Water Touch-and-Bounce from a Soft Viscoelastic Substrate: Wetting

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Water touch-and-bounce from a soft viscoelastic substrate: Wetting, dewetting and rebound on bitumen Jae Bong Lee, Salomé dos Santos, and Carlo Antonini Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01796 • Publication Date (Web): 25 Jul 2016 Downloaded from http://pubs.acs.org on July 28, 2016

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Langmuir Lee et al. la-2016-01796v

submitted to Langmuir

Water touch-and-bounce from a soft viscoelastic substrate: Wetting, dewetting and rebound on bitumen

Jae Bong Lee1,2, Salomé dos Santos3,* and Carlo Antonini4,*

1

KAERI, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Youseong-Gu, Daejeon 305-353, Republic

of Korea 2

ETH Zurich, Chair of Building Physics, Wolfgang-Pauli-Strasse 15, CH-8093 Zürich, Switzerland

3

Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Road Engineering/Sealing

Components, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland 4

Empa, Swiss Federal Laboratories for Materials Science and Technology, Functional Cellulose Materials,

Überlandstrasse 129, CH-8600 Dübendorf, Switzerland

* Corresponding authors: [email protected], [email protected]

Keywords: Drop rebound; Soft surfaces; Viscoelasticity; Wetting; Hydrophobicity; Bitumen; Adhesion

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Lee et al. la-2016-01796v

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Abstract. Understanding the interaction between liquids and deformable solid surfaces is a fascinating fundamental problem, in which interaction and coupling of capillary and viscoelastic effects, due to solid substrate deformation, give rise to complex wetting mechanisms. Here we investigated as a model case the behavior of water drops on two smooth bitumen substrates with different rheological properties, defined as hard and soft (with complex shear moduli in the order of 107 and 105 Pa, respectively, at 1 Hz), focusing both on wetting and on dewetting behavior. By means of classical quasi-static contact angle measurements and drop impact tests, we show that the water drop behavior can significantly change from the quasi-static to the dynamic regime on soft viscoelastic surfaces, with the transition being defined by the substrate rheological properties. As a result, we also show that on the hard substrate, where the elastic response is dominant under all investigated conditions, classical quasi-static contact angle measurements provide consistent results that can be used to predict the drop dynamic wetting behavior, such as drop deposition or rebound after impact, as typically observed for non-deformable substrates. Differently, on soft surfaces, the formation of wetting ridges did not allow to define uniquely the substrate intrinsic advancing and receding contact angles. In addition, despite showing a high adhesion to the soft surface in quasi-static measurements, the drop was surprisingly able to rebound and escape from the surface after impact, as it is typically observed for hydrophobic surfaces. These results highlight that measurements of wetting properties for viscoelastic substrates need to be critically used and that wetting behavior of a liquid on viscoelastic surfaces is a function of the characteristic time scales.

Introduction Wetting and dewetting of solid surfaces is a complex problem, which is relevant both from a fundamental perspective and for the application to any field where liquid-solid interfaces come into play. Although most of the studies have been traditionally focused on the interaction between liquid and hard non-deformable substrates1,2 (also referred to as rigid or stiff), in the recent years there has been a remarkable interest on wetting and dewetting of soft deformable substrates3–17. Elasto-capillary effects which occur due to the interplay between capillary and elastic forces associated with substrate deformation play a key role in many relevant natural phenomena such as wetting of leaves18,19, animal wings20 and insects21, as well as bacteria adhesion on surfaces22, self-organization of cell tissues23 and spreading of cells24. As an example, in the field of cell 3D printing25,26, where the aim is to print functional tissues and organs by using cell suspensions in liquids, it is essential to preserve cell function and viability within the printed construct. Therefore, the process of printing and the interaction of the cell suspensions with the substrate has to be understood to guarantee the viability of the cells during impact with a hard or soft substrate27. The understanding of liquid wetting and dewetting on substrates with a viscoelastic behavior, which exhibit a combined solid-like (elastic) and liquid-like (viscous) response, introduces a further increase of complexity, due to combined Page 2 of 26


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visco-elasto-capillary effects. When a sessile drop is deposited on a deformable substrate, the substrate is pulled outwards at the three-phase contact line by the normal component of the liquid-air surface tension, and simultaneously, pushed on the entire substrate-liquid interface by the Laplace capillary pressure. As a result, in the case of a soft elastic or viscoelastic substrate a wetting ridge forms at the contact line4,28,29. Substrate viscoelasticity and the formation of wetting ridges influences the wetting and dewetting characteristics in quasi-static10,12–14 and dynamic conditions15, as well as the evaporation of sessile drops30,31. A particular aspect that has recently stimulated research is the configuration of the wetting ridge6–8,11,12,14, and the applicability of Young’s and Neumann’s laws, which express the force balance at the three-phase contact line. Wetting of viscoelastic substrates represents in fact an intermediate state between the two ideal extremes: The wetting of a perfectly smooth and rigid substrate, where Young’s law applies, and the wetting of a liquid substrate, where Neumann’s law applies. A recent study using high-resolution transmission X-ray microscopy by Park et al.11 confirmed that the geometry of the cusp at the wetting ridge can be predicted using a dual scale approach, as previously proposed by Style et al.6. By measuring both the microscopic and the macroscopic contact angles, Park et al.11 showed that Neumann’s law correctly predicted the cusp configuration over the microscopic scale, whereas the macroscale drop configuration obeyed the Young’s law. As a consequence, in static conditions the cusp shape and geometry is constant for a specific liquid-soft substrate system, and is independent from the drop size and substrate thickness7. The transition between micro- and macroscopic behavior is defined by the elasto-capillary length

γ E , where γ is the surface tension

of the liquid and E is the elastic modulus of the substrate. The contact line motion on deformable substrates also presents peculiarities, including complex patterns for advancing and receding motions, not observed on hard substrates. One of such complex behaviors is the stick-slip motion of the three-phase line, in which the contact line moves intermittently because of the wetting ridge formation. As an example, Pu et al.

12–14

have observed stick-slip behaviour in advancing and receding motions in Wilhelmy plate measurements

performed on viscoelastic polymer substrates, reporting the response of the viscoelastic substrates to the plate velocity. Kajiya et al.10 investigated the wetting of water on viscoelastic poly(styrene-butadiene-styrene)–paraffin gels, highlighting the existence of a stick-slip behavior of the contact line in the advancing motion of the contact line for surfaces with shear modulus in the order of 103 Pa. The authors reported the existence of three different regimes, which were identified on the basis of the drop characteristic spreading frequency ≈ / , where is the contact line velocity and D is the diameter of the drop, in comparison to the (bulk) substrate cross frequency,

f cross , where the

storage modulus equals the loss modulus, G ' = G '' . It was shown that, for the investigated system, the contact line

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moved continuously for ≪

and ≫

, and moved intermittently when

f ≈ fcross .

Similar behavior was

found for receding contact line on dip-coating experiments16. Chen et al.5,32 investigated the initial stages of spontaneous wetting process, and found that spreading is initially dominated by both inertial effects and wettability, and follows the same scaling of rigid surfaces33; however, the duration of the inertial spreading, as well as spreading rate at later stages until equilibrium is reached, are affected by surface softness. In particular, the duration of the inertial regime decreased for increasing surface softness (i.e. decreasing shear modulus). Also, during later stages of spontaneous wetting, spreading slowed down on softer surfaces by “viscoelastic braking”29, an effect caused by the energy dissipation associated to the displacement of the wetting ridge while the contact line moves. Very recently, Karpitschka et al.17 investigated the advancing contact line motion on silicone gels (with shear modulus G in the order of 103 Pa), providing a quantitative theoretical background for contact line sliding on the wetting ridge. The goal of the present study is to develop a framework to understand the wetting and dewetting of liquids on viscoelastic substrates, ranging from quasi-static to dynamic conditions. Thus, we focused on the advancing (wetting) and receding (dewetting) contact line motion of water on bitumen substrates, investigating drop behavior ranging from quasi-static conditions, with velocities in the order of 10-4 – 10-3 m/s, to fast dynamic conditions developed during drop impact, with velocities in the order of 1 m/s. The use of bitumen, a material obtained from the distillation of crude petroleum34, as a substrate is relevant from both fundamental and practical perspectives. Bitumen mechanical properties, and in particular the storage ( G ' ) and loss (

G '' ) moduli, can be tuned either through the content of high molecular weight fractions of polycondensed aromatic rings or through the polarity using oxidation processes, which results in aggregation of polar molecules into larger colloidal structures35. In addition, the shear moduli show a strong dependence on frequency in dynamic shear rheometer measurements: this means that bitumen viscoelastic response changes significantly in static, quasi-static and dynamic conditions. Finally, bitumen is widely used in road construction and in waterproofing membranes, due to its thermoplastic characteristics, the high adhesion to many materials and the waterproofing properties. Optimization of all of these characteristics requires an adequate comprehension of water-bitumen interaction. By comparing the wetting behavior of hard and soft viscoelastic bitumen substrates, we identified a significant difference between quasi-static and dynamic response to wetting. In particular, on a hard bitumen quasi-static measurements can be used to predict the drop dynamic behavior during a drop impact event (e.g. drop deposition vs. rebound after impact), using the same criteria established for rigid substrates. As reported in a previous paper by Antonini et al.36, complete drop rebound after impact can be observed only on surfaces with

θ R > 100o ;

if the

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receding contact angle is lower, then drop remains deposited on the surface or may breakup in the recoiling phase to rebound partially. Also, on micro- and nano-textured hydrophobic surfaces exhibiting high receding contact angles, drop rebound can be hindered at impact exceeding a critical speed, because of liquid impalement into the microtexture, with transition from Cassie-Baxter to Wenzel state. The behavior on soft bitumen reported here is in fact the opposite: under quasi-static conditions, water showed a stickslip behavior, when the contact line was advancing, and a high adhesion to the substrate in the receding phase, with receding contact angle well below 90o, a characteristic that usually identifies a surface as hydrophilic. However, under dynamic conditions during drop impact tests, a water drop did not remain trapped and stuck on the substrate, but was capable of rebounding, as typically happens on rigid hydrophobic surfaces. This clearly allows to identify different wetting regimes on viscoelastic substrates, shedding new light on the understanding of wetting properties and potentially enabling the design of surfaces that can trap or allow rebound of drops, by tuning their rheological properties.

Experimental section Substrate preparation and characterization For the preparation of the substrates, we used two types of bitumen, referred to as hard and soft. Table 1 presents the results obtained from elemental analysis of carbon, hydrogen, nitrogen, sulphur and oxygen for both bitumens. The carbon and hydrogen content in the two bitumens is similar, with hydrocarbon content higher than 90 wt% and molar ratios of hydrogen to carbon of around 1.4, although slightly higher for soft bitumen. This ratio is intermediate between 1, corresponding to aromatic structures, and 2, for saturate alkanes. Larger differences are observed for the heteroatoms content. The hard bitumen contained a higher amount of oxygen than the soft one, but a lower content of nitrogen and sulphur.

Table 1 Relative content of carbon, hydrogen, nitrogen, sulphur and oxygen in hard and soft bitumens. H/C is the molar ratio of hydrogen to carbon and (N+S+O)/C is the molar ratio of heteroatoms to carbon. Bitumen

C (wt %)

H (wt %)

N (wt %)

S (wt %)

O (wt %)

H/C

(N+S+O)/C

Hard

84.31

10.00

0.82

4.14

0.72

1.41

0.03

Soft

83.75

10.21

1.00

4.80

0.22

1.45

0.03

Hard/Soft ratio

1.01

0.98

0.82

0.86

3.27

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Thermogravimetric analysis (TGA) measurements were performed for both bitumens by using a TG 209F1 standard/P thermogravimetric analyzer where approximately 6 mg of the sample were heated from 30 to 700 °C at a heating rate of 20 °C/min, under a N2 and O2 atmospheres. The measurements were performed both under nitrogen (N2) and oxygen (O2) atmosphere and the results are shown in Figure 1.

Figure 1: TGA curves for the hard and soft bitumens obtained under nitrogen, N2 (open symbols) and oxygen, O2 (lines). The curves obtained under N2 show one step for both bitumens, with 80 % of weight loss at 700 °C for hard bitumen and 83 % weight loss at 600 °C for soft bitumen. The curves obtained under O2 show four main steps with increasing weight losses of 4 %, 18 %, 38 % and 40 %, for hard bitumen and three main steps, 24 %, 38 % and 38 % for soft bitumen. The inset shows a close up where significant weight loss started.

The TGA curves show an initial plateau until the onset temperature, where a significant weight loss started. The onset temperature was different for the hard (260 °C O2) and soft (205 °C O2) bitumen, observed both in the curve obtained under N2 and O2. The difference indicates that the hard bitumen started decomposing at higher temperatures. Therefore, it is expected that hard bitumen contains molecular fractions with higher molecular weight and/or different chemical characteristics as compared with the compounds that decomposed for soft bitumen. After the first step observed in the O2 curve where hard bitumen presented a decomposition of 4 %, a second weight loss step of 18 % occurred whereas it was absent for soft bitumen where only one step of 24 % was observed. This further indicates that hard bitumen contains molecular fractions that are absent in soft bitumen; these compounds could be oxidized species. After the first large step for soft bitumen and the two first steps for hard bitumen, two other large steps were observed for both bitumens with similar weight losses before reaching complete decomposition. Bitumen substrates were prepared on glass slides by spreading bitumen homogeneously on the surface of glass microscope slides and heating them in a ventilated oven at 110 °C for 20 min. Afterwards, the hot substrates were left to cool down at room temperature for 24 h prior to the measurements. Depending on the test method, the size of the Page 6 of 26


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substrate with thickness lower than 1 mm, was changed: 3 × 3 mm2 for attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy measurements, 8 × 8 mm2 for atomic force microscopy (AFM) measurements and 70 × 20 mm2 for wetting measurements. For the dynamic shear rheometer measurements, bitumen was prepared in silicone molds of cylindrical shape with 8 mm diameter and 2 mm height. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy measurements were performed at room temperature in a Tensor 27 spectrometer (Bruker) in the ATR mode using a diamond crystal. The bitumen samples were placed with the top surface against the diamond crystal. The spectra were collected in the 4000 – 600 cm-1 range with a resolution of 4 cm-1 and each final spectrum represented an accumulation of 32 spectra. The ATR-FTIR spectra for hard and soft substrates are shown in Figure 2.

Figure 2 ATR-FTIR spectra for hard and soft bitumen substrates. Most relevant functional groups and respective vibrational modes are indicated: νas = asymmetric stretching, νs = symmetric stretching; δas = asymmetric deformation, δs = symmetric deformation, δ = deformation (aro stands for aromatic), and ρ = rocking deformation type. The spectrum of the hard bitumen was shifted vertically by 0.13 relatively to the soft bitumen spectrum for better visualization. The zoom-in shows a close up in the ν C=O wavenumber range (no vertical shifting).

Despite the qualitative similarity between the two ATR-FTIR spectra, hard bitumen showed higher amount of carbonyl functional groups (C=O) than the soft bitumen, as indicated by the difference in absorbance in the close up in Figure 2. This agrees with the elemental analysis showing 0.72 wt% of oxygen for hard and 0.22 wt% for soft bitumen as well as with the thermogravimetric measurements.

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The rheological properties, such as the complex ( |G*| ), the storage ( G' ) and the loss ( G'' ) moduli, were obtained using a Physica MCR 301 dynamic shear rheometer from Anton Paar. The oscillatory measurements were performed by using a plate-plate geometry with 8 mm diameter and gap of 1 mm in the frequency range 0.1 – 20 Hz. Figure 3 shows the three moduli ( |G*| , G' , and G'' ) as function of the oscillation frequency (

f

). The measurements

were performed in the temperature range 0 < T < 30 oC , within the linear viscoelastic region, at temperature incremental steps of 10 °C. A thermal equilibration time of 10 minutes was used to ensure homogeneous temperature in the sample. Since bitumen behaves according to the time-temperature superposition principle, the obtained values of

|G*| as function of frequency at different temperatures were shifted by using the Williams–Landel–Ferry (WLF) equation37. As such, we obtained the reconstructed “master curve” for |G*| at the reference temperature of 20 °C in the frequency range 10-2-10-4 Hz, as shown in Figure 3.

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Figure 3: |G*| as a function of frequency for a) hard and b) for soft bitumen showing the fcross at 20 °C (fcross_20 °C), where

G ' = G '' . The insets show the measured values of complex ( |G*|), storage ( G' ) and loss ( G'' ) moduli as a

function of the oscillation frequency for 0 < T < 30 oC .

The rheological measurements confirmed that the hard bitumen (see Figure 3a) exhibited higher |G*| , G' and G'' than the soft bitumen (see Figure 3b), at the reference temperature of 20 oC. Additionally, the values of the frequency fcross at the reference temperature of 20 °C, where the transition from liquid-like ( G '' > G ' ) to solid-like ( G '' < G ' ) occurred, were determined by identifying first the value of |G*| at transition from the raw measurements and second the corresponding fcross from the reconstructed “master curve”. For the hard substrate (Figure 3a), fcross ≈ 10-1 Hz, corresponding to the characteristic cross time of ~ 101 s, while for the soft substrate (Figure 3b) fcross ≈ 103 Hz, corresponding to the characteristic cross time of ~ 10-3 s. Page 9 of 26


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Additional information regarding mechanical properties of the bitumen is given in the Supporting Information. Atomic force microscopy (AFM) measurements were performed at room temperature and using a Bruker MultiMode 8 atomic force microscope, with a Nanoscope V controller and the software Nanoscope 8.15. Bruker TAP150A tips made of 0.01 – 0.025 Ωcm Antimony (n) doped Si, with height 15-20 µm and radius ~ 20 nm were used. Every image was built up by 256 × 256 pixels. Offline data analysis was performed using Bruker Nanoscope Analysis 1.40. Figure 4 shows representative topography maps of the hard and soft substrates. Although the average roughness, calculated from the full scanned area, was relatively higher on the soft substrate ( Ra = 6.4 nm , see Figure 4b) than on the hard substrate ( Ra = 2.4 nm , Figure 4a), because of undulated structures formed after temperature annealing treatment38,39, both substrates had roughness in the nanometer range and can be considered smooth from the perspective of millimetric drop wetting.

Figure 4: AFM topography images of a) hard and b) soft substrates. The arithmetic average of the absolute values of the surface height measured from the mean plane, Ra, is 2.4 nm for the hard and 6.4 nm for the soft substrate.

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For the quasi-static measurements, advancing,

θ A , and receding, θ R , contact angles were measured through the sessile

drop method, expanding and contracting the volume of a millimetric water sessile drop on the horizontal substrate. Advancing and receding contact angle measurements are a standard characterization to evaluate surface wetting properties, providing a measure of surface repellency and drop mobility. The advancing and receding contact angles also identify the range of possible contact angles that can be observed on a sessile drop, i.e. in static conditions40–44. Measurements were performed with a Contact Angle System (OCA20, Dataphysics), and images were post-processed to measure the evolution of contact angles, volume, contact point position and contact diameter using the Datasystem SCA20 (Dataphysics) image analysis software. To evaluate the drop wetting and dewetting behavior at different drop inflation and deflation rate, we performed tests at multiple flowrates, ranging from 0.1 to 4.0 µl/s, and drop volumes between 2 and 20 µl. The measurements were repeated at least on two different substrates and on three different locations, for both the hard and the soft substrates, to ensure reproducibility. For dynamic wetting measurements, water drop impact tests were performed using a high-speed recording system. The impinging water drop was generated at a flattened needle tip using a syringe pump to make a reproducible drop with 2.0 or 2.5 mm of diameter (± 1%) and accelerated by gravity up to velocities ranging from 0.2 to 3.0 m/s (± 2%), as summarized in Table 2. Tests were repeated at least three times for each condition to ensure reproducibility. The drop impact event was captured by using a high-speed camera (IDT NX7-S2), with a frame rate of 5000 fps, pixel resolution of 7.3 µm (Navitar 12x zoom lens), exposure time of 5 µs per frame, and back-illumination using a LED lamp (SCHOTT LLS2). Images were automatically analyzed using an in-house code developed in MATLAB (MathWorks Inc.). The image analysis processing provided the initial droplet diameter, D0, spreading drop diameter, D, the dynamic contact angle, θD, and the contact line velocity, VCL . All measurements were performed within 48 h after substrate preparation to minimize the influence of chemical, microstructural and rheological changes that may occur with time. In addition, each contact angle measurement and impact test was performed in a different location of the substrate, to avoid the interference caused by substrate deformation of previous experiments.

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Table 2: Water drop impact conditions. Corresponding water properties are: density ρ = 998kg m3 , viscosity −3 µ = 10−3 Pa s and surface tension γ = 73 × 10 N m .

Drop diameter

Impact velocity

Weber number

Reynolds number

Ohnesorge number

D0 (m)

Vi (m/s)

We = ρVi 2 D0 γ

Re = ρVi D0 µ

Oh = We Re

2.0 × 10-3

0.2 – 3.0

1.1 – 247

391 – 5871

2.7 × 10-3

2.5 × 10-3

0.2 – 3.0

1.4 – 308

489 – 7338

2.4 × 10-3

Results and discussion Quasi-static wetting and dewetting measurements Figure 5 shows representative advancing and receding contact angle results for a water drop on the hard substrate at different water inflation and deflation rate, 0.1 and 4.0 µl/s, providing indication on surface repellence and drop mobility. The advancing and receding contact angle was measured as the contact angle at the moment of incipient motion. The contact angle remained constant during the entire advancing (wetting) phase and equal to the initial value,

θ A = 109o , measured when the contact line starts advancing. Also, θA was not affected by the flowrate within the investigated range. However, the correct evaluation of the receding contact angle requires particular attention to avoid the underestimation of

θ R due to dynamic effects45. For instance, by taking the receding contact angle, θ R , for a

flowrate of 0.1 µl/s, which is typically used in quasi-static experiments43, its value was of 83°; however, at the highest flowrate, 4.0 µl/s,

θ R = 78 o , with an underestimation of the receding contact angle by 5o.

These results confirm the

need to measure the receding contact angle using low flowrates, to avoid undesirable dynamic effects. The corresponding contact angle hysteresis,

∆θ = θ A − θR , for the hard substrate was thus ∆θ = 26o .

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Figure 5: Advancing and receding contact angles for the water drop on the hard substrate, at flowrates of 0.1 and 4.0 µl/s, as a function of the contact point position (arbitrary offset).

Figure 6: a) Schematic illustration of drop stick-slip behavior during the advancing (wetting) phase on a soft deformable substrate. b) Advancing and receding contact angles for the water drop on the soft bitumen substrate, at flowrates of 0.1 and 4.0 µl/s, as a function of the contact point position (arbitrary offset).

The scenario changed significantly when measuring the contact angles on the soft bitumen substrate, which has a modulus in the order of 105 Pa at frequency of 1 Hz (see Figure 3c). As shown in Figure 6, due to the stick-slip behavior Page 13 of 26


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during the advancing phase, the contact angle did not have a unique value10 (see Figure 6b). On the soft bitumen substrate, the normal component of the water surface tension pulled the substrate at the three phase contact line, and a wetting ridge formed at the contact line (see schematic in Figure 6a). Thus, the contact line remained pinned for a certain time at a certain location and, thereafter, advanced intermittently instead of continuously. Consequently, the advancing contact angle, plotted as function of the contact point position in Figure 6b, did not remain constant. During the stick phase, the contact angle increased, because the liquid-substrate contact area remained constant, while the drop volume increased. After the contact angle reached a critical value, the contact line suddenly moved forward to a new location (slip phase), causing the contact angle to decrease, and a new stick-slip cycle occurred. However, the critical value of the contact angle at which the contact point slips was not constant, as best visualized by looking at the values of contact angles as function of the drop volume (see Figure 7a). The intermittent stick-slip motion can be understood by visualizing stick phase,

θˆstick , representing the contact angle increase during the stick phase, as function of the duration of the

tstick

(see Figure 7). The results clearly suggest that the longer the stick phase duration,

tstick , the higher

θˆstick . In other words, the longer the contact point remains pinned in one location, the higher the contact angle needs to grow, before the contact point can slip again. This behavior is associated with the characteristic viscoelastic response of the substrate. The substrate deformation induced by capillary forces represents an obstacle for contact point motion10 and grows with time. Therefore, the longer contact point remains pinned in a certain position, the higher the deformation and thus the higher the contact angle needs to increase for the contact line to slip forward. In Figure 7b data for

θˆstick , measured from tests at different inflation flowrates (in the range 0.1 to 4.0 µl/s), are collectively presented as

a function of the stick time,

0.4 tstick . The data are fitted with a power law showing the following dependence θˆstick ∝ tstick .

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Figure 7: a) Advancing contact angle as a function of drop volume for the water drop on the soft substrate (flowrate of 0.1 µl/s). The inset shows a close up for the lowest volumes. b) Advancing contact angle increase, contact point is pinned, during the stick phase, as function of the stick phase duration,

θˆstick , while the

tstick . The fitting dotted curve is:

0.4 . θˆstick ( tstick ) = 7.1 tstick

In addition, as shown in Figure 6b, we observed that the receding contact angle measurements did not provide a unique value for θ R , and even an opposite trend was observed when compared to the hard substrate. Figure 8a shows the values of the receding contact angles as function of the drop deflation rate for both hard and soft substrates. For the hard substrate, as mentioned above, an accurate measurement of θ R can be achieved by using low flowrates (e.g. 0.1 µl/s), to avoid dynamic effects. Differently, for the soft substrate, the values of the receding contact angle range from θR = 42o at the lowest flowrate (0.1 µl/s) to θ R = 77o at the highest flowrate (Figure 8a). θ R appear to increase by increasing the flowrate because of substrate deformation. At low flowrates, the drop stays longer at maximum spreading before the contact point starts to recede (dewetting) and thus, the substrate deformation has more time to grow, resulting in higher Page 15 of 26


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pinning and in a reduction of the receding contact angle. This is clearly shown by visualizing

θR

as function of

tstick

(Figure 8b), which is the time of pinning, and corresponds to the time when the drop is at maximum spreading, before it starts receding:

θR

decreased monotonically with increasing

tstick .

As such, measurement of the receding contact

angles becomes inconclusive due to conflicting requirements. At high flowrates the dynamic effects become prominent (as on hard substrates), whereas at low flowrates the substrate viscoelastic response led to a time-dependent increase of drop adhesion. These phenomena highlights important questions related to

θR

measurements on viscoelastic substrates,

and the use of quasi-static measurements to study contact line behavior in dynamic conditions. This is also critical, since it is well known that the receding contact angle is a key wetting parameter controlling the drop mobility on a surface36,44,46. As an example, results in Figure 8 would suggest that identified, is always lower than

θR

θ R for the soft substrate, although not uniquely

for the hard substrate; however, are we allowed to conclude that the hard substrate

is more hydrophobic than the soft substrate? The answer is no, as demonstrated by drop impact tests presented in the following section.

Figure 8: a) Receding contact angle on hard and soft substrates as function of the deflation rate; and b) receding contact angle as function of

tstick

(see explanation in the text). Dotted lines are used to guide the eyes.

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Drop impact tests Figure 9 highlights the typical outcomes after water drop impact on the hard and soft substrates, for different impact velocities. At low impact velocity, the drops deposited in a similar way on both substrates, as shown by the image sequence in Figure 9a, corresponding to the impact at low velocity, Vi = 0.3 m/s, on the soft substrate. However, by increasing the impact velocity (e.g. Vi = 1.1 m/s in Figure 9b), transition to partial rebound on both substrates was observed. By increasing the velocity further (Vi = 2.5 m/s in Figure 9c), the behavior between the two substrates significantly deviated: On the hard substrate the drop partially rebounded, whereas on the soft substrate complete drop rebound occurred.

Figure 9: Image sequence of the outcome for water drop, D0 = 2.0 mm, impacting on hard and soft substrates, at different impact velocities, Vi: a) 0.3 m/s, b) 1.1 m/s, and c) 2.5 m/s. In c), numbering indicates the progressive number of fragmented drops.

To quantitatively characterize the different regimes, we measured the volume of the drop remaining on the substrates,

V dep (Figure 10), the drop contact diameter and contact angle dynamics (Figure 11) , and the number of drops generated by fragmentation (Figure 12). Page 17 of 26


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Figure 10 shows the non-dimensional volume,

V dep V drop , where V drop is the initial drop volume before impact as a

function of drop impact velocity. Once partial rebound has occurred, the drop remaining on the substrate comes to rest within few tens of milliseconds. Under the assumption of spherical cap shape,

V dep is simply determined by the contact

diameter of the remaining drop DCL and the drop height. As mentioned above, three different regimes were identified. In the low impact velocity regime (Vi < 0.6 m/s),

V dep V drop = 1 for both substrates, since the drop remained

completely deposited on the surface after impact. At high impact velocity (Vi > 1.4 m/s), drop fully rebound on the soft substrate ( V dep

V drop = 0 ), whereas on the hard substrate only ~ 35% of the drop volume detached form the surface,

and ~ 65% remained on the substrate. In the intermediate velocity range (0.7 < Vi < 1.4), a transition regime was observed, where drop partial rebound occurred.

Figure 10: Deposited drop volume ratio,

V dep V drop , on hard and soft substrates as a function of drop impact

velocity, Vi. Schematic illustrations for different outcomes for different impact velocity regimes are presented: deposition, partial rebound and complete rebound.

The unexpected complete rebound on the soft substrate, despite the low receding contact angles and high adhesion of drops observed in quasi-static measurements, can be understood by performing a scaling analysis of viscoelastic energy dissipation. Although it is known that energy based models may not always bring to accurate prediction of drop deformation17,47–49 or may need experimentally determined fitting parameters, a scaling analysis can provide useful estimation to understand wetting kinetics. The drop initial kinetic energy before impact is E k = 1 2 mVi 2 , which for a

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millimetric drop for our impact conditions is in the order of 10-5 J. Based on previous work of Carré et al.29 and Alizadeh et al.15, the viscoelastic dissipation, W, can be estimated as:

W∝

γ 2Vi timp D0 2π G* ε

(1)

where ε is a characteristic length near the contact line (in the order of 1 µm15), and timp is the duration of impact. The viscoelastic dissipation is inversely proportional to the shear modulus G

*

, which for the soft surfaces varies

significantly from 103 to 107 Pa in the frequency range 10-2 – 104 Hz (see Figure 3c). The viscoelastic dissipation is in the order of 10-4 J for G * ≈ 10 3 Pa at low frequency, corresponding to quasi-static measurement, whereas it becomes negligible (in the order of 10-8 J) compared to kinetic energy for G * ≈ 10 7 Pa at frequencies in the range 102 – 103 Hz, corresponding to drop impact tests. In other words, at the characteristic timescale of impact conditions even the soft substrate responded as a hard material, because of the high modulus at high frequency. However, the lack of viscoelastic dissipation during impact conditions is not sufficient to explain drop rebound. For that, it is useful to compare the evolution of the contact diameter (Figure 11a) and the dynamic contact angle (Figure 11b) in the high velocity regime. Drop deformation was similar for both substrates in the spreading phase, which is inertia dominated. However, recoiling occurred slightly faster on the soft substrate, because of higher dynamic contact angles. In particular, after 8 ms the contact angle on the soft substrates became higher than 90o and reached at 12 ms a steady state value of 100o, which has been identified in the past as a minimum threshold for the receding contact angle to achieve complete drop rebound36. This clearly unravels the hydrophobic nature of the soft bitumen, which was hindered in quasi-static experiment by the viscoelastic dissipation. Drop behavior was clearly different on the hard substrate (

θ R = 83o ), on which the dynamic contact angle remained mainly below 90o, except after 15 ms when drop fragmentation due to break-up of the vertical liquid column (see insert in Figure 11a) caused strong oscillation of the dynamic contact angle. Additional information regarding the maximum spreading can be found in the Supporting Information, showing that there is no difference on the maximum spreading on hard and soft substrates, since in this phase inertial effects play the prominent role50,51 and advancing contact angle for the two surfaces are comparable.

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Figure 11: Drop impact on hard and soft substrates with Vi ~ 2.5 m/s. Time evolution of: a) the non-dimensional spreading factor, D/D0, and b) the dynamic contact angle θD. Inset in a) shows the contact line velocity, VCL , calculated as

0.5dD dt .

Drop fragmentation also explains the non-monotonic trend observed in Figure 10 for

V dep V drop at increasing impact

velocity, Vi. For Vi > 0.6 m s , the elongated liquid column, formed in the later stages of drop recoiling, breaks-up in multiple drops because of Plateau–Rayleigh instability (see Figure 9b and c). Figure 12 shows the number of fragmented drops as a function of impact velocity. Drop breakup leads to propagation of capillary waves on the drop surface down to the contact line, where either positive or negative interference with contact line receding motion takes place. In particular, capillary waves may either accelerate the recoiling process, promoting rebound and minimizing the remaining volume on the surface,

V dep V drop , or decelerate it and cause a bigger volume to remain deposited on the

substrate. This explains the non-monotonic trend observed in the intermediate velocity regime. The role of Page 20 of 26


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fragmentation becomes less important in the high impact velocity regime ( Vi > 1.4 m s ), due to the increase of drop kinetic energy available in the recoiling phase to drive contact line retraction.

Figure 12: Number of fragmented drops on hard and soft substrates as a function of impact velocity. Symbols represent the average of fragmented drops for drops with D0 = 2.0 and 2.5 mm. Error bars show the standard deviation.

4. Conclusions In this work, we have studied the wetting and dewetting behaviour of water on two viscoelastic bitumen substrates with different chemical and stiffness properties. In quasi-static experiments, we observed that on hard surfaces the inflation flowrate did not significantly influence the outcome of the advancing contact angle, whereas high deflation rate led to the underestimation of the receding contact angle due to dynamic effects. Differently, on the soft substrate the drop experienced a stick-slip both in the advancing and in the receding phase, with the contact angle becoming a function of the stick time. In particular, we showed that the receding contact angle could not be identified uniquely, due to the conflicting requirements of minimizing at the same time dynamic effects and the influence of substrate deformation. These issues are also reflected into the inability to predict the outcome of drop impacts, which occur at a different time scale. For the hard bitumen substrate, it is possible to use quasi-static properties, such as the value of the receding contact angle, to predict the impact outcome. In particular, the drops are not able to rebound from the surface, since

θR

is

lower than the critical threshold of 100o, necessary to achieve drop rebound for millimetric water drops36. Differently, on the soft substrate, despite the drop showed a high-adhesion to the substrate and values of receding contact angles well below 90o during quasi-static measurements, complete rebound was observed for impact velocity Vi > 1.4 m s .

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In particular, we identified the existence of three different regimes on soft surfaces based on the impact outcome (deposition, partial rebound and complete rebound). We could interpret such outcomes as the result of the interplay between different effects, including inertia, drop fragmentation, and substrate viscous dissipation. On the soft substrate, when the contact line moves slowly (quasi-static experiments), the substrate has the time to reach a higher deformation, which further hinders drop receding motion: as such, the contact line sticks and the receding contact angle decreases. When the contact line moves faster (drop impact experiments), the substrate deformation is lower and it does not affect the receding motion significantly: as such, the contact angles in the receding phase are higher, and the drop can eventually rebound. As an outlook, results from this study can also be relevant to understand the wetting behavior of liquid drops on hybrid solid-liquid substrates, such as the slippery liquid-infused surfaces52–54, where an infused lubricating liquid is locked in place by a nano and/or microtextured substrate, to achieve a “wet” non-wetting state.

Acknowledgments SdS is thankful to the Swiss National science Foundation (SNSF) for financial support (200020_152980/1). JBL is thankful to the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2012M2A8A4025885).

Supporting information Additional bitumen properties and universal scaling of the maximum spreading

Table of contents

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Water Touch-and-Bounce from a Soft Viscoelastic Substrate: Wetting

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