Influence of Surface Wettability on Discharges from Water Drops in

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Influence of surface wettability on discharges from water drops in electric fields Christos Stamatopoulos, Pascal Bleuler, Martin Pfeiffer, Sören Hedtke, Philipp Rudolf Von Rohr, and Christian Franck Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00374 • Publication Date (Web): 18 Mar 2019 Downloaded from http://pubs.acs.org on March 23, 2019

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Influence of surface wettability on discharges from water drops in electric fields Christos Stamatopoulos,†,‡,¶ Pascal Bleuler,†,‡,¶ Martin Pfeiffer,‡,¶ Sören Hedtke,‡ Philipp Rudolf von Rohr,∗,† and Christian M. Franck∗,‡ †Transport Processes and Reactions Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland ‡High Voltage Laboratory, Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland ¶Contributed equally to this work E-mail: [email protected]; [email protected] KEYWORDS: wettability, electric discharge, hydrophilic, hydrophobic superhydrophobic, drop lift-off, corona, nanostructuring Abstract It is known that electrified droplets deform and may become unstable when the electric field they are exposed to reaches a certain critical value. These instabilities are accompanied by electric discharges due to the local enhancement of the electric field caused by the deformed droplets. Here we report and highlight an interesting aspect of the behaviour of unstable water droplets and discharge generation: by implementing wettability engineering we are able to manipulate these discharges. We demonstrate that wettability strongly influences the shape of a droplet that is exposed to an electric field. The difference in shape is directly related to differences in the critical value of the applied electric field at which inception of discharge occurs. Using theoretical models

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we are able to predict and sufficiently support our observations. Thus, by tailoring the wettability of the surface we are able to control droplet’s behaviour from expediting the discharge inception to completely restricting it.

INTRODUCTION The behavior of liquids inside electric fields has been studied extensively in literature for a range of applications such as electrospinning of nanofibers, 1 nanoprinting 2 and electrohydro-dynamic spraying. 3,4 It has been shown experimentally and computationally that a droplet deposited on a surface deforms under a homogeneous DC electric field perpendicular to the surface. 5,6 With increasing field strength the drop elongates in the direction of the field and its surface eventually becomes unstable. 7–9 For a droplet on a superhydrophobic surface, however, it has been observed that it may lift-off due to electrostatic forces before reaching instability. 5,10,11 A deformed droplet acting as an electrode perturbs the electric field and can lead to the onset of an electric discharge from its tip by assuming a specific shape called a Taylor cone. 12–15 An electric discharge is a current flow from an electrode into a dielectric medium that surrounds it. Free electrons are accelerated by an electric field and ionise neutral gas molecules through collisions. This results in an avalanche-like increase of free electrons which can be arrested within the dielectric (a so-called partial discharge) or form a conductive path between the conductor (full breakdown). 16 One manifestation of this phenomenon are the so-called corona discharges on high voltage overhead lines caused by water drops deposited on the lines through rain. 12,14 Discharges from water drops contribute significantly to audible noise, corona power losses, radio interference and, in the case of DC transmission lines, ground level ion currents and associated human sensation levels. 17,18 These factors play an essential role in the technical viability of overhead lines. Therefore, understanding the mechanism that lies behind discharge inception from a water droplet is of vital importance. Even though a broad range of studies has focused on the deformation of droplets in electric fields before 5,6,19–23 and after 24–28 surface instability occurs only a limited 2


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number of works has investigated the correlation between this deformation and discharge inception. 14,15 To the best of our knowledge, the effect of different surface wettabilities 29,30 and respective drop deformation on discharge onset has not been explored for DC fields perpendicular to the surface in a combined computational and experimental study. Here, we report that surface wettability has a direct effect on the droplet deformation in an electric field as well as on the discharge inception. To validate our experiments we theoretically predict this dependence. We also reveal that the mechanism of discharge inception from a droplet strongly depends on its local topographical characteristics which are formulated according to the wetting properties of the surface. Thus, by tailoring the surface wetting properties we are able to manipulate and control the inception of a discharge.

