as a result of contact line pinning of the advancing edge (3.9 ms). Subsequently, the primary droplet coalesces with the precursor film, and the straight edge eventually jumps like an avalanche (7.8 and 15.6 ms), resulting in a fast forward flow. (D) Schematic drawing showing the spreading dynamics of a primary droplet in the forward direction, which consists of pinning of the advancing edge, coalescence, and subsequent hydraulic jump with the precursor film accumulated in the reentrant cavity. The area in green corresponds to the reentrant structure.

  • Fig. 3 Microscopic pinning dynamics and quantification of rectification coefficient.

    (A) SEM images showing the pinning of advancing liquid at the reentrant structure (top). The red lines in the magnified SEM image (below) denote the pinning of the liquid at the reentrant edge. (B) Schematic drawing of the effect of reentrant structure (in green) on the liquid penetration. In conjunction with the concave meniscus in the diverging channel, the advancing edge in the primary droplet fails to coalesce with the precursor liquid. (C) SEM image of the breakdown of the liquid pinning on control surface without the reentrant structure. It is clear that the advancing liquid penetrates the cavity, and the pinning effect is collapsed as depicted by the red dashed line. The inset shows the side view of the cavity with a straight sidewall. (D) Schematic drawing of the flow pathways in spreading and pinning directions. (E) Plot of the rectification coefficient (k) versus R′, the ratio of hydraulic resistances between two different directions. Here, the R′ can be tailored by varying sizes in the cavity length or width. The red triangles indicate a series of surfaces with increasing cavity length (l/L = 1/6, 1/3, 1/2, 2/3, and 5/6), but with constant width (d/D = 3/5), as shown in table S2 and fig. S8A. The blue squares indicate a series of surfaces with increasing cavity width (d/D = 1/5, 3/10, 2/5, 1/2, and 3/5), but with constant length (l/L = 2/3), as shown in table S3 and fig. S8B. (F) Comparison of the transport performances between different surfaces. The blue and green symbols indicate the spreading lengths normalized by the droplet radius at the spreading direction and pinning direction, respectively. The red symbol denotes the rectification coefficient (k) on different designs. The inset images present the optical image of spreading drops on the respective surfaces.

  • Fig. 4 Generality of the liquid diode.

    (A) Comparison of transport performances among different surfaces. The green area and the blue area indicate the surfaces with wettability gradients and asymmetric geometries, respectively (see fig. S12). The red triangle denotes the unidirectional liquid transport on the natural peristome of a pitcher plant. The red circle represents the as-designed liquid diode. (B) Continuous and directional water transportation on surfaces with circular and spiral pathways. (C) Variation of the rectification coefficient under different temperature gradients, showing the stability of the directional liquid transport. (D) Generality of directional liquid transport for all kinds of liquids. The liquid diode exhibits a high rectification coefficient for low–surface tension liquid, such as hexane, and high-viscosity liquid, such as ethylene glycol.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/eaao3530/DC1

    section S1. Characterization of microscopic spreading behavior of the precursor on liquid diodes

    section S2. Comparison of liquid pinning behavior on liquid diode and control surfaces

    section S3. Flow hydraulic resistance analysis

    section S4. Characterization of macroscopic spreading dynamics on control surfaces

    section S5. Comparison of liquid self-transportation on various surfaces

    section S6. Temperature gradient effect on the liquid diode

    fig. S1. Sample fabrication.

    fig. S2. Characterization of precursor film and water droplet spreading velocity.

    fig. S3. Selected snapshots showing the microscopic wetting dynamics on the liquid diode.

    fig. S4. Representative SEM images showing the liquid pinning rendered by the reentrant structure.

    fig. S5. Selected snapshots showing the pinning dynamics of water on the liquid diode.

    fig. S6. Selected snapshots showing the breakdown of pinning on the control surface without the presence of a reentrant feature.

    fig. S7. Schematic diagrams showing the flow pathways on the control surface without the presence of a cavity.

    fig. S8. Effects of structural topography on the flow resistance parameter R′.

    fig. S9. Effects of structural topography on the rectification coefficient k.

    fig. S10. SEM characterization of control surfaces.

    fig. S11. Spreading dynamics on the control surfaces.

    fig. S12. Comparison of transport performances among different surfaces.

    fig. S13. Effect of temperature gradient on the directional transport.

    table S1. Structural parameters of the liquid diode and control surfaces.

    table S2. Structural parameters of liquid diodes with varying sizes in cavity length.

    table S3. Structural parameters of liquid diodes with varying sizes in cavity width.

    table S4. Physical and chemical properties of tested liquids.

    movie S1. Unidirectional spreading of a single water droplet.

    movie S2. Microscopic wetting dynamics on the liquid diode.

    movie S3. Corner flow in the divergent channel.

    movie S4. Hydraulic jump mechanism on the liquid diode.

    movie S5. Directed water transportation on circular surface.

    movie S6. Directed water transportation on spiral surface.

  • Supplementary Materials

    This PDF file includes:

    • section S1. Characterization of microscopic spreading behavior of the precursor on liquid diodes
    • section S2. Comparison of liquid pinning behavior on liquid diode and control surfaces
    • section S3. Flow hydraulic resistance analysis
    • section S4. Characterization of macroscopic spreading dynamics on control surfaces
    • section S5. Comparison of liquid self-transportation on various surfaces
    • section S6. Temperature gradient effect on the liquid diode
    • fig. S1. Sample fabrication.
    • fig. S2. Characterization of precursor film and water droplet spreading velocity.
    • fig. S3. Selected snapshots showing the microscopic wetting dynamics on the liquid diode.
    • fig. S4. Representative SEM images showing the liquid pinning rendered by the reentrant structure.
    • fig. S5. Selected snapshots showing the pinning dynamics of water on the liquid diode.
    • fig. S6. Selected snapshots showing the breakdown of pinning on the control surface without the presence of a reentrant feature.
    • fig. S7. Schematic diagrams showing the flow pathways on the control surface without the presence of a cavity.
    • fig. S8. Effects of structural topography on the flow resistance parameter R′.
    • fig. S9. Effects of structural topography on the rectification coefficient k.
    • fig. S10. SEM characterization of control surfaces.
    • fig. S11. Spreading dynamics on the control surfaces.
    • fig. S12. Comparison of transport performances among different surfaces.
    • fig. S13. Effect of temperature gradient on the directional transport.
    • table S1. Structural parameters of the liquid diode and control surfaces.
    • table S2. Structural parameters of liquid diodes with varying sizes in cavity length.
    • table S3. Structural parameters of liquid diodes with varying sizes in cavity width.
    • table S4. Physical and chemical properties of tested liquids.
    • Legends for movies S1 to S6

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.avi fomat). Unidirectional spreading of a single water droplet.
    • movie S2 (.avi fomat). Microscopic wetting dynamics on the liquid diode.
    • movie S3 (.avi fomat). Corner flow in the divergent channel.
    • movie S4 (.avi fomat). Hydraulic jump mechanism on the liquid diode.
    • movie S5 (.avi fomat). Directed water transportation on circular surface.
    • movie S6 (.avi fomat). Directed water transportation on spiral surface.

    Files in this Data Supplement:

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