Research ArticleAPPLIED SCIENCES AND ENGINEERING

Coalescence-induced jumping of droplets on superomniphobic surfaces with macrotexture

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Science Advances  09 Nov 2018:
Vol. 4, no. 11, eaau3488
DOI: 10.1126/sciadv.aau3488
  • Fig. 1 Coalescence-induced self-propulsion with and without a ridge.

    (A) Schematic of the experimental setup used to study the coalescence-induced self-propulsion of liquid droplets. The inset shows the ridge height hr. A series of snapshots showing the coalescence-induced self-propulsion of water droplets (R0 ≈ 600 μm) on superomniphobic surfaces (B) without a ridge (experimental), (C) without a ridge (numerical), (D) with a ridge (experimental), and (E) with a ridge (numerical). In (D) and (E), the ridge height hr ≈ 500 μm. Time difference between the experimental snapshots and the corresponding numerical snapshots is <0.2 ms (also see movies S1 and S2).

  • Fig. 2 Droplet dynamics without a ridge.

    (A) Evolution of the nondimensional excess surface energy (E*surf,ex) and the nondimensional upward kinetic energy (E*kin,up) during the coalescence of water droplets (R0 ≈ 600 μm) on a superomniphobic surface without a ridge. The inset shows the coordinate system. The three stages (I, II, and III) of coalescence are shown with different colors. (B to F) A series of snapshots showing the pressure distribution and velocity vectors within the droplet on a superomniphobic surface without a ridge. The colors represent the magnitude of pressure and velocity. The dotted orange arrows at droplet periphery indicate the direction of droplet deformation (also see movie S3).

  • Fig. 3 Droplet dynamics with a ridge.

    (A) Evolution of the nondimensional excess surface energy (E*surf,ex) and the nondimensional upward kinetic energy (E*kin,up) during the coalescence of water droplets (R0 ≈ 600 μm) on a superomniphobic surface with a ridge (ridge height hr ≈ 500 μm). The inset shows the coordinate system. The three stages (I, II, and III) of coalescence are shown with different colors. (B to F) A series of snapshots showing the pressure distribution and velocity vectors within the droplet on a superomniphobic surface with a ridge. The colors represent the magnitude of pressure and velocity. The dotted orange arrows at droplet periphery indicate the direction of droplet deformation (also see movie S3).

  • Fig. 4 Coalescence-induced self-propulsion of low–surface tension and high-viscosity droplets.

    A series of snapshots showing the coalescence-induced self-propulsion of n-tetradecane droplets (R0 ≈ 480 μm and γlv ≈ 26.6 mN m−1) on a superomniphobic surface with a ridge— (A) experimental and (B) numerical (also see movie S4). A series of snapshots showing the coalescence-induced self-propulsion of water + 90% glycerol droplets (R0 ≈ 480 μm and μ ≈ 220 mPa·s) on a superomniphobic surface with a ridge—(C) experimental and (D) numerical (also see movie S5).

  • Fig. 5 Jumping velocity of coalescing droplets with and without a ridge.

    (A) Jumping velocity of droplets with different radii on superomniphobic surfaces with different ridge heights (data from numerical simulations). (B) Both numerical and experimental data collapse onto a single nondimensional straight line of Weber number at droplet departure (or jumping) versus nondimensional ridge height, in accordance with Eq. 3. Error bars in the experimental data represent the error associated with velocity, droplet radius, and ridge height measurements.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau3488/DC1

    Supplementary Text

    Fig. S1. Morphology of the superomniphobic ridge.

    Fig. S2. Computational domain.

    Fig. S3. Components of the total kinetic energy.

    Fig. S4. Velocity vectors and pressure distribution (yz view).

    Fig. S5. Coalescence-induced jumping of smaller droplets.

    Fig. S6. Coalescence of low–surface tension and high-viscosity droplets.

    Fig. S7. Schematic of a superrepellent surface with periodic arrangement of triangular ridges.

    Fig. S8. Schematic of two coalescing droplets and a ridge with maximum ridge angle.

    Fig. S9. Schematic depicting the influence of nondimensional ridge height h* on the maximum ridge angle αmax.

