Anisotropic Spreading of Bubbles on Superaerophilic Straight Trajectories Beneath a Slide in Water

water

Article Anisotropic Spreading of Bubbles on Superaerophilic Straight Trajectories beneath a Slide in Water

Chengxu Tu 1,2,3 , Qincan Yang 1, Yeyu Chen 1, Yuhang Ye 1, Yukun Wang 1, Pengfei Du 1, Sensen Yang 1, Fubing Bao 1,*, Zhaoqin Yin 1, Renjie Jiang 4 and Xiaoyu Liang 1

1 Zhejiang Provincial Key Laboratory of Flow Measurement Technology, China Jiliang University, Hangzhou 310018, China; [email protected] (C.T.); [email protected] (Q.Y.); [email protected] (Y.C.); [email protected] (Y.Y.); [email protected] (Y.W.); [email protected] (P.D.); [email protected] (S.Y.); [email protected] (Z.Y.); [email protected] (X.L.) 2 College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China 3 LEO Group Co., Ltd., Wenling 317500, China 4 Institute of Naval Architecture and Ocean Engineering, Ningbo University, Ningbo 315211, China; [email protected] * Correspondence: [email protected]; Tel.: +86-571-8767-6277

Received: 10 February 2020; Accepted: 9 March 2020; Published: 12 March 2020

Abstract: Although the bubble contacting a uniformly superaerophilic surface has caused concern due to its application potential in various engineering equipment, such as mineral flotation, very little is known about the mechanism of how the bubble spreads on a surface with anisotropic superaerophilicity. To unveil this mystery, we experimentally studied the anisotropic behavior of a bubble (2 mm in diameter) spreading on the superaerophilic straight trajectories (SALTs) of different widths (0.5 mm–5 mm) in water using a high-speed shadowgraphy system. The 1–3 bounces mostly happened as the bubble approached the SALTs before its spreading. It is first observed that the bubble would be split into two highly symmetrical sub-bubbles with similar migration velocity in opposite directions during the anisotropic spreading. Two essential mechanisms are found to be responsible for the anisotropic spreading on the narrow SALTs (W 2 mm with two subregimes) and the wide ≤ SALTs (W 3 mm with four subregimes). Considering the combined effect of the surface tension ≥ effect of SALT and Laplace pressure, a novel model has been developed to predict the contact size r(t) as a function of time. The nice agreement between this model and our experiments reconfirms that the surface tension effect and Laplace pressure prevail over the hydrostatic pressure.

Keywords: superaerophilic trajectory; anisotropic spreading; bubble dynamics

1. Introduction Bubbles and drops spreading or attaching with the walls have been widely investigated and can be seen in nature and various industrial processes, such as diving bell spiders (Argyroneta Aquatica) [1], wastewater treatment, recovery of coal and minerals, and heat transfer [2,3]. For instance, the delay in the departure of air bubbles formed on the heater surface could impede the effectiveness transfer of heat with the surrounding medium [4]. Similarly, one of the greatest problems hindering the efficiency of the fuel cell is the adhesion of the electrochemically generated bubbles to the electrodes [5]. If the disturbed bubbles could be directionally transported to the designated areas or reduce the air film area, then the coverage area of the gas film can be significantly decreased after the bubble attachment, and the performance of the fuel cell and the heat transfer can be greatly enhanced. SALT proposed in this article seems to be a very promising method. Especially, due to being covered by a thin plastron

Water 2020, 12, 798; doi:10.3390/w12030798 www.mdpi.com/journal/water Water 2020, 12, 798 2 of 14 of air, most of the superhydrophobic surfaces have remarkable super-aerophilic properties in the water and recently successfully been used in the directional and continuous transport of air bubbles in water [6,7]. In general, for the spreading of both bubbles and drops, the capillary length, surface tension, and gas/liquid density are three critical factors that play a very important role in interfacial hydrodynamics [8]. The balance among the friction, surface tension, and gravity has a significant effect on the bubble resistance motion [8,9]. As a millimetric bubble approaches a no-slip surface before spreading, it may repeatedly bounce on the surface [10]. The drainage of the liquid film [11,12] between the bubble and surface is the most crucial factor of rebounding behavior, as a result of bubble deformation and velocity. Tsao and Koch [13] found that the collision mechanism can be explained by the transition among the kinetic energy, surface energy, and potential energy. Pelletier and Béguin [14] experimentally investigated that, based on the restitution relations, the aspect ratio of a bouncing bubble before a rebound can be predicted after a rebound. On the other hand, the contact of bubbles with different boundary walls present interesting phenomena, and many of them have broad potential in engineering applications. Compared to hydrophilic and hydrophobic surfaces, the bouncing probability of bubbles’ impact with aerophilic plates falls from 100% to 40% [15]. In addition, the rising bubble would slide on a hydrophobic wall, because the wall hydrophobicity thins the liquid layer between the wall and the bubble below its critical thickness and leads to the rupture of this liquid layer, and finally, a three-phase contact (TPC) is formed [16,17]. Wang et al. [18] observed the bubble bursting on lotus leaves and found that the height, width, and distribution of the hierarchical structures were responsible for the air bubble bursting on superhydrophobic surfaces, and the spreading time of bubbles is within milliseconds. De Maleprade and Clanet [15] experimentally studied the spreading of bubbles contacting the aerophilic surface and found that during the approaching and bouncing process, wall-effects affect the initial shape. The surface tension and later buoyancy are two crucial factors to drive the rapid evolution of bubbles spreading in three typical stages and further confirmed that the characteristic spreading time (10 ms) of the bubble on a superaerophilic surface (SALS) is much shorter than that in other plates, which agrees well with the results of Wang et al. [18]. Moreover, Ma et al. [19] combined the geometry-gradient structure with the spreading of bubbles on the upper SALS to manipulate the directional transport of bubbles without energy input. As discussed above, previous research has been devoted to studying the dynamics of bubbles collision with surfaces [14], the directional and continuous transport of bubbles on superhydrophobic plates [19], or isotropic spreading on SALSs [15]; however, to our knowledge, no results aimed at the anisotropic spreading of bubbles on the SALSs have yet been reported. The anisotropic spreading of bubbles on the designated superaerophilic areas may motivate the novel technologies to enhance or reduce the reaction rate, mass, and heat transfer rate in some specific positions and then to improve the equipment performances in mineral flotation, selective aeration, bubble reactors, and so on. Here, we focus on bubbles’ anisotropic spreading on superaerophilic straight trajectories beneath a slide immersed in water. Concentrated efforts have led to understanding the effects of the width of the trajectories on bubble spreading for better prediction of bubble dynamic behavior as it is spreading. The SALT width can be regarded as an important characteristic parameter indicating the anisotropy of the spreading. Therefore, a bubble (2 mm in diameter) approaching and spreading on a series of width superaerophilic trajectories was investigated. The results will offer people ideas to manipulate bubbles in an aqueous environment.

2. Materials and Methods

2.1. Preparation for Superaerophilic Straight Trajectories (SALT) The superaerophilic straight trajectories (SALT) are obtained using spray coating with a silica nanoparticle solution (Glaco, Soft99 Co., Japan, SiO2 of 30-nm primary diameter). After solvent Water 2020, 12, 798 3 of 14

evaporation, the coating is further dried in a vacuum drying chamber at 150 ◦C for 30 min, and this coatingWater 2020 for a, 12 trajectory, 798 was repeated three times. Based on these procedures, silica particles can3 of adhere 14 to the trajectory surface, forming a superhydrophobic nanostructure with a typical roughness of about coating for a trajectory was repeated three times. Based on these procedures, silica particles can 100 nm, as reported by Maleprade et al. [15]. Other necessary operation steps for surface treatment are adhere to the trajectory surface, forming a superhydrophobic nanostructure with a typical roughness as follows:Water First, 2020, 12 the, 798 glass surface is ultrasonically cleaned with ethanol solution for 5 min3 of and 14 then is of about 100nm, as reported by Maleprade et al. [15]. Other necessary operation steps for surface rinsed with deionized water and is dried in the vacuum drying chamber. Second, the designated areas treatmentcoating are for as a follows: trajectory First, was therepeated glass threesurface times. is ultrasonically Based on these cleaned procedures, with silicaethanol particles solution can for 5 of trajectoriesminutesadhere and areto then the constructed trajectory is rinsed surface,with using deionized forming a mask a water tosuperhydrophobic achieved and is dried diﬀerent nanostructure in the trajectory vacuum with drying widths a typical chamber. (0.5 roughness mm–5 Second, mm) on thethe slides. designatedof about Finally, 100nm, areas the superaerophilicityas of reported trajectories by Maleprade are constructed of the et al. trajectories [15]. using Other a would necessarymask beto operation testedachieved by stepsdifferent ejecting for surface watertrajectory drops andwidths thentreatment spreading (0.5 mm–5 are bubblesasmm) follows: on the on First, them.slides. the glass TheFinally, microscopicsurface the superaerophilicityis ultrasonically morphology cleaned of of the thewith trajectories trajectory ethanol solution would surface forbe produced tested5 throughby ejectingminutes the above water and then steps drops is isrinsed and shown withthen in deionized spreading Figure 1water. bubbles It can and be is on dried seen them. in from the The vacuum the microscopic SEM drying images chamber. morphology that Second, the surface of the is the designated areas of trajectories are constructed using a mask to achieved different trajectory almosttrajectory uniformly surface covered produced with through the SiO the2 nanoparticles. above steps is shown in Figure 1. It can be seen from the widths (0.5 mm–5 mm) on the slides. Finally, the superaerophilicity of the trajectories would be tested SEM images that the surface is almost uniformly covered with the SiO2 nanoparticles. by ejecting water drops and then spreading bubbles on them. The microscopic morphology of the (a) (b) trajectory surface produced through the above steps is shown in Figure 1. It can be seen from the SEM images that the surface is almost uniformly covered with the SiO2 nanoparticles. (a) (b)

FigureFigure 1. SEM 1. SEM images. images. (a) Large-area(a) Large‐area SEM SEM image image of of the the surface surface of of the the SALTs.SALTs. (b) Enlarged view view from from (a). (a). Figure 1. SEM images. (a) Large‐area SEM image of the surface of the SALTs. (b) Enlarged view from 2.2. Experimental Setup (a). 2.2.The Experimental tank (150 mmSetup 150 mm 150 mm) is ﬁlled with puriﬁed water. The slide sits horizontally on 2.2. Experimental Setup× × two standardThe tank gauge (150 blocks mm× 150 (30 mm× mm 1509 mmmm) is70 filled mm, with vertically) purified to water. located The itself slide 6 sits mm horizontally above the nozzle on × × outlet,two standard as shownThe tankgauge in (150 Figure blocks mm×2a. 150(30 The mm× bubbles 150 9 mm× mm) 70 areis filled mm, released withvertically) purified from to water. this located submillimetric The itself slide 6 sits mm horizontally above nozzle the (0.16 on nozzle mm two standard gauge blocks (30 mm× 9 mm× 70 mm, vertically) to located itself 6 mm above the nozzle in inneroutlet, diameter) as shown atin theFigure bottom 2a. The of thebubbles tank are by released pushing from an injector this submillimetric using a syringe nozzle pump (0.16 (Harvardmm in outlet, as shown in Figure 2a. The bubbles are released from this submillimetric nozzle (0.16 mm in inner diameter) at the bottom of the tank by pushing an injector using a syringe pump (Harvard Pump 11inner Elite, diameter) Holliston, at the MA) bottom and of a Tygonthe tank tube by pushing to connect an injector the nozzle using and a syringe the injector. pump (Harvard The calibrated equivalentPumpPump 11 diameter Elite, 11 Elite, Holliston, ofHolliston, the bubbleMA) MA) and and (d aeq Tygona) Tygon is 2 mm, tube tube which toto connect is calculated the the nozzle nozzle and from and the the its injector. initialinjector. The volume Thecalibrated calibrated just before eq theequivalent bubbleequivalent separating diameter diameter fromof the of the the bubble bubble nozzle, (d (d)eq at is) is which2 2 mm, mm, whichwhich moment isis calculated calculated the bubble from from is its highly itsinitial initial volume axisymmetrical. volume just beforejust before the bubblethe bubble separating separating from from the the nozzle, nozzle, at at which which momentmoment the the bubble bubble is ishighly highly axisymmetrical. axisymmetrical. (a) (a) PurePure Water Water (b)

SuperaerophilicSuperaerophilic TrajectoryTrajectory

W W Bubble 6mm Bubble 6mm Nozzle Block Glass Slide Nozzle Block Glass(e) Slide (c) (d) r(t) 2rs(t) (c) (d) (e) d(t) h(t) r(t) hL(t) 2rs(t)h R(t)

d(t) R h(t) hL(rtL)( t) rR(t) hR(t)

R rL(t) rR(t) Figure 2.FigureExperimental 2. Experimental setup. setup. (a )(a) Schematic Schematic of the the experimental experimental system. system. (b) Schematic (b) Schematic of the of the superaerophilicsuperaerophilic trajectories trajectories (SALT) (SALT) and and the the SALT SALT characterizedcharacterized by by its itswidth, width, W. (cW) An.( cair) An bubble air bubbleof of radiusFigure Rradius before 2. Experimental R before contacting contacting setup. the the superaerophilic superaerophilic(a) Schematic slideslideof the or or SALT. SALT.experimental (d ()d The) The spreading system. spreading of ( bthe) of Schematicbubble the bubble occurs of occursthe aftersuperaerophilic contact.after contact. (e) The trajectories (e) bubbleThe bubble (SALT) rupture rupture and takes takes the placeSALT place oncharacterized a a SALT SALT (W (W =by 2–5= its2–5 mm) width, mm) after W afterthe. (c )transition An the air transition bubble to a of to a radiuscritical R before r(t). contacting the superaerophilic slide or SALT. (d) The spreading of the bubble occurs critical r(t). after contact. (e) The bubble rupture takes place on a SALT (W = 2–5 mm) after the transition to a critical r(t).

Water 2020, 12, 798 4 of 14

Water 2020, 12, 798 4 of 14 In the present study, the spreading of bubbles on SALTs of different widths were experimentally ® investigatedIn the using present a high-speed study, the spreading camera (Phantomof bubbles onv2012, SALTs Vision of different Research widths Inc., were Wayne, experimentally NJ, USA) at 50,000 or 89,000 frame/s with 1024 400 or 512 ® 384 pixels and the shadowgraphy light source investigated using a high‐speed camera× (Phantom× v2012, Vision Research Inc., Wayne, NJ, USA) at composed50,000 ofor high-light89,000 frame/s LED with (LLBK1-LA-W-0022, 1024 × 400 or 512 AITEC × 384 pixels SYSTEM and CO.,the shadowgraphy LTD., Japan) and light a disourceffuser platecomposed (see in Figure of high2).‐light Both LED top-view (LLBK1 and‐LA‐ side-viewW‐0022, AITEC images SYSTEM were obtainedCO., LTD, using Japan) this and high-speed a diffuser shadowgraphyplate (see in system Figure but 2). wereBoth nottop‐ simultaneousview and side observations.‐view images were When obtained the superhydrophobic using this high surfaces‐speed wereshadowgraphy immersed underwater, system but the were air pocket not simultaneous would be trapped observations. in this area When [20 ].the The superhydrophobic experiments were conductedsurfaces after were immersing immersed the underwater, slides in the the water air pocket tank for would 30 min be totrapped ensure in that this the area plastron [20]. ofThe air on theexperiments SALT was were uniform conducted and stable. after immersing Corresponding the slides to di inff erentthe water widths tank of for our 30 SALTs minutes and to di ensurefferent heightsthat between the plastron the nozzleof air on and the the SALT plate, was bubbles uniform tend and tostable. have Corresponding a flattened shape to different on the surface widths andof bounceour oSALTsff the surfaceand different several heights times between [15]. Further, the nozzle the rupture and the of plate, the interveningbubbles tend liquid to have layer a flattened between shape on the surface and bounce off the surface several times [15]. Further, the rupture of the the bubble and the SALS (or SALT; in practice, the plastron of air on it) always occurs after the bubble intervening liquid layer between the bubble and the SALS (or SALT; in practice, the plastron of air contacts the wall for a short while, and hence, the initial velocity of the bubble plays a limited role on it) always occurs after the bubble contacts the wall for a short while, and hence, the initial velocity in its spreading. Therefore, this article concentrates on the spreading of bubbles, and the initial gap of the bubble plays a limited role in its spreading. Therefore, this article concentrates on the spreading between the bubble and SALT would not be changed. of bubbles, and the initial gap between the bubble and SALT would not be changed. 3. Results and Discussion 3. Results and Discussion 3.1. Bubbles Bouncing against SALTs 3.1. Bubbles Bouncing Against SALTs Sequence of snapshots of high-speed shadowgraph pictures illustrating the contact of bubbles Sequence of snapshots of high‐speed shadowgraph pictures illustrating the contact of bubbles withwith horizontal horizontal SALTs SALTs or SALS or SALS are are presented presented in Figurein Figure3. The 3. The time time interval interval between between adjacent adjacent frames frames is 8.6 msis 8.6 and ms 5 and ms for 5 ms single-bounce for single‐bounce (Figure (Figure3a) and 3a) non-bouncingand non‐bouncing (Figure (Figure3b),3b), respectively. respectively.

(a) (b) d

0.4 d W -2 Single-bounce 3mm Two-bounce 1mm Bouncing Probability 0.2 Three-bounce 1mm Non-bouncing 4mm

0 -3 012345 0 20406080100120 W /mm t /ms Figure 3. Bubble dynamics during contacting SALTs’ different widths (W) of with r = 1 mm. Sequence Figure 3. Bubble dynamics during contacting SALTs’ different widths (W) of with r = 1 mm. Sequence of snapshots of a bubble colliding with the SALT before spreading: either bubbles experience bounce off of snapshots of a bubble colliding with the SALT before spreading: either bubbles experience bounce the surface for single-bounce (a) to three-bounce or non-bouncing (b), and the last image both in (a) and off the surface for single‐bounce (a) to three‐bounce or non‐bouncing (b), and the last image both in (b) show that the bubbles stop with their flattened shapes on the trajectory just before their spreading. (a) and (b) show that the bubbles stop with their flattened shapes on the trajectory just before their Imagesspreading. are separated Images byare 8.6 separated ms and by 5 ms 8.6 for ms the and single-bounce 5 ms for the single case (‐abounce) and the case non-bouncing (a) and the non case‐ (b), respectively.bouncing case (c ()b Probability), respectively. of bouncing (c) Probability against of bouncing the SALTs against of diff theerent SALTsW.( dof) Thedifferent vertical W. ( positiond) The (depth)vertical of the position bubble (depth) d as a function of the bubble of time d as t, and a functiond = 0 corresponds of time t, and to d the = 0 depth corresponds of the SALTs’ to the depth low side. of the SALTs’ low side. Many previous researches indicated that bubbles tend to bounce when they approach a solid plate [10,Many21] and previous they are researches not sensitive indicated to the normalthat bubbles wettability tend to of bounce the surface when (aerophilic they approach/hydrophobic a solid or aerophobicplate [10,21]/hydrophilic) and they [22 ].are The not bouncing sensitive almost to occursthe withnormal the bouncingwettability probability of the surface of about

Water 2020, 12, 798 5 of 14

100%; however, the surface superaerophilicity can decrease this bouncing probability and results in non-bouncing before spreading [15]. As can be observed, the bouncing mostly happened when the bubble collided with SALTs (superaerophilicity) of different widths, and in our findings, non-bouncing only takes place for W = 4 mm. This behavior agrees with the previous results [15] but with a significantly higher bouncing probability, as shown in Figure3c. Due to the wall-e ffect, despite the surface wettability, the liquid film between the wall and the bubble was drained and the shape of the bubble oscillates [23], and it tends to bounce downward against the direction of the buoyancy force. During this process, part of the total energy is dissipated due to viscous loss [2], and then, the spherical bubble at the largest depth can return to the approach to the wall for its second collision if the total remaining energy is enough. After repeated bouncing motions several times, the energy has completely dissipated, and the bubble transits to be flattened and stops on the wall. When it comes to the SALSs [15] or SALTs (present work), the bubble will perform spreading after exceeding this dynamical threshold. The whole bouncing processes for SALTs are described using d(t) plotted as a function of time t, and some typical cases are shown in Figure3d. A high consistency was found for the evolution of d(t) between these bubble-wall collisions at different W and bounce times. This property indicates that neither SALTs’ width nor bounce times have a significant influence on the d(t) evolution before bubble spreading. Compared with the similar superaerophilic solids [15], a similar d(t) evolution can be seen for the bubble colliding with the SALTs; that is, the rebound amplitude sharply decreased as the bounce time increased. Except for W = 4 mm, the bubbles always execute multi-time rebounds on the SALTs with the bouncing probability of 100%, while the bouncing probability has fallen from 100% to 85% for W = 4 mm, and the bubble may spread after the first touch to the surface rather than bounce back, as seen in Figure3b. Clearly, as seen in Figure3c, the bouncing probability is highest for three-bounce (above 55%) and is lowest for single-bounce (~10%, W = 1 mm, 3 mm) or non-bouncing (~15%, W = 4 mm). As reported by De Maleprade et al. [15], during the bubble approaching the superaerophilic surface, it decreases linearly, and the water layer between the bubble and SALT is gradually squeezed away. At the moment, a thin plastron of air on the superaerophilic surface will induce slips [15]. In the present work, when W exceeds a critical value (~4 mm), bubbles may stop on the SALT without bouncing, but the probability of non-bouncing is significantly smaller than that for the bubbles contacting the superaerophilic walls (~60%) [15]. This change can be attributed to the difference in the coating methods between our study (spray) and that of De Maleprade et al. [15] (dip-evaporation), which may build a thicker coating with lower uniformity, and this will be discussed further in Section 3.3.

3.2. Bubble Anisotropic Spreading on the SALTs As proposed by several critical previous studies [15,18], the spreading of bubbles after contacting the SALS is very rapid, with a characteristic time of about 10 ms, and the spreading velocity, which usually corresponds to the moving contact line, can be up to ~4 m/s. To our knowledge, however, existing studies are limited to the isotropic (or quasi-isotropic) spreading of bubbles contacting walls of uniform wettability (hydrophobic, hydrophilic, aerophilic, and aerophobic). It is interesting to look what will happen if the bubbles are spreading on a surface of anisotropic aerophilicity, such as on SALTs. Consequently, the similarities and differences between the spreading of the flattened bubbles, after bouncing, contacting the uniform SALSs and SALTs are discussed from a bubble dynamical point of view. It is clear that the bubble, owing to the anisotropic aerophilicity distributed on the SALTs, will perform anisotropic spreading along the SALTs, and two contact lines moving in the opposite direction (left and right from side-view) will be formed. Half of the distance between the two outside contact lines (approximately perpendicular to the SALT at r(t) > 0.5deq) is denoted as the contact size of the SALTs (r), like SALS, and then rL and rR denote the respective distances of the left contact lines and the right contact lines to the point of puncturing, where the rupture of the fluid layer between the bubble and the SALT first happens. According to the spreading velocity (which equals the change rate of the Water 2020, 12, 798 6 of 14

Water 2020, 12, 798 6 of 14 contact size r) and the interface dynamics, the isotropic spreading of the bubble on the SALS with uniformrate of superaerophilicity the contact size r) and can the be dividedinterface into dynamics, three dynamical the isotropic stages: spreadingr t atof rthe< Rbubble1 (= 0.4 ondeq the), r 1/3 1/2 ∝ 1/∝2 t SALSat R with< r < uniforma, and r superaerophilicityt at r > a, as suggested can be divided by De into Maleprade three dynamical et al. [15 stages:]. Where r ∝ ta at= r ( <γ /Rρ1 g(=) 1 ∝ (~2.50.4d mmeq), r for ∝ t water)1/3 at R1 is < ther < capillarya, and r ∝ length, t1/2 at rγ > isa, theas suggested surface tension, by De Malepradeρ is the fluid et al. density, [15]. Where and g is 1/ 2 thea=( gravityγ/ρg) acceleration. (~2.5 mm for As water) shown is inthe Figure capillary4e, length, the evolution γ is the surface of r(t) tension, on SALS ρ is in the our fluid experiments density, (Lavender plus, present work) and that in the previous study [15] (blue circle) is very similar. However, and g is the gravity acceleration. As shown in Figure 4e, the evolution of r(t) on SALS in our there is still a distinguishable deviation between them, that may be related to the different preparation experiments (Lavender plus, present work) and that in the previous study [15] (blue circle) is very methods:similar. dipping However, utilized there is by still De a Maleprade distinguishable et al. deviation [15] and spraybetween by them, us for that the superaerophilicmay be related to surface. the Additionally,different preparation the different methods: definitions dipping of the utilized initial by moment De Maleprade of the spreading et al. [15] and can leadspray to by this us deviation.for the Thissuperaerophilic earlier study providessurface. Additionally, insights into the the different mechanisms definitions underlying of the initial the whole moment dynamical of the spreading process of thecan bubble lead fastto this spreading deviation. on This the SALS.earlier Instudy addition provides to these insights three into dynamical the mechanisms stages, underlying a short transition the regimewhole (r ~dynamicala = 2.5 mm) process is identified of the bubble for SALSs fast andspreading the wider on the SALTs SALS. (W In= addition3 mm–5 mm),to these and three a new modeldynamical of higher stages, accuracy a short is proposedtransition toregime replace (r~a the = 2.5 corresponding mm) is identified previous for modelSALSs atand the the third wider stage (r >SALTsa). (W = 3 mm–5 mm), and a new model of higher accuracy is proposed to replace the corresponding previous model at the third stage (r > a). (a) Superaerophilic Slide (b) W = 1mm (e) 10

+++ ++++ ++++ ++++ ++++ a ++++ +++++++ +++++ +++++ +++++++ r +++++ ++++ +++ 1 R1 = 0.4deq ++ + + mm +++ (c) W = 2mm (d) W = 3mm / ++ 1mm r ++ 2mm + 3mm W + 4mm 5mm + + SALS 0.1 De Maleprade et.al

0.01 0.1 1 10 t /ms FigureFigure 4. 4.Spreading Spreading of of ﬂattened flattened bubbles bubbles on the superaerophilic superaerophilic surface surface (SALS) (SALS) and and SALTs SALTs of different of diﬀerent widths.widths. (a)–( (a)–(d)d Top) Top view view of theof the propagation propagation of of contact contact lines lines for for SALS SALS and and SALTs SALTs with withW W= 1= mm,1 mm, 2 mm,2 andmm, 3 mm, and respectively; 3 mm, respectively; the interval the interval between between adjacent adjacent images images is “∆t is ʺ∆56t≈µ56s”,μs andʺ, and the the blue blue dashed dashed lines ≈ indicatelines indicate the boundaries the boundaries of the SALTs.of the SALTs. (e) Contact (e) Contact size r plottedsize r plotted as a function as a function of time of timet for t the for bubble the

of dbubbleeq = 2 of mm deq on= 2 SALTsmm on ofSALTs different of different widths widths depicted depicted with with different different symbols; symbols;R1 R10.8 ≈ 0.8 mm mm means means the ≈ 1/2 1/2 upperthe boundaryupper boundary of the of initial the initial spreading spreading driven driven by the by capillary the capillary effect, effect, and aand= (γa/ =ρ (gγ) /ρg)(~2.5 (~2.5 mm) is the capillary length. mm) is the capillary length. During the first regime, the bubble suffers a rapid spreading within a short time (< 3 ms) on both During the first regime, the bubble suffers a rapid spreading within a short time (< 3 ms) on both the SALSs and SALTs, and the contact size r is proportionally related to time t at r < R1, as shown the SALSs and SALTs, and the contact size r is proportionally related to time t at r < R1, as shown in in thethe Figure 44e.e. Figure Figure 4a–d4a–d showed showed the the top top view view of ofthe the moving moving contact contact lines, lines, which which resulted resulted in the in thecircular circular rims rims for for SALSs SALSs and and SALTs SALTs with with WW = =1 mm,1 mm, 2 mm, 2 mm, 3 mm, 3 mm, respectively, respectively, and and this this highly highly dynamicdynamic behavior behavior was was captured captured using using a a high-speed high‐speed at a a rate rate of of 89,000 89,000 fps, fps, and and the the blue blue dashed dashed lines lines indicatedindicated the the boundaries boundaries of of the the SALTs. SALTs. After After thethe squeezed water water between between the the flattened flattened bubbles bubbles and and thethe aerophilic aerophilic surfaces surfaces (coated (coated by by a a thin thin plastron plastron of of air) air) being being punctured,punctured, this this water water film film of of thickness thickness δ retracts,δ retracts, and thenand then the contact the contact line expandsline expands [15]. [15]. Note Note that thethat puncture the puncture of this of interveningthis intervening film film cannot be triggered,cannot be triggered, and no bubble and no spreading bubble spreading occurred occurred at SALT at widths SALT widths below below 1mm (1mmW = 0.5(W mm).= 0.5 mm). WhereWhere this this retracting retracting water water film film can can bebe treatedtreated as a a horizontal horizontal ruptured ruptured soap soap film, film, which which had had beenbeen modeled modeled by by Culick Culick [24 [24]] based based on on balancing balancing surfacesurface tension tension 2 2γγ andand inertia inertia ρδρδV2V, and2, and a constant a constant retractionretraction velocity velocity can can be be given: given: 1/2 V = (2γ/ρδ) 1/2 (1) V = 2γ / ρδ (1)

Water 2020, 12, 798 7 of 14 where the factor of 2 is here because the water film has two sides. Thus, the linear relation between r and time is identified: !1/2 2γ r(t) = t (2) ρδ Regarding the spreading velocity being stable around 4 0.4 m/s, as reported by De Maleprade et ± al. [15], this relation implies a film thickness δ = 9 2 µm. Despite using the different coating methods, ± the spreading velocity on both SALSs and SALTs measured in our experiments ranged from 3.0 m/s to 4.1 m/s, agreeing well with that of this previous literature [15]. Thus, we can say that the anisotropic aerophilicity of the SALTs has a slight effect on the spreading of the bubble in the first regime, even at SALTs’ widths smaller than the bubble radius. It is noted that the scattered data in the first regime (t < 3 ms) are all obtained from a typical test without averaging. The highly linear relation between r and time also can be found for SALTs of different widths during the initial spreading. The linear r-t relations of both SALSs and SALTs in the first regime change at about t 0.3 ms with ≈ r R (= 0.4deq), and two different typical r(t)-t relations with different numbers of subregimes emerge ≈ 1 for W = 1–2 mm and other wider SALTs and SALSs, respectively. Like the previous work [15], the spreading of bubbles is divided into three subregimes: for SALTs of W = 3–5 mm and SALS, denoted as regime (IIb), regime (III) and regime (IV). Note that the transition regime (III) has not been discussed yet, though it can be easily identified in Figure3d at t 5.5 ms in this reference. Where (b) indicates ≈ the subregime corresponding to the SALTs of W = 3–5 mm and SALS, and thus, regime (IIa) denotes the second subregime for the narrower SALTs (W = 1 and 2 mm). Due to r a (~2.5 mm) in regime ≤ (IIb), the contact size is smaller than the SALT width ( 3 mm), and then the SALT can be equivalent ≥ to the SALS. Considering these results and bubble volume conservation of Ω ~ hr2, the balance of dynamical pressure ρV2 (at high Reynold number ~1000) with Laplace pressure γh/r2, as proposed by reference [15], yields !1/6 γΩ r(t) t1/3 (3) ≈ ρ This inertiocapillary law with the exponent of 1/3 agrees well with the corresponding data, as presented in Figure4e. This power law suggests that the e ffects of resisted inertia and Laplace pressure is dominant in regime (IIb). In the reference [15], the upper boundary of the regime (IIb) is fixed at the capillary length ~2.5 mm; whereas, in our study, the surface geometry determines it, which decreases with the decreasing W, as shown in Figure5. For the SALTs of W = 4 mm and 5 mm, and SALS, the spreading bubble would experience a short transition (~1ms and named regime (III)), which also can be seen in Figure4d from the reference [15], but is hardly mentioned, while the interval of regime (III) for W = 3 mm would be significantly expanded. The detailed views of these transitional regimes are presented in Figure6. This property seems related to the bubble rupture and will be discussed in Section 3.3. Water 2020, 12, 798 8 of 14 Water 2020, 12, 798 8 of 14 Water 2020, 12, 798 8 of 14 (a) (b) (e) W W = 2mm W = 3mm + hL 2mm 10 10 W (a) rL (b) rL (e) hR 2mm W = 2mm W = 3mm + hL 2mm 10 rR 10 rR x hL 3mm rL rL hR 2mm /mm 1 /mm 1 2 hR 3mm rR rR x hL 3mm L,R L,R hL 4mm /mm r /mm 1 r 1 2 hR 3mm hR 4mm L,R L,R hL 4mm r 0.1 0.1r 1.5 h hL 5mm 1 5101520 1 5101520 R 4mm 0.1 0.1 1.5 + hR 5mm t /ms t /ms + hL 5mm (c) 1 5101520(d) 1 5101520 + Superaerophilic 1 ++++ hR 5mm

/mm + W t=/ms 4mm W =t /ms5mm +x++++++++ Slide 10 10 +xx ++++++ Superaerophilic (c) (d) h 1 +x ++ rL rL ++xx +++++++ /mm ++xx ++++ W = 4mm W = 5mm xx++++x+x+x+x+x +++++++++++++Slide++ 10 rR 10 rR x +x+x+x+x+xxx h 0.5 x +++xx rL rL xxx ++x+x+x+x+x+x+x+xxxx

/mm x +xxx /mm xx ++++++x+x+x+x+x+x+x+x+x+xxxxx 1 1 xxxxxxxx xxxxxx rR rR 0.5 xxxxx L,R L,R xxxxxxxxxx

/mm xxx r /mm 1 r 1 xxxxxxxxxxxxxxxxxxxx 0 L,R L,R 0 5 10 15 20 r 0.1 0.1r 0 t /ms 0.11 51015200.11 5101520 0 5 10 15 20 t /ms t /ms t /ms 1 51015201 5101520 t /ms t /ms Figure 5. Contact size (rL and rR) and thickness of the two ruptured bubbles plotted as a function of Figure 5. Contact size (rL and rR) and thickness of the two ruptured bubbles plotted as a function of timeFigure t. (5.a)–( Contactd) The sizerL, R ‐(tr curvesL and r Rat) andW = thickness2 mm, 3 mm, of the 4 mm,two rupturedand 5 mm, bubbles respectively. plotted (e as) The a function thickness of time t.(a)–(d) The rL, R-t curves at W = 2 mm, 3 mm, 4 mm, and 5 mm, respectively. (e) The thickness oftime the t .two (a)–( rupturedd) The rL, bubbles R‐t curves plotted at W as= 2 a mm, function 3 mm, of 4t atmm, different and 5 mm,SALT respectively. widths. (e) The thickness of the two ruptured bubbles plotted as a function of t at diﬀerent SALT widths. of the two ruptured bubbles plotted as a function of t at different SALT widths. W =4mm (a) W =3mm (b) 2.8 r W =4mm (a) 5 r W =3mm (b) 2.8 r 5 r 2.5 4 2.5 4 /mm

/mm 2.2 r r 3 /mm

/mm 2.2 r r 3 1.9 2 1.9 2 1 1.6 24681012 3456 t /ms t /ms 1 1.6 24681012 3456 (c) t /ms tW/ms=5mm (d) Superaerophilic Slide (c)3.5 3 r W =5mm (d) r Superaerophilic Slide 3.5 3 r 2.8 r 3 2.8 3 /mm /mm 2.6 r r /mm /mm 2.6 r 2.5 r 2.4 2.5 2.4

2 2.2 45678 4567 t /ms t /ms 2 2.2 45678 4567 t /ms t /ms FigureFigure 6. The6. The detailed detailed views views corresponding corresponding to to the the concentrated concentrated transitional transitional regime regime (regime (regime (III)) (Ⅲ)) of of the r-t curvestheFigure r‐t curves 6. in The Figure indetailed Figure4e around views4e aroundr correspondinga .r ≈ a. to the concentrated transitional regime (regime (Ⅲ)) of ≈ the r‐t curves in Figure 4e around r ≈ a. Further,Further, De De Maleprade Maleprade et et al. al. [ 15[15]] deduced deduced thatthat the contact contact size size exceeding exceeding r =r =a woulda would grow grow followingfollowingFurther, a powera power De lawMaleprade law with with an anet exponent al.exponent [15] deduced ofof 11/2,/2, dependingdependingthat the contact on on the the size balance balance exceeding between between r = thea thewould hydrostatic hydrostatic grow pressurepressurefollowing (ρgh ( ρa)gh power and) and the lawthe water waterwith inertia aninertia exponent ( ρ(VρV22).). of DuringDuring 1/2, depending h ≤ 0.80.8 mm mm on in inthe this this balance inertia inertia-hydrostatic ‐betweenhydrostatic the regimehydrostatic regime (the (the 2 ≤ −2 2 thirdthirdpressure stage stage in(ρ ghin their) theirand study), thestudy), water just just inertia the the spreading spreading(ρV ). During velocityvelocity h ≤ 0.8 of mm ~ 10 10 in− thism/sm / inertiascan can be‐ be hydrostaticgenerated generated byregime byh ofh (theofthis this velocityvelocitythird level.stage level. in It It istheir is obvious obvious study), that thatjust the thethe hydrostatic hydrostaticspreading velocity energy is isof too too ~ 10slight slight−2 m/s to to canprovide provide be generated a apractical practical by spreading h spreading of this velocityvelocity of oflevel. ~ 0.3~ 0.3 mIt m/s,/iss, obvious and and thus, thus, that it itthe is is not nothydrostatic thethe dominantdominant energy driving driving is too slight force force tofor for provide the the spreading spreading a practical of ofthe spreading the bubble. bubble. TheThevelocity propagating propagating of ~ 0.3 bubbles m/s, bubbles and in thus,in regime regime it is (IV) not(IV) the forfor dominant SALTsSALTs of driving 3–5mm force would would for be the be ruptured rupturedspreading into intoof twothe two bubble.similar similar 2 sub-bubblessubThe‐ bubblespropagating with with a bubbles velocitya velocity in of regimeof ~ ~ 0.3 0.3 m(IV) m/s/s (Re~Ofor (Re~O SALTs2). Therefore, Therefore,of 3–5mm it would it can can be be inferred ruptured inferred that thatinto the thetwo dominant dominantsimilar driving force is the surface tension related to the2 superaerophilicity, and the dominant resistance is drivingsub‐bubbles force is with the surface a velocity tension of ~ related 0.3 m/s to (Re~O the superaerophilicity,). Therefore, it can and be theinferred dominant that the resistance dominant is the thedriving water force inertia. is the Inspired surface tensionby the relatedmodel ofto the superaerophilicity,retracting soap film and with the twodominant surfaces resistance [24], and is water inertia. Inspired by the model of the retracting soap ﬁlm with two surfaces [24], and regarding the water inertia. Inspired by the model of the retracting soap film with two surfaces [24], and

Water 2020, 12, 798 9 of 14 the only single side of the bubble interface, the balance between the surface tension γ and the inertia ρδV2 leads to r γ r(t) t (4) ≈ ρhL,R where hL,R is the characteristic height of the ruptured bubble (at left or right), and it is denoted as h for SALS, as seen in Figure1. Based on hL,R in the range of 0.2 mm–0.4 mm at t > 6 ms corresponding to the regime (IV), the spreading velocity predicted from Equation (4) ranges from 0.4 m/s to 0.6 m/s, which is close to the measurement results 0.3 m/s V 0.44 m/s. Additionally, the data in Figure4 showed a ≤ ≤ significantly better fit to this linear relation (R2~0.98) than to the power-law with an exponent of 1/2 (R2~0.5). This finding reconfirms the above r(t)-t linear relation. As further enhancing the anisotropic wettability by narrowing SALTs to W = 1 and 2 mm, the relations obtained above (regimes (II)–(IV)) for other, wider SALTs and SALS is invalid, and a unified sub-regime (regime (IIa)) over a broad time interval (t > 0.3 ms) emerges. In other words, only two major subregimes can be found for 1-mm and 2-mm SALTs, and the r(t)-t linear relations in their first regimes agree well with that for other SALTs and SALS. It is very interesting to find that the bubbles can spread observably faster on SALTs of W = 1 and 2 mm than on other SALTs and SALS. It would be curious to elucidate what happens to this increase in the bubble spreading velocity. Note that applying Equation (4) to the spreading of bubbles on SALTs of smaller widths (W = 1 and 2 mm) with the larger sub-bubble heights (~0.6 mm–0.7 mm corresponding to V of ~ 0.3 m/s) gives smaller V than that for other SALTs and SALS, contrary to our experimental data (V = 0.77 m/s and 0.51 m/s for W = 1 and 2 mm, respectively) in Figure4e. This contradiction implies that there are other key factors, in addition to the surface tension, motivating the bubble spreading on the narrower SALTs. With concerning the remarkably increase in h for W = 1 and 2 mm, the more curved bubble interfaces in the transverse direction—in particular, near the two peak values of h—can be formed, and it is reasonably assumed that the Laplace pressure is another dominant driving force to accelerate the spreading. By summing the two principal velocity components derived from the surface tension and Laplace pressure (in transverse), respectively, the spreading velocity on these two narrower SALTs can be obtained as

 s r   γh γ  r(t)  + t (5)  2  ≈  ρRT ρh