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Spontaneous droplet trampolining on rigid superhydrophobic surfaces

Nature volume 527, pages 82–85 (2015)Cite this article

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Abstract

Spontaneous removal of condensed matter from surfaces is exploited in nature and in a broad range of technologies to achieve self-cleaning1,2, anti-icing3,4,5,6 and condensation control7,8. But despite much progress5,6,7,9,10,11,12,13,14, our understanding of the phenomena leading to such behaviour remains incomplete, which makes it challenging to rationally design surfaces that benefit from its manifestation15,16,17,18. Here we show that water droplets resting on superhydrophobic textured surfaces in a low-pressure environment can self-remove through sudden spontaneous levitation and subsequent trampoline-like bouncing behaviour, in which sequential collisions with the surface accelerate the droplets. These collisions have restitution coefficients (ratios of relative speeds after and before collision) greater than unity19 despite complete rigidity of the surface, and thus seemingly violate the second law of thermodynamics. However, these restitution coefficients result from an overpressure beneath the droplet produced by fast droplet vaporization while substrate adhesion and surface texture restrict vapour flow. We also show that the high vaporization rates experienced by the droplets and the associated cooling can result in freezing from a supercooled state20,21 that triggers a sudden increase in vaporization, which in turn boosts the levitation process. This effect can spontaneously remove surface icing by lifting away icy drops the moment they freeze. Although these observations are relevant only to systems in a low-pressure environment, they show how surface texturing can produce droplet–surface interactions that prohibit liquid and freezing water-droplet retention on surfaces.

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Figure 1: Droplet trampolining on a rigid surface.
Figure 2: Vaporization can accelerate droplet recoil.
Figure 3: The effect of microtexture on droplet impact and trampolining dynamics in a low-pressure environment.
Figure 4: Freezing can trigger spontaneous droplet launching from a wide range of materials and microtextures.

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Acknowledgements

T.M.S. acknowledges the ETH Zurich Postdoctoral Fellowship Program and the Marie Curie Actions for People COFUND programme (FEL-14 13-1). Partial support of the Swiss National Science Foundation under grant number 200021_135479 is also acknowledged. We thank L. J. Yi for his participation in the trampoline experiment, U. Drechsler for advice on surface fabrication and J. Vidic and B. Kramer for assistance in chamber construction.

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Author notes

  1. Thomas M. Schutzius and Stefan Jung: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical and Process Engineering, Laboratory of Thermodynamics in Emerging Technologies, ETH Zurich, 8092, Zurich, Switzerland

    Thomas M. Schutzius, Stefan Jung, Tanmoy Maitra, Gustav Graeber, Moritz Köhme & Dimos Poulikakos

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  1. Thomas M. Schutzius
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Contributions

T.M.S., S.J. and D.P. conceived the project and planned the experiments. T.M., G.G. and T.M.S. fabricated the samples. T.M.S., S.J., G.G. and M.K. carried out the experiments. T.M.S., S.J. and D.P. analysed the data and developed the theoretical analysis. T.M.S., S.J. and D.P. wrote the paper. All authors proofread the paper, made comments and approved the manuscript.

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Correspondence to Dimos Poulikakos.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Schematic idealizing the droplet trampolining phenomenon as a hybrid MSD–projectile system.

MSD and projectile motion apply when y < 0 and y ≥ 0, respectively. The variables are mass m, droplet ‘stiffness’ k, damping coefficient c, initial droplet velocity v0, droplet impact velocity v1 and droplet recoil velocity v2; f(t) is the forcing function. The horizontal dashed line indicates where y is zero.

Extended Data Figure 2 Comparing experimental and theoretical results for droplet trampolining.

Quantities plotted are dimensionless. a, Plot of y as a function of t for experimental (blue circles) and theoretical (black line) cases. Inset, the droplet at the moment of impact (note that it is non-spherical). b, The applied force f required to generate the theoretical solutions in a as a function of time t. The magnitude of this force was determined iteratively by matching the value of ε from the theory with that from the corresponding experiments. The impact properties for the droplet shown in a are Bo = mg/σR0 = 0.42 and v1 = −0.5R0/τ (first impact). The properties of the superhydrophobic surface were [d, l, h] = [1.4, 6.5, 4.8] μm.