    Table S1. Density, viscosity, surface tension, apparent advancing contact angle, apparent receding contact angle, and roll-off angle of test liquids on superomniphobic surfaces.

    Table S2. Influence of the ridge angle α on the energy conversion efficiency η in coalescence-induced jumping of droplets with radius R0 = 600 μm at different nondimensional ridge heights h*.

    Movie S1. This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets of water (R0 ≈ 600 μm) on a superomniphobic surface without a ridge.

    Movie S2. This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets of water (R0 ≈ 600 μm) on a superomniphobic surface with a ridge (ridge height hr ≈ 500 μm).

    Movie S3. This video illustrates the evolution of the velocity vectors within two droplets of water (R0 ≈ 600 μm) during their coalescence on a superomniphobic surface with and without a ridge.

    Movie S4. This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets (R0 ≈ 480 μm) of a low–surface tension liquid (n-tetradecane with γlv ≈ 26.6 mN m−1) on a superomniphobic surface with a ridge.

    Movie S5. This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets (R0 ≈ 480 μm) of a high-viscosity liquid (water + 90% glycerol with μ ≈ 220 mPa·s) on a superomniphobic surface with a ridge.

    Movie S6. This video illustrates the coalescence of two low–surface tension droplets (n-tetradecane with γlv ≈ 26.6 mN m−1 and R0 ≈ 480 μm) and two high-viscosity droplets (water + 90% glycerol with μ ≈ 220 mPa·s and R0 ≈ 480 μm) on a superomniphobic surface without a ridge.

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Text
    • Fig. S1. Morphology of the superomniphobic ridge.
    • Fig. S2. Computational domain.
    • Fig. S3. Components of the total kinetic energy.
    • Fig. S4. Velocity vectors and pressure distribution (yz view).
    • Fig. S5. Coalescence-induced jumping of smaller droplets.
    • Fig. S6. Coalescence of low–surface tension and high-viscosity droplets.
    • Fig. S7. Schematic of a superrepellent surface with periodic arrangement of triangular ridges.
    • Fig. S8. Schematic of two coalescing droplets and a ridge with maximum ridge angle.
    • Fig. S9. Schematic depicting the influence of nondimensional ridge height h* on the maximum ridge angle αmax.
    • Table S1. Density, viscosity, surface tension, apparent advancing contact angle, apparent receding contact angle, and roll-off angle of test liquids on superomniphobic surfaces.
    • Table S2. Influence of the ridge angle α on the energy conversion efficiency η in coalescence-induced jumping of droplets with radius R0 = 600 μm at different nondimensional ridge heights h*.
    • Legends for movies S1 to S6.

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets of water (R0 ≈ 600 μm) on a superomniphobic surface without a ridge.
    • Movie S2 (.mp4 format). This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets of water (R0 ≈ 600 μm) on a superomniphobic surface with a ridge (ridge height hr ≈ 500 μm).
    • Movie S3 (.mp4 format). This video illustrates the evolution of the velocity vectors within two droplets of water (R0 ≈ 600 μm) during their coalescence on a superomniphobic surface with and without a ridge.
    • Movie S4 (.mp4 format). This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets (R0 ≈ 480 μm) of a low–surface tension liquid (n-tetradecane with γlv ≈ 26.6 mN m−1) on a superomniphobic surface with a ridge.
    • Movie S5 (.mp4 format). This video illustrates (experimentally and numerically) the coalescence-induced self-propulsion of two droplets (R0 ≈ 480 μm) of a high-viscosity liquid (water + 90% glycerol with μ ≈ 220 mPa·s) on a superomniphobic surface with a ridge.
    • Movie S6 (.mp4 format). This video illustrates the coalescence of two low–surface tension droplets (n-tetradecane with γlv ≈ 26.6 mN m−1 and R0 ≈ 480 μm) and two high-viscosity droplets (water + 90% glycerol with μ ≈ 220 mPa·s and R0 ≈ 480 μm) on a superomniphobic surface without a ridge.

    Files in this Data Supplement:

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