Drop Rebound after Impact: The Role of the Receding Contact Angle

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Drop rebound after impact: the role of receding contact angle Carlo Antonini, Fabio Villa, Ilaria Bernagozzi, Alidad Amirfazli, and Marco Marengo Langmuir, Just Accepted Manuscript • DOI: 10.1021/la4012372 • Publication Date (Web): 19 Aug 2013 Downloaded from http://pubs.acs.org on August 22, 2013

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Drop rebound after impact:

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the role of receding contact angle

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C. Antonini1,2*, F. Villa1, I. Bernagozzi1, A. Amirfazli3, M. Marengo1*

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Department of Engineering, University of Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italy.

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Laboratory of Thermodynamics in Emerging Technologies, Mechanical and Process Engineering Department, ETH Zurich , Sonneggstrasse 3, 8092 Zurich, Switzerland.

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Department of Mechanical Engineering, York University, Toronto, ON, M3J 13P, Canada. *Corresponding authors: [email protected], [email protected]

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Abstract

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Data from literature suggest that rebound of a drop from a surface can be achieved when wettability is low, i.e.

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when contact angles, measured at the triple line (solid-liquid-air), are high. However, no clear criterion exists to

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predict when a drop will rebound from a surface, and which is the key wetting parameter to govern drop re-

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bound, e.g. the “equilibrium” contact angle, θ eq , the advancing or the receding contact angles, θ A and θ R , re-

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spectively, the contact angle hysteresis, ∆θ , or any combination of these parameters. In order to clarify the

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conditions for drop rebound, we conducted experimental tests on different dry solid surfaces with variable

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wettability, from hydrophobic to superhydrophobic surfaces, with advancing contact angles 108° < θ A < 169° ,

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and receding contact angles 89° < θ R < 161° . It was found that receding contact angle is the key wetting parame-

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ter that influences drop rebound, along with surface hydrophobicity: in the investigated impact conditions

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(drop diameter 2.4 < D0 < 2.6 mm , impact speed 0.8 < V < 4.1 m/s , Weber number 25 < We < 585 ), rebound was

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observed only on surfaces with receding contact angle higher than 100°. Also, drop rebound time decreased by

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increasing receding contact angle. It was also shown that in general care must be taken when using statically

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defined wetting parameters (such as advancing and receding contact angles) to predict dynamic behavior of a

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liquid on a solid surface, since the dynamics of the phenomenon may affect surface wetting close to the impact

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point (e.g. due to transition from Cassie-Baxter to Wenzel state, in case of the so called-superhydrophobic sur-

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faces) and thus affect drop rebound.

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Introduction

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Water repellency of natural and artificial superhydrophobic surfaces (SHS) has been increasingly attracting the

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scientific and industrial communities in the last years. The static and dynamic behavior of water on water repel-

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lant surfaces is on one hand a multidisciplinary scientific challenge straddling fluid mechanics and physical

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chemistry. On the other hand, understanding drop behavior on SHS offers potential solutions in many fields,

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where predicting and/or controlling water collection due to impacting drops is required. For example, use of

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water repellant surfaces would be useful in icing conditions, where otherwise impacted drops may stick to the

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surface and freeze, causing ice accretion1.

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The property of “superhydrophobicity” is traditionally attributed to surfaces with high contact angles (>150°)

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and low contact angle hysteresis ( 0 , otherwise drop will remain at-

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tached to the surface. Using Eq. 1, it was concluded that drop rebound can be observed for equilibrium contact

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angles higher than 90°, and the tendency of drop rebound increases as the maximum spread increases (e.g. by

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increasing impact speed, V ), and when the contact angle increases.

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Drop rebound time18 (i.e. time between impact and rebound instants, also referred to in literature as residence

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time19 or contact time8) on SHS was found by Quéré and co-workers8-9 to be and function of drop mass, m , and

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liquid surface tension, σ , and independent from impact speed, V :

(

t R = 2.6 ρ D03 8σ

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)

(2)

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where ρ is density, and D0 drop initial diameter. The value of rebound time is close to the first-order vibra-

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tion period of a freely oscillating drop20, the so called Rayleigh time:

tRayleigh = π

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(

2 ρ D03 8σ

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)

(3)

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the only difference being the numerical pre-factor. The similarity between rebound and Rayleigh time was first

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reported by Watchers and Westerling19 for the case of drop impacting on a hot surface in Leidenfrost condi-

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tions. Page 6 of 21


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In Ref. 11, Rioboo et al. proposed a schematic drop impact regime map, identifying four different outcomes: deposition, rebound, sticking, and fragmentation. For the specific system analyzed (water drops on superhydrophobic polypropylene surface), the transition from rebound to fragmentation was found to be governed by 2

Weber number, We = ρV D0

σ ; the threshold value between two regimes was found to be We ≈ 60 . For

the deposition-rebound limit, it was experimentally observed11 that the transition does not only depend on the Weber number, but also on two wetting parameters: the average contact angle, θ AV , defined as the average between advancing, θ A , and receding, θ R , contact angles (measured expanding and contracting quasistatically the volume of sessile drop on a horizontal surface21), and the contact angle hysteresis, ∆ θ . This was an important result, which stressed the need to characterize a surface by means of advancing and receding contact angles (as already discussed in a previous study by Šikalo et al.22), and as the study tried to correlate wetting parameters to drop impact dynamics. The interested reader may refer to Refs. 23 and 24 to further appreciate the importance of wettability characterization, and in particular why it is more appropriate to provide a range for the contact angles (i.e. provide advancing and receding contact angles), rather than a single value of the contact angle. Li et al.14 investigated the effect of surface texturing on the receding phase and thus drop contact time. Through tests performed on textured silicon surfaces, decorated by square arrays of pillars with different geometries, they showed that surface texture has a direct effect on receding contact angle, thus modifying retraction dynamics and, in case of rebound, drop rebound time.

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Very recently, Duvivier et al.25 performed impact tests of different ferroﬂuid drops on superhydrophobic surfaces in a magnetic field, to simulate changes of the gravitational acceleration g, and proposed a rebound map based on a combination of Weber, Reynolds, and Bond numbers. With respect to the available literature on drop rebound, the present study expands our understanding of surface wetting, and in particular the role of the receding contact angle, θ R , for drop rebound. Results for drop impact on several hydrophobic and superhydrophobic dry surfaces are presented.

Defining superhydrophobicity As mentioned above, the generally stated definition of superhydrophobicity considers surfaces with contact angles (both θ A and θ R ) higher than 150° and ∆θ < 10° . Contact angles provide a measure of surface “repellency”21, whereas hysteresis provides an indication of drop “mobility”. Nonetheless, the above reported definition for superhydrophobicity is somewhat arbitrary and, taken literally, may be misleading. As an example, should a surface with θ A = 180° and θ R = 160° not be considered SHS, only due to a relatively high hysteresis (i.e., ∆θ = 20° )? If one agrees that advancing and receding contact angles are probably the most significant parameters to quantitatively characterize surface wettability, then a general definition of superhydrophobicity should be founded on a more rational basis. Superhydrophobicity is achieved thanks to the so-called Cassie-Baxter wetting state, in which gas pockets are present at the liquid-solid interface, thus reducing the contact between the liquid (in our case, water) and the solid substrate. Differently, in the Wenzel state, the liquid completely wets the solid substrate, and mobility is typically low. By studying the stability of Cassie-Baxter and Wenzel wetting state for pillar-like structures on the Page 8 of 21


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basis of the thermodynamic principle of energy minimization, it was shown in Ref. 26 that the minimum value of the receding contact angle for the investigated pillar structures is θ R ,min = 138.6° . Although such limit applies to a specific structures and, in principle, does not hold for other complex micro- and nano-structured topography, this theoretical value is very close to 135°, a limit that was proposed recently by Rioboo et al. 27 on the basis of their experimental results. Driven by the need to define a better criterion for superhydrophobicity, Rioboo et al. 27 proposed a new methodology based on controlled drop slide on a horizontal surface. The authors found that only when the receding contact angle is above 135° the drop slides and introduce an index of superhydrophobicity (SHI), corresponding to the percentage of the total number of receding static contact angles greater than 135°, taken during one sliding experiment on a given fixed length. Based on the above discussed experimental27 and theoretical26 results, we decided to use the value of 135° as threshold for superhydrophobicity in the present paper, as one can find a more rational basis than the conventionally reported value of 150°. As a consequence, all surfaces with a receding contact angle higher than 135° will be labeled as SHS, irrespective of contact angle hysteresis value.

Materials and Methods Eight surfaces with different wetting parameters were produced, characterized by means of sessile drop method (i.e. measuring the advancing, θ A , and receding, θ R , contact angles on a horizontal surface) and tested in drop impact experiments. The tested samples were named as following: (i) A1-Teflon, (ii) A2-Teflon; (iii) B1-PP; (iv) B2-PP, (v) SHS-FAS, (vi) SHS-Teflon, (vii) SHS-CNR1, (viii) SHS-CNR2. Surfaces (i) to (iv) were hydrophobic surfaces (with roughness ranging from 0.9 to 433 nm), whereas surfaces (v) to (viii) were textured superhydrophobic surfaces (roughness ~1-5μm) – see Table 1 for details. Surfaces (i) and (ii) were Teflon coated glasses, page 9 of 21


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and surfaces (iii) and (iv) were thin polypropylene layers deposited on glass, which served as rigid substrates (more details of surfaces (i) to (iv) can be found here28). SHS-FAS was fabricated by means of a one-step wet reaction, by treating an aluminum sample in a water solution of sodium hydroxide and perfluoroctyltriethoxysilane (FAS)29. SHS-Teflon was fabricated on an aluminum substrate by aluminum etching in acid solution (to achieve the desired surface roughness) and subsequent spraying with Teflon® (10:1 v/v solution of FC-75 and Teflon® from DuPont™)30. Surfaces (vii) and (viii) were produced and supplied by ISTEC CNR (Italy) and were tested as received (no details on surface fabrication were provided due to confidentiality). Values of advancing and receding contact angles, and their difference (contact angle hysteresis, ∆ θ ), are illustrated in Figure 2: surface advancing contact angles are in the range 108° < θ A < 169° , and receding contact angles in the range

89° < θ R < 161° . Note that SHS-Teflon ( θR < 145° , ∆θ = 15° ) is included among SHS, according to the definition for superhydrophobicity discussed above. A typical experimental apparatus for drop impact studies was used, in which a drop is generated at the tip of a needle, then is accelerated by gravity and impacts onto the dry solid surface. Experimental conditions were: impact speed in the range 0.8 < V < 4.1 m/s , drop diameter 2.4 < D0 < 2.6 mm , Weber numbers in the range

25 < We < 585 , and Ohnesorge number, Oh = µ

ρσ D0 , in the range 0.0023 < Oh < 0.0024 . Images of

drop impact were recorded using a high-speed camera (PCO 1200-hs), with a typical frame rate of 1015 fps and pixel resolution of 35 μm/pixel (all this visualization parameters represent the best compromise between spatial and temporal resolution, and field of view). Tests were repeated at least ten times for each condition to establish reproducibility. Images were manually analyzed to identify the drop impact outcome and eventually measure drop rebound time, in case rebound occurs. Rebound time was measured manually, since the presPage 10 of 21


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ence of prompt splash and/or break-up, characterized by secondary drop ejection (which occurs in the majority of tested cases, especially for SHS), did not allow the use of automatic measurement systems. Table 1: Surface roughness for all tested samples. For surfaces (i) to (iv), i.e. smooth hydrophobic surfaces, the rms surface 28

roughness, Rq, was measured using Atomic Force Microscope MFP-3D (Asylum Research) . For surfaces (v) to (viii), i.e. superhydrophobic surfaces, the reported value corresponds to the mean surface roughness, Ra, measured using a roughness meter (Diavite DH-5, resolution 0.01 μm).

i ii iii iv v vi vii viii

Figure 2: Advancing,

Surface A1-Teflon A2-Teflon B1-PP B2-PP SHS-FAS SHS-Teflon SHS-CNR1 SHS-CNR2

Roughness 0.9 nm 433 nm 8.9 nm 34.7 nm 1.08 μm 1.91 μm 2.42 μm 4.56 μm

θ A , and receding contact angles, θ R , and contact angle hysteresis ( ∆ θ page 11 of 21


) for all tested samples.

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Results and Discussion Water drop impact tests showed that complete drop rebound occurs on the following surfaces: A1-Teflon, A2Teflon, SHS-FAS, SHS-Teflon, SHS-CNR1 and SHS-CNR2. Drops never rebounded on B1-PP and B2-PP. Figure 3a illustrates time evolution of the spread factor, ξ ( t ) = D ( t ) D0 (i.e. the contact diameter, made nondimensional using initial drop diameter) for four tested samples. For Figure 3a, test conditions were:

V = 1.0m/s , D0 = 2.5mm , and We = 33 . In the initial stages ( t < 2.5 ms ), spreading was dominated by inertia, and solid surface wettability did not play any role. In the final stages of spreading, however, contact line speed decreased to zero and the effect of wettability become apparent. As an example, on A2-Teflon (Δθ=13°) contact angle hysteresis was lower than that of B1-PP (Δθ=17°), and thus recoil starts earlier. The effect of Δθ on Δtξmax, i.e. the time at maximum spreading, is intuitive: as the contact angle hysteresis increases, more time is needed for the contact angle to change from the value reached during spreading to the value needed for the contact line to recede15. Wettability effect became even more remarkable in the recoiling stage ( t > 3.5 ms ), where different outcomes were observed, from deposition to rebound (occurring when ξ = 0 ), depending on the value of the receding contact angle (illustrated in Figure 2).

Analysis of rebound time, t R , for different impact speed, V , revealed that t R was independent from V not only for SHSs, as predicted by Quéré and co-workers8, but also for the two hydrophobic surfaces (A1-Teflon and A2-Teflon) on which rebound occurred. However, t R was not the same for all surfaces, but depended on surface wettability: more precisely, rebound time related well to receding contact angle, θ R . As illustrated in Figure 3b, data show that drop t R decreased with increasing θ R . The three SHS surfaces (SHS-FAS, SHS-CNR1 and

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SHS-CNR2), which have receding contact angles higher than 150°, showed average rebound time that were well predicted by Eq. 2 (i.e., a rebound time of ~14ms). On SHS-Teflon, receding contact angle was 145° and the average rebound time increased to 16ms. For the two hydrophobic surfaces, A1-Teflon and A2-Teflon, average rebound time increases to ~22ms (see Figure 3b).

a Figure 3. a. Spread factor time evolution,

b

ξ ( t ) = D ( t ) D0 ,

for four tested samples (single runs). Test conditions were:

V = 1.0m/s , D0 = 2.5mm , and We = 33 . The numeric values reported in the graph correspond to the value of the receding contact angle,

θ R , for each specific sample. b. Rebound time, t R , as function of surface receding contact angle, θ R , for the six surfac-

es (out of eight tested) on which rebound occurs. Data are obtained as average for all investigated impact speeds. The rebound time predicted by Eq. 2 is ~14ms.

Note that, for the range of values considered in the experiments, the contact angle hysteresis, Δθ, did not have an effect on drop impact outcome (bouncing/sticky drop) and also did not correlate to rebound time. As an example, surfaces B1-PP, A2-Teflon and SHS-Teflon had a similar hysteresis (equal to 17°, 13° and 15°, respectively) but a different water drop impact behavior: drop did not rebound on B1-PP (low receding contact angle), page 13 of 21


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and rebounded on A2-Teflon and SHS-Teflon. Furthermore, recoil was overall faster on SHS-Teflon, due to higher θR, and despite contact angle hysteresis, Δθ, being 2° higher that of A2-Teflon. Also, surface roughness did not have a direct effect on drop impact behavior. Indeed, for the investigated roughness range (average surface roughness from 0.9 to 433 nm), it was observed that roughness had an effect mainly on contact angles hysteresis: by increasing roughness, contact angle hysteresis increases. As an example, drop rebounded on A2-Teflon (R=433 nm), on which roughness was two orders of magnitude higher than that of B1-PP (8.9nm). All other surface with higher roughness (R>1μm) showed transition to superhydrophobic behavior, thus an increase of receding contact angles, due to Cassie-Baxter wetting state. In our previous study15, we identified two different regimes: a moderate Weber number regime (We200), in which wettability effect is secondary, because capillary forces are overcome by inertial effects. With respect to characteristic time of drop dynamics, we observed that for a hydrophobic/superhydrophobic surface, spreading time was constant at moderate Weber numbers ( We < 200 ) and decreased when increasing Weber number ( We > 200 ). Also, in Ref. 15 we showed that there was a time span, in which the drop stayed at maximum spreading, tξmax. This time generally depends on both contact angle hysteresis and We: for the surfaces considered here, which have low hysteresis, tξmax is usually 1.5 to 2.5ms. This confirmed that the differences between surfaces on rebound time have to be mainly found in the recoil phase, which lasted for ~10-12ms on SHS and ~17ms on A1-Teflon and A2-Teflon. In addition, this result confirmed that drop spreading is inertia dominated for We > 200 , and wettability affects spreading only for We < 200 15; differently, during the recoiling phase wettability plays a dominant role even for higher Weber numbers (up to We = 585 in the present study). In Page 14 of 21


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particular, the knowledge of surface receding contact angle, which is measured quasi-statically, represents a valuable information for predicting the dynamic behaviour of a drop on a surface (for the impact conditions investigated here). As an additional note, drop impalement, with transition from Cassie-Baxter to Wenzel state, did not occur on any of the tested SHS, and drops rebounded at all impact speeds in the investigated range.

Data from present study showed that drops did not rebound for θ R ≈ 90° (B1-PP and B2-PP), whereas they rebounded on surfaces with θ R of 104° and 108° (A1-Teflon and A2-Teflon, respectively). Data from Šikalo et al. 22

showed that drop was not rebounding on wax surface with θ R = 95° . As such, experimental data suggest that

θ R = 100° is the minimum value required to observe drop rebound. The identification of receding contact angle as the principal wetting parameter to influence drop recoil and rebound allows defining a criterion for drop rebound. On hydrophilic surfaces, which have low receding contact angles (lower than 90°), rebound does not occur and the drop remains deposited (i.e. stuck) on the surface. For hydrophobic and superhydrophobic surfaces, rebound takes place only if θ R > 100° . With respect to SHS, drop rebound was observed for all tested conditions (0.8

Drop Rebound after Impact: The Role of the Receding Contact Angle

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