Extended Data Figure 3 Determining the damping ratio ζ for droplets impacting superhydrophobic surfaces under standard pressure conditions.

a, b, Plots of −v1τ/R0 versus ε (a) and ζ (b) as determined from experiments on superhydrophobic surfaces. Square symbols represent experiments performed in this work (advancing and receding contact angles , ; [d, l, h] = [1.5, 6.5, 13.3] μm); errors represent the standard deviation of the measurement and triangles are experimental data from ref. 19 ( and ). In a, the dashed green line represents the theoretical upper limit for ε for droplet impact (); the solid black line is the average value of ε from the experiments performed in this study. In b, the solid black and dashed green lines represent the average values of ζ obtained from experiments in this study and the theoretical lower limit of ζ, respectively. The theoretical lower limit is estimated with using and tc/τ = 1.09 (ref. 19). Error bars in the plots represent measurement uncertainty.

Extended Data Figure 4 The role of environmental pressure on the contact time of a droplet with a superhydrophobic substrate for a single impact cycle.

Plot of droplet–substrate contact time tc/τ versus −v1τ/R0 for water droplets impacting a superhydrophobic surface with a wetting fraction of ϕ = 0.04 under low-pressure (circles) and standard-pressure (squares) conditions. The properties of the superhydrophobic surfaces were [d, l, h] = [1.5, 6.5, 13.3] μm (squares) and [d, l, h] = [1.4, 6.5, 4.8] μm (circles). The horizontal dashed line denotes the so-called minimum contact time tc/τ ≈ 1.09. Error bars in the plots represent measurement uncertainty.

Extended Data Figure 5 Spreading behaviour of a water droplet.

Plot of Rmax/R0 versus −v1τ/R0 for droplets impacting onto a superhydrophobic surface in a low-pressure, low-humidity environment. The properties of the superhydrophobic surface were [d, l, h] = [1.4, 6.5, 4.8] μm. Error bars in the plots represent measurement uncertainty.

Extended Data Figure 6 The role of environmental pressure on the vaporization flux of a water droplet in a low-humidity environment.

Plot of vaporization flux J versus environmental pressure P for a millimetre-scale water droplet in contact with a superhydrophobic surface. The properties of the surface used were [d, l, h] = [1.4, 6.5, 18.2] μm. Error bars for P and J represent the uncertainty of the measurement and s.d., respectively. Each data point is the average of five measurements.

Extended Data Figure 7 Exploiting trampolining dynamics with a cantilever.

a, Overlaid image sequence (20 ms between the two images) of a droplet attached to a cantilever beam of length L exploiting droplet trampolining to create mechanical motion. b, Plot of beam deflection δ as a function of t for a similar sequence to that in a. See Supplementary Video 5 for further details. The properties of the surface used were [d, l, h] = [1.5, 6.5, 13.3] μm.

Extended Data Figure 8 Schematic showing the environmental chamber used throughout the study.

We generated dry conditions in the chamber with nitrogen (N2), and the pressure was reduced with a vacuum pump. The front and back of the chamber were equipped with transparent windows that were removable to facilitate placement of substrates and droplets. The coordinates XC, YC and ZC are denoted by blue, red and green, respectively.

Extended Data Table 1 Experimental details on the engineered surfaces used in this study
Full size table
Extended Data Table 2 Experimental probability of ice levitation as a function of droplet size on the CNF–PMC coating under dry, low-pressure conditions for an environment at room temperature
Full size table

Related audio

Supplementary information

Determining the environmental pressure for which droplet trampolining occurs for a water droplet

The superhydrophobic silicon micropillar surface had the following properties: [d,l,h] = [1.6,6.5,3.5] μm. Also shown is the trampolining dynamics for a relatively large droplet. The uncertainty in environmental pressure is 0.02 bar. (MP4 10609 kb)

Video sequences of a water droplet and a person trampolining on rigid and deformable surfaces, respectively

The two cases had the following properties: For the droplet, R0 = 9⋅10-4 m; m ≈ 3⋅10-6 kg; σ = 0.072 N m-1; for the person, the height is 2L ≈ 1.7 m; m ≈ 65 . In the former case, the surface is superhydrophobic with a liquid-solid area wetting fraction of ϕ = 0.04, and the dynamics are taking place in a dry, low-pressure environment (approximately 0.01 bar). Also shown is a quantitative plot of dimensionless vertical position vs. time for the droplet and person with the length and time scales adjusted to show the similarities between the two cases. Droplet and human dynamics were filmed and played back at frame rates of 5,000 & 50 s-1 and 25 & 11.9 s-1, respectively. The superhydrophobic surface used had the following properties: [d,l,h] = [1.4,6.5,4.8] μm. (MP4 18762 kb)

High-speed videos comparing the effect of environmental pressure (approximately 0.01 and 1.0 bar; dry conditions) on the process of a droplet impacting (ν1= -0.9(R0/τ)) onto a superhydrophobic surface (ϕ = 0.04).

The videos of dynamics occurring under low pressure and standard pressure conditions were filmed and played back at frame rates of 5,000 & 12.9 s-1, respectively. The droplet radii were R0 ≈ 0.09 cm. The superhydrophobic surface used had the following properties: [d,l,h] = [1.4,6.5,4.8] μm. (MP4 1359 kb)

High-speed video comparing the effect of environmental pressure (approximately 0.01 and 1.0 bar; dry conditions) on the rebound process of a droplet impacting (ν1= -0.6(R0/τ)) onto a superhydrophobic surface (ϕ = 0.04)

The drop sizes were R0 ≈ 0.09 cm cm. Both processes were recorded with a frame rate of 50,000 s-1 and they are played back with a rate of 29.97 s-1. The superhydrophobic surface used had the following properties: [d,l,h] = [1.4,6.5,4.8] μm. (MP4 4044 kb)

High-speed video demonstrating how the previously observed droplet trampoline dynamics can drive continuous motion of a cantilever beam

The superhydrophobic surface has (ϕ = 0.04) , the environment is dry. Also shown is the beam dynamics with and without a droplet in a low and ambient pressure environment. Finally, the video shows one half-cycle of the beam oscillation with relatively high temporal resolution, demonstrating the power of vaporization in driving the dewetting process. The superhydrophobic surface used had the following properties: [d,l,h] = [1.5,6.5,13.3] μm. (MP4 18261 kb)

Dynamics of a water/acetone droplet (70/30 wt. ratio) on a superhydrophobic silicon micropillar surface under low-pressure environmental conditions

The superhydrophobic silicon micropillar surface had the following properties: [d,l,h] = [1.6,6.5,3.5] μm. Under these conditions, after the droplet dewets the substrate, it can no longer make contact with it and sustain bouncing indicating that the vaporization flux is high enough to support a Leidenfrost state. The uncertainty in environmental pressure is 0.02 bar. (MP4 5110 kb)

High-speed video demonstrating how the sudden heat release associated recalescence freezing can drive a vaporization process —in addition to that already occurring due to the low-pressure and room temperature environment— which results in spontaneous de-wetting (in this case launching) of the liquid/solid droplet from the silicon-based, micropillar superhydrophobic surface (R0 ≈ 0.05 cm)

The video was recorded at a frame rate of 2,000 s-1 and it is played back at a rate of 30 s-1 (~67x slower). The superhydrophobic surface used had the following properties: [d,l,h] = [2.0,4.6,13.5] μm. (MP4 566 kb)

High-speed video demonstrating how the sudden heat release associated recalescence freezing can drive a vaporization process —in addition to that already occurring due to the low-pressure and room temperature environment— which results in spontaneous de-wetting of the liquid/solid droplet from the aluminum-based superhydrophobic surface

The video was recorded at a frame rate of 5,000 s-1 and the playback rate is 10 s-1 (500x slower). (MP4 6421 kb)

Synchronized optical (frame rate: 4,000 s-1) and thermographic (frame rate: 1,253 s-1) high-speed videos of a water droplet freezing and levitating on a superhydrophobic polymer nanocomposite surface (PMC-CNF)

The optical and thermographic videos are played back at a rate of 25.5 s-1 (~157x slower) and 8.0 s-1 (~157x slower) for the first sequence. In the second sequence both videos are played back ~six times slower than the first sequence (~1000x slower). (MP4 7557 kb)

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Schutzius, T., Jung, S., Maitra, T. et al. Spontaneous droplet trampolining on rigid superhydrophobic surfaces. Nature 527, 82–85 (2015). https://doi.org/10.1038/nature15738

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