MATERIALS AND METHODS Surface fabrication.Three different copper-based surfaces are fabricated: a hydrophilic, a hydrophobic and a superhydrophobic surface. As received copper samples 1 mm thick (Cu CW004A Cu-ETP, Metall Service Menziken AG) are laser cut in circular shape of 49.9 mm diameter. To fabricate the hydrophilic surface, the circular sample was grinded with P800 and subsequently with P1200 grit size sandpaper using Multipol 2 rudimentary machine with rotating speed of 100 rpm. The hydrophilic surface exhibits roughness factor fr ≈ 1.003 defined as the ratio of the real surface area to the projected one. 31 Next, the sample is cleaned employing ultrasonication and using in a sequence a bath of hydrochloric acid, aceton, isopropanol and water. For the fabrication of the hydrophobic sample we utilize the process implemented for the case of the hydrophilic surface with the addition of a step; a coating of a self-assembled monolayer (SAM) is applied by dipping the sample in an ethanolic solution of 1 mM perfluorodecathiol (Merck) for 1h to decrease its surface energy.Then sample is cleaned with ethanol and dried using nitrogen. With this method, Wenzel wetting state is achieved, 32,33 as indicated by the corresponding value of roughness factorfr ≈ 1.009 and

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the measured contact angles (see next section). Regarding the fabrication of the superhydrophobic surface, briefly, after implementing the cleaning protocol mentioned previously, the circular sample is dipped in an aqueous solution of 77.5 mM sodium hydroxide (Merck) and 3.1 mM ammonium persulfate (Merck) for 25 min. Subsequently, the sample is immersed in an aqueous solution of 2.5 M sodium hydroxide and 0.1 M ammonium persulfate for 5 min. 34,35 Then sample is cleaned with water and dried with nitrogen. With this process a cluster of copper hydroxide nanoneedles is grown 36 resulting in a significant increase of the surface roughness, compared to that of the hydrophobic, with a roughness factor of fr ≈ 1.915. Therefore, after decreasing the surface energy of the substrate by applying a coating of perfluorodecathiol similarly to the hydrophobic surface, Cassie-Baxter state is reached which is confirmed by the acquired contact angles 31–33 presented in the next section. Surface Characterization. Employing the dynamic sessile drop technique using a commercial goniometer Drop Shape Analzyer-DSA25 by Kr¨ uss surfaces are characterized in terms of wettability by acquiring 3-10 pairs of advancing and receding contact angle measurements by depositing a 5 µl water droplet at different spots of the surface each time. Hydrophilic surface exhibits advancing and receding contact angle θa = 86.7◦ ± 10.3◦ , θr = 9.6◦ ± 11.6◦ respectively, hydrophobic surface shows θa = 126.7◦ ± 3.4◦ , θr = 76.5◦ ± 2.6◦ , and superhydrophobic surface exhibits θa = 163.1◦ ± 1.7◦ , θr = 160.2◦ ± 1.5◦ . Equilibrium contact angles θ are acquired with a digital single-lens reflex camera Nikon D5300, on-site at the test section and at the beginning of each series of experiments namely for E∞ = 0. Surface morphology of the tested samples is acquired with the use of a PLu neox profilometer (Sensorfar) and a 50× objective lens, in cocfocal scanning mode. Based on the surface morphology data and using software Gwyddion, roughness factor values fr are obtained. Using a scanning electron microscope (SEM, Quanta 200F FEI) the surface morphology is examined optically. Employing Energy-dispersive X-Ray spectroscopy (EDX) with system EDAX Octane Super embedded on the SEM we perform chemical analysis of the tested surfaces.SEM images for optical inspection of surface roughness and EDX graphs for chemical analysis of the sample sur-

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face are given in Supporting Information (See Figure S1).Regarding electrical conductivity, hydrophilic and hydrophobic surfaces are considered conductive, whereas superhydrophobic surface is non-conductive (see Figure S2 for further details about the characterization of the surface conductivity). Experimental Setup and Procedure. A homogeneous electric field is created by two circular parallel electrodes separated with a gap of 50 mm. The edges of the electrodes are rounded to suppress undesired discharge activity that influences significantly the observation of the behavior of individual electrified droplets. 15 Evolution of droplet shape with applied electric field is investigated using two cameras: (i) A digital single-lens reflex camera Nikon D5300 for the observation of droplet shape evolution for 0 ≤ E∞ ≤ E∞,cr (ii) A high-speed camera Photron FASTCAM Mini UX100 equipped with a macro lens Nikon 200 mm f/4 AFD, for the observation of droplet’s behavior for a period of approximately 10 ms before the inception of a discharge or droplet lift-off. A LED backlight system with a light diffuser is used to ensure uniform back illumination and optimum contrast of droplet’s shape. Droplets of deionised water (with a measured conductivity of 3.3 µScm−1 ±0.5%) are deposited on the test samples using a pipette (Eppendorf Research plus) which enables the control of droplet size (5 µl — 50 µl). In the present study electrical charging of the droplets by pipetting has no noticeable effect (see Discussion S1). 37 Partial discharges are measured with the use of an Omicron MPD600 system and voltage is applied with an in-house built SuperCube high voltage source. Further details regarding the experimental setup and procedure are given in the Supporting Information (Discussion S1 and Figure S3). Numerical Simulations. A model proposed by Gliere et al. 5 is used in order to compute the shape of drops deformed by an electric field (see Discussion S2 and Figure S4 for details about the numerical model). This model is based on an augmented Young-Laplace equation 38–40 which gives the equilibrium shape of the drop surface accounting for buoyant,

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gravitational and electrostatic forces: ε γ∇ · n = −(ρwater − ρair )gz + ∆p + (E · n)2 , 2

(1)

where γ is the surface tension of water and ∇ · n is the local mean curvature of the droplet’s water/air interface which is the divergence of the unit vector n normal to the corresponding position. The term −(ρwater − ρair )gz is related to the net force of the buoyant and gravitational forces where ρwater and ρair are the volumetric mass density of water and air respectively, g is the gravitational acceleration and z is the vertical distance from the bottom of the droplet. ∆p = pwater (0) − pair (0) is the pressure difference between the drop and the surrounding air at z = 0. Finally, 2ε (E · n)2 is the electrostatic pressure and is related to the electrostatic force, where E is the local electric vector field at the droplet’s water/air interface and ε is the dielectric permittivity of air. The drop is assumed axisymmetric, of constant volume and the radius of its contact disc does not change with increasing E∞ which is the case for our hydrophobic and hydrophilic surfaces. Physical properties are taken at temperature T = 25 ◦C. Water’s density and surface tension are γ = 71.97 × 10−3 Nm−1 and ρwater = 997.05 kgm−3 . Density of air is ρair = 1.18 kgm−3 . Gravitational acceleration is g = 9.81 ms−2 and the dielectric permittivity is = 8.854 × 10−12 Fm−1 . Drop shapes are experimentally obtained through analysis of video frames in MATLAB. The extracted shapes are fitted to polynomial shapes for hydrophilic surfaces and to ellipses for the hydrophobic and superhydrophobic cases. The fitted shapes are used in COMSOL Multiphysics to compute the local field for the prediction of self-sustained discharges as discussed later (see Water droplet and electric field interactions of Results and Discussion section).

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RESULTS AND DISCUSSION Effect of surface wetting behaviour on the inception of an electric discharge. Three copper-based surfaces are fabricated with different wettabilities i.e. a hydrophilic, a hydrophobic and a superhydrophobic surface (Figure 1a, left panel, see also Figure S1 for further details about surface fabrication and characterisation). Samples are tested in a vertical homogeneous electric field E∞ created by two parallel electrodes (Figure 1a, right panel). Drops of deionised water are deposited on a test sample placed at the lower electrode. The upper electrode is grounded whereas a positive DC voltage is applied to the lower electrode. After deposition, for E∞ = 0 the droplets reach an equilibrium contact angle θ ∈ [θr , θa ]. Taking into account that E∞ increases with a rate of 0.02 kV cm−1 s−1 and the charge relaxation time of water droplets 41 is in the order of 10−5 s the field is considered quasistatic. Observations of the droplets with increasing E∞ are made with a camera and simultaneously discharge activity and applied field strength are measured (see Discussion S1 and Figure S3 for further details about the experimental setup). The applied electric field E∞ causes a total electrostatic force parallel to it on the deposited drops resulting in their elongation (Figure 1a, right panel). 9,24 E∞ increases until a critical value E∞,cr is reached; at this point either a partial electric discharge (Figure 1b(i)) followed by an electric breakdown of the entire insulation gap between the electrodes due to the droplet deformation (e.g.formation of a Taylor cone, Figure 1b(ii)) 15 or a droplet lift-off 11 (Figure 1b(iii)) is observed. It should be noted that due to the homogeneity of the applied electric field, a partial discharge immediately leads to an electric breakdown (Figure 1b(ii)). 14 Therefore, in these experiments, both partial discharge inception field strength and breakdown field strength have the same value E∞,cr . The hydrophilic (Figure 1c, inset (i)) and hydrophobic (Figure 1c, inset (ii)) surfaces are evaluated in terms of partial discharge for droplet sizes (volume) Ω ranging from 5 µl to 50 µl (Figure 1c). For each drop size, E∞,cr is higher for hydrophilic surfaces than it is for hydrophobic ones indicating that the less wettable a surface (i.e. the higher the 7


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Figure 1: Equilibrium contact angle and its influence on the inception of an electric discharge. a, Left panel: Three copper-based surfaces that exhibit different wettabilities are tested: a hydrophilic, a hydrophobic and a superhydrophobic surface. Scanning electron images and schematic representation of the surfaces at the top and bottom of the panel, respectively. Perfluorodecanethiol covers the hydrophobic and superhydrophobic surfaces forming a self-assembled monolayer (black solid line) to lower the surface energy of the substrate. Nanoneedles form on the superhydrophobic substrate which consist of Cu(OH)2 (purple). Right panel: Schematic diagram of the test setup in which the different surfaces are tested. At the bottom electrode high voltage (HV) is applied whereas the top electrode is grounded. A sessile droplet is placed on the surface and remains undeformed when E∞ = 0 (drop shape indicated with black solid line). The applied voltage generates a homogeneous electric field (E∞ 6= 0) resulting in the elongation of the droplet in the direction of the field (drop shape indicated with red dashed line). b, (i) Artificially coloured image of a droplet (green) deformed due to an electric field. Droplet has a conical shape, known as a Taylor cone, that exhibits infinite curvature at the apex resulting in the inception of a partial discharge (magenta). (ii) Electric breakdown generated from a droplet that reaches a conical shape under the effect of an electric field. (iii) Lift-off of a droplet on a superhydrophobic surface without the occurrence of a partial discharge. c, Box plot (central mark indicates median, data fall between the 25th and 75th percentiles and whiskers extend to the most extreme data points) of applied critical electric field E∞,cr vs droplet volume Ω for a range of sizes 5 µl − 50 µl. Insets illustrate droplets that exhibit equilibrium contact angle θ for E∞ = 0, lying on a hydrophilic (i), a hydrophobic (ii) and a superhydrophobic (iii) surface. Critical applied electric field E∞,cr corresponds to the inception of a partial discharge (case 8 i and ii) or a lift-off (case iii). Experiments ACS Paragon are Plus compared Environmentto theoretical predictions (dashed red line).

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equilibrium contact angle at E∞ = 0), the weaker the electric field required to induce a partial discharge. Moreover, for both cases E∞,cr decreases with droplet size. This suggests that larger droplets or droplets on less wettable surfaces undergo larger deformations for the same E∞ and therefore they would reach a deformation sufficient to induce a discharge at smaller E∞,cr . 19,24 In the superhydrophobic case (Figure 1c, inset (iii)) we observe a different phenomenon. An increase of E∞ to a critical value E∞,cr leads to a lift-off of the droplet without any measurable discharge. The low contact angle hysteresis ∆θ = θa − θr = 2.8◦ indicative of the surface’s high slippery behaviour enables the droplet’s contact disc to shrink to zero at which point the droplet leaves the substrate. 10,11,42,43 The background field strength at lift-off E∞,cr increases with droplet volume and thus mass (Figure 1c). All of these observations agree with our theoretical predictions presented below. Theoretical prediction of critical applied electric field E∞,cr . We now compare the experimental results with theoretical predictions (Figure 1c). The applied electric field E∞ can increase up to a critical value at which the equilibrium expressed by equation (1) can no longer be fulfilled at every point of the droplet’s surface for a set of constant volume and contact disc and the computed droplet fails to describe a physically possible shape. 38 As shown later, this correlates to the electric field at which the droplet’s apex reaches an infinitely large curvature leading to a partial discharge. 14,15,24,44 This numerical critical value is observed to correspond to the measured discharge onset field strength. Therefore, we consider the measured discharge onset field strength and the applied electric field E∞ at which the model exhibits numerical instabilities as the same critical field E∞,cr . Results show that there is a good agreement between experiments and predictions (Figure 1c) for the hydrophobic and hydrophilic case and explicitly demonstrate the diminishing trend of E∞,cr with droplet size and static contact angle. Furthermore, it is worth noting that mean experimental and predicted values deviate by maximum 6% which supports the validity of our prediction method for E∞,cr .

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For the superhydrophobic case, we use a different and simpler model to estimate the E∞,cr value at which a droplet lifts off. It is based on a force balance where the electrostatic force Fel resulting from the applied electric field, the buoyant force Fb ,the gravitational force Fg , the capillary adhesion force Fc derived from the surface tension forces at the droplet’s triple-phase contact line (solid-water-air) 31,45–47 and the force Fp due to ∆p are considered. 5 It is worth noting that Fel is induced by the asymmetrical perturbation of the applied electric field due to the zero field inside the droplet 23 (see also Supporting Information, Discussion S3). The overall force balance at the droplet is described by the following equation (see also Discussion S3 and Figure S5):

2 +Fel . ρwater Ωg + 2πrdisc γ sin(θ) = ρair Ωg + ∆pπrdisc | {z } | {z } | {z } | {z } Fg

Fb

Fc

(2)

Fp

For the conditions of our study and for reasons of simplification, Fb is neglected since ρwater ρair . Based on equation (2) Fc and Fp are considered negligible at the instant of lift-off since the radius of the contact disc rdisc becomes marginally zero. 39,48 Finally, it is derived that E∞,cr scales with Ω1/6 (see Discsussion S3 and Figure S5 for a complete derivation of the E∞,cr estimation). This trend is verified experimentally as shown in Figure 1c where a good agreement between experiments and predictions for the superhydrophobic case is depicted with a maximum deviation that reaches 9%. Effect of contact angle hysteresis on the inception of a partial discharge. As mentioned previously, both the equilibrium contact angle and the contact angle hysteresis influence the partial discharge inception of a water drop on a surface. In fact, a droplet with a large equilibrium contact angle i.e. θ > 145◦ and considerably large contact angle hysteresis i.e. ∆θ > 10◦ can show partial discharge instead of lift-off. Furthermore, based on the previous analysis, the aforementioned surface is expected to show a partial discharge onset at lower E∞,cr compared to the hydrophilic and hydrophobic cases. Practically, in our current study, a surface that exhibits such properties is an originally superhydrophobic surface that

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undergoes degradation of the hydrophobic coating and the surface morphology due to several electric breakdowns occurring on it, leading to the creation of local pinning sites. 31 These changes of the surface wetting behaviour characterised by θr and θa are indicative of the chemical and/or mechanical degradation of the test surface and therefore are widely used in research studies for durability characterisation (see Figure S6 for further details about the wetting behaviour of the degraded surface). 49–51 Figure 2 highlights the effect of the altered surface wetting behaviour on the inception of a partial discharge. Droplets of 40 µl are deposited on the superhydrophobic surface (Figure 2a upper panel) and the same superhydrophobic surface after degradation (Figure 2a lower panel). Under the absence of electric field both droplets have similar equilibrium contact angle θ ≈ 166◦ (Figure 2a, upper and lower panels). This is attributed to the fact that the contact angle is not influenced by possible pinning sites (for the case of the degraded surface) that are confined within the contact disc of the deposited droplet, but it is determined by the air-water-solid interactions at the droplet contact line. 52 The droplets deform into a prolate spheroidal shape. 9,53,54 This deformation causes the gradual decrease of the equilibrium contact angle θ. When θ < θr = 159◦ the contact line recedes (Figure 2a, t = −2 ms, upper panel) until the area of the contact disc radius becomes marginally zero. 55 At this time instant (Figure 2a, t = 0 ms, upper panel) and based on equation (2), given that the electrostatic force Fel is marginally greater than the gravitational force Fg , the droplet detaches from the surface (Video S1). 5,42 After the droplet lifts off Fel > Fg and the drop thus accelerates and reaches the top electrode (Figure 2a, t = 40 ms, 60 ms, upper panel). It should be noted that prior, during and after the droplet lift-off no partial discharge is observed (Figure 2b and Video S1) since the measured value is close or below the background noise threshold of 0.3 pC. However, after degradation the surface shows a different behaviour. While E∞ increases to E∞,cr = 7.74 kV cm−1 , the droplet elongates and its contact line recedes until it reaches several pinning sites that prevent the contact disc from further shrinkage (Figure 2a, t =

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Figure 2: Contact angle hysteresis and its effect on the droplet behaviour in an electric field. a, Upper panel: Time lapse images of a 40 µl droplet deposited on a superhydrophobic surface. Initially, E∞ = 0 with the droplet reaching an equilibrium contact angle θ ≈ 166◦ . For E∞ = E∞,cr = 7.39 kVcm−1 droplets contact disc shrinks (t = −2 ms) and finally lifts off t = 0 ms. Insets show a magnified view of the droplets base. Lower panel: Time lapse images of a 40 µl droplet deposited on a degraded surface (originally superhydrophobic). For E∞ = E∞,cr = 7.74 kVcm−1 droplet contact disc remains at a certain value due to local pinning sites (t = −2, 0, 4.7 ms). The droplet deforms and its apex attains a shape of high curvature causing a partial discharge inception (t = 0 ms) that leads finally to an electric breakdown (t = 4.7 ms). Insets show a close-up view of the droplets apex. For both panels, scale bars of the time lapse images and the insets correspond to 2 mm and 500 µm respectively. b, Partial discharge amplitude vs time for the case of the superhydrophobic and the degraded surface. For the case of the superhydrophobic surface no significant partial discharge event was measured since all measurements (red triangle) were below or close to the threshold of 0.3 pC that corresponds to the background noise. The degraded surface shows a sequence of discharges that lead to an electric breakdown the amplitude (grey circle) of which is 2287 pC. 12 ACS Paragon Plus Environment

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−2 ms, lower panel). This is reflected to the equilibrium contact angle which at this instant is θ = 126◦ , suggesting that θr < 126◦ . Further deformation of the droplet gradually leads to a considerable increase of the apex’s curvature (Figure 2b, t = −2 ms, 0 ms, lower panel) resulting in the inception of a partial discharge with an amplitude of 1785 pC (Figure 2b). After the first discharge, we observe a sequence of partial discharge pulses that coincide with oscillations of the droplet’s apex, finally leading to an electric breakdown after 4.7 ms. Each discharge pulse from the pinned droplet corresponds to the exact video frame where its apex reaches a maximum curvature. After every pulse, the apex flattens rapidly before growing sharper until the next pulse (see Video S1). These oscillations could be caused by the discharges themselves (change in local gas pressure or space charge). Discharge onset occurs at E∞,cr = 7.74 kV cm−1 on the degraded surface which is even lower than E∞,cr of the hydrophilic (11.82 kV cm−1 ) and hydrophobic (9.82 kV cm−1 ) cases for the same droplet size of 40 µl. This is in agreement with our previous observation that E∞,cr increases with wettability. Experimental and numerical analysis of droplet shape evolution in electric fields. To better understand the relationship between wettability and associated deviations of the partial discharge inception field strength E∞,cr , we further investigate the deformation of the droplet’s shape with increasing applied electric field E∞ ≤ E∞,cr for the cases of hydrophobic and hydrophilic surfaces. To this end, Gibbs free energy change ∆G = G−G0 of the droplet for a specific electric field E∞ (where G and G0 are the droplet’s Gibbs free energy at E∞ and for zero electric field, respectively) is used as an indicator of the deformation the droplet undergoes. 56–58 Since the contact disc of both surfaces remains unchanged, Gibbs free energy change of the droplet (see Discussion S4 and Figure S7 for a complete derivation of droplet ∆G) is expressed as ∆G = γ∆A

(3)

where ∆A = A − A0 is the difference between the droplet’s lateral surface area for E∞ and zero electric field. 13


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Figure 3 shows the Gibbs free energy change of 10 µL droplets versus the applied electric field E∞ on hydrophilic and hydrophobic surfaces. Up to E∞ ≈ 6.5 kVcm−1 deposited droplets on both surfaces show negligible ∆G (Figure 3, insets E∞ = 0 and 6.1 kVcm−1 ). However, for E∞ > 6.5 kVcm−1 the droplet on hydrophobic sample shows considerably higher ∆G (Figure 3, insets E∞ = 9, 10.5 and 10.7 kVcm−1 ) than that on the hydrophilic surface (Figure 3, insets E∞ = 10.6, 13 and 13.4 kVcm−1 ). Alternatively, it means that for the same value of a droplets ∆G, a stronger electric field is needed for the hydrophilic surface than the hydrophobic one suggesting that E∞,cr increases with wettability. In both cases whilst E∞ reaches E∞,cr , ∆G increases abruptly 6,20 indicating that deformation is accelerated at this phase (Figure 3, insets E∞ = 10.5 and 10.7 kVcm−1 (hydrophobic surface) and insets E∞ = 13.0 and 13.4 kVcm−1 (hydrophilic surface)). This abrupt increase is attributed to the mutual interaction between the deformed droplet and the applied electric field: the presence of the deformed droplet, which acts as an electrode, enhances the electric field around the apex due to its increased curvature which in return causes an increased electrostatic force on the droplet. Further increase of this force results in further deformation of the droplet’s shape and subsequently local enhancement of the electric field. In addition, we compare the experimental drop shapes with the ones obtained by the model based on equation (1) and described previously. 5 The shapes for each background field value are computed for two different no field contact angles (corresponding to the hydrophilic and hydrophobic surfaces). From the shapes we calculate the theoretical Gibbs free energy change of the droplets and plot them versus applied electric field strength. For both cases, the predicted deformation is in good agreement with that of the experiment. Even though for the hydrophobic surface a deviation between theory and experiments is observed around E∞ = 7 to 10 kVcm−1 , the predicted ∆G versus E∞ graphs of both cases explicitly show similar trends to the experimental curves: initially, the droplets exhibit negligible deformation and shortly before E∞,cr an abrupt increase of ∆G occurs that reaches a margin (Figure 3). The theoretical margin (that corresponds to the onset of the numerical

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Figure 3: Evolution of drop shape with applied electric field for different wettabilities. Gibbs free energy change ∆G of 10 µL droplets vs applied electric field E∞ for the hydrophilic and hydrophobic surfaces. ∆G is calculated experimentally (grey circles correspond to hydrophilic and grey triangles to hydrophobic) and theoretically (solid orange line corresponds to hydrophilic and solid green line to hydrophobic). Insets above the green solid line (E∞ = 0, 6.1, 9, 10.5 and 10.7 kVcm−1 ) and below and right of the orange solid line (E∞ = 0, 6.1, 10.6, 13 and 13.4 kVcm−1 ) show evolution of droplets shape on the hydrophobic and hydrophilic surface respectively. Dashed red lines represent the predicted droplet shapes. Scale bars correspond to 1.5 mm.

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instabilities in the model) and the experimental one (vertical green and orange dashed lines, Figure 3) shows small deviation which, for a 10 µL drop, reaches 2.5% and 4.4% for the case of hydrophilic and hydrophobic surface, respectively.This supports our previous assertion that E∞,cr can be adequately predicted with the proposed method. Water droplet and electric field interactions. Figure 4a shows drop shapes and the computed electric field strength in the surrounding air for a period of 9 ms before the critical event i.e. partial discharge inception or drop lift-off. The evolution of the droplet is observed with a high speed camera (Figure 4a, see also Video S2). The shapes of the droplet extracted from the videos are used to simulate the corresponding local electric field computed in 2D axisymmetric mode based on the drop’s axis of symmetry (Figure 4a). The instant t = 0 ms corresponds to the last recorded frame before partial discharge inception (hydrophobic and hydrophilic surfaces) or lift-off (superhydrophobic surface) occurs. It is apparent that for both the hydrophobic and hydrophilic surfaces, E around the apex considerably increases during those last 9 ms. The degree of inhomogeneity Emax /E∞ , where Emax is the maximum local electric field strength (which occurs at the drop apex), grows from 4.9 for the hydrophilic and 9.3 for the hydrophobic surface at t = −9 ms to over 17 at t = 0 ms for both. Even though both surfaces exhibit the same degree of inhomogeneity at t = 0 ms the droplet on the hydrophilic surface is subjected to an electric field strength E∞ = 15 kVcm−1 approximately 1.4 times greater than the droplet on the hydrophobic surface i.e. E∞ = 10.6 kVcm−1 . The drop on the superhydrophobic surface before lift-off shows negligible deformation and its degree of inhomogeneity remains constant at approximately 4 (E∞ = 6.1 kVcm−1 ). Next, using only the drop shapes and the computed local electric fields, we predict the possibility of partial discharges and verify the strong correlation to surface wettability. Along the axis of symmetry of the droplet, the maximum local electric field Emax can become greater than the electric field strength limit which is E0 = 24.4 kVcm−1 for air at atmospheric pressure. 16 Exceeding this value is a necessary condition for the initiation of any of the

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Figure 4: Influence of droplet shape on the deformation of the local electric field and on discharge inception. a, Time lapse images of a 10 µL droplet deposited on the hydrophilic (upper panel), the hydrophobic (middle panel) and the superhydrophobic surface (lower panel). At time instants −9 and 0 ms, computed electric fields (right) with a magnified view (insets) are also shown. At t = 0 ms the inception of partial discharge occurs (hydrophobic and hydrophilic surfaces) or the droplet lifts off (superhydrophobic surface). For the hydrophilic surface at t = 2.6 ms and hydrophobic surface at t = 0.2 ms the partial discharges closes the gap between the electrodes and a full breakdown occurs. For the superhydrophobic surface at t = 32.4 ms, the droplet continues its lift-off without any measurable discharge. Scale bars correspond to 1 mm. b, Natural logarithm of the number of free electrons in the formed avalanche N vs time t. For the hydrophilic and hydrophobic surfaces N exceeds Ncr while it remains at approximately 0 for the superhydrophobic surface. 17


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considered ionisation processes. An additional and sufficient condition is required for the discharges to occur: The number of free electrons N in the electron avalanche should exceed a critical value Ncr ≈ 12·1015 . 16 Figure 4b shows the logarithm of N versus t. N is estimated by the following equation: 16

N =e

Rz

0 zapex αeff dz

,

(4)

where αeff is the effective ionisation coefficient and zapex and z0 are the respective vertical coordinates of the droplet’s apex and the position at which the local electric field strength along the axis of symmetry of the droplet is E0 (see Figure S8). When N > Ncr the ionisation process is self-sustained enabling partial discharges. 16 For the case of hydrophilic and hydrophobic surfaces Ncr is exceeded at t = −0.55 ms and t = −0.33 ms when the apex exhibits infinite curvature. The discharge measured at t = 0 denotes that the shape deformation is a predominant factor that abruptly increases the number of electrons in the avalanche due to the local field enhancement. It confirms that the more wettable the surface and thus the more difficult it becomes for the drops to deform, the stronger the background field required for a discharge. On the contrary, for the superhydrophobic case the negligible deformation of the droplet causes minor distortion to the electric field and as a result the region where E > E0 is either non existent or so small that N ≈ 0 and hence no discharge occurs.

CONCLUSIONS In our study, we quantifiably describe the influence of surface wettability on the inception of electric discharges from water drops when subjected to a homogeneous background DC field perpendicular to the surface. We show that the higher the static contact angle of a pinned droplet, the lower the applied electric field required for the inception of an electric discharge. On the other hand, a superhydrophobic surface leads the droplet to lift-off with18


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out the inception of a measurable electric discharge. To support the experimental findings, we computationally predict the aforementioned behaviour with good agreement to measurements. We show that the more wettable the surface the smaller the droplet’s deformation under the same applied field by determining the shape of a drop of any size on a surface of any wettability for an arbitrary background field value. It is observed that the droplets abruptly deform marginally before the inception of a discharge due to an interplay between the droplet’s high curvature apex and the local electric field. We show that this specific shape is a key factor in creating the conditions for an electric discharge. Contrary to the case of the hydrophilic and hydrophobic surfaces, for the superhydrophobic surface this interplay is weak even at lift-off field. Therefore, it does not lead to an abrupt local intensification of the electric field and thus any discharge. In addition, we predict that the critical shape of the droplets on the hydrophilic and hydrophobic surfaces cause self-sustained discharges. This fundamental understanding of the interaction between electric fields, water droplets and surface wettability can be extended to other conductive liquids as well (see equation (1)) such as polar and ionic ones, 22,59 thus accommodating the ability to optimise a wide range of applications. To this end, our observations can facilitate the design of the surface of high voltage overhead transmission lines to significantly improve their environmental performance. 17,18 Furthermore, our findings can be implemented for the enhancement of the efficiency of energy systems e.g. heat exchangers that involve interfacial phase change phenomena such as condensation. Recently, a number of studies 60–63 has shown that, on a cooled superhydrophobic surface, coalescence-induced droplet jumping coupled with the use of external electric fields improves significantly condensate droplet removal and thus condensation heat transfer. Our study advances a step further and suggests that external electric fields can be implemented for the removal of condensate droplets before the occurrence of a droplet jumping event at scales smaller than the capillary length. That means, an applied electric field of E∞ = 0.5 kVcm−1 would be required for a droplet of 10 µm to lift-off, a typical radius for the occurrunce of a coalescence-induced jumping droplet event. 60,62 Last

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but not least, this study offers an alternative perspective for the control and optimisation of microplasmas 64,65 from liquid electrodes by manipulating their shapes through surface engineering.

ASSOCIATED CONTENT Supporting Information The Supporting information is available free of charge on the ACS Publications website at DOI: xx.xxxx/ascami.xxxxxxx. The following files are available. Scanning Electron Microscope Images (SEM) and Energy Dispersive X-Ray Spectroscopy (EDX) analysis of the tested surfaces, conductivity characterization of the tested surfaces, experimental setup, details on the numerical model, derivation of E∞,cr for droplet liftoff, Wetting behaviour of degraded and superhydrophobic surfaces, derivation of Gibbs free surface energy, geometrical considerations for the calculation of the number of free electrons N, supporting figures (S1-S8) (PDF) Droplets on surfaces exhibiting different contact angle hysteresis in electric fields reaching E∞,cr (AVI) Shape evolution of droplets on surfaces of different wettabilities until reaching an electric breakdown (AVI)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected], Phone: +41 44 632 24 88, Fax: +41 44 632 13 25 (P.RvR); [email protected], Phone: +41 44 632 13 25 (C.F.) Author Contributions C.S. and M.P. conceived the idea to perform this research. C.F., P.RvR., C.S., M.P. and S.H. guided the research scientifically and technically throughout. P.B., C.S. and M.P., executed 20


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experiments and analysed data. M.P. and P.B. performed simulations. C.S. fabricated test surfaces. C.S., P.B., M.P., C.F. and P.RvR. wrote the paper. All authors discussed the content of this work and reviewed the manuscript. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

¶

C.S., P.B. and M.P. contributed equally to this work.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS We gratefully acknowledge the financial support from an ETH Zurich Career Seed Grant (SEED-CORONA-SH, 0-20209-16). We also gratefully acknowledge Dr. Alain Gliere for kindly providing us with the source code for the prediction of the droplets shape deformation due to an electric field. We thank Mr. Massimo Saracino for the permission to use Figure 1b(i) that was taken with the PhaseOne DF+ camera system. We thank Dr. Kunze Karsten from Scientific Center for Optical and Electron Microscopy, ETH Zurich for his support in the acquisition of SEM and EDX data and Mr. Reto Suter for his contribution in the fabrication and wettability characterization of the test surfaces. We also thank Prof. Nicholas Spencer and Dr. Andrea Arcifa from the Laboratory for Surface Science and Technology for the acquisition of surface morphology data of the tested samples. The authors thank Mr. HansJuerg Weber from the High Voltage Laboratory, ETH Zurich and Prof. Dimos Poulikakos from the Laboratory of Thermodynamics in Emerging Technologies, ETH Zurich for their insightful comments within the context of this work.

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Influence of Surface Wettability on Discharges from Water Drops in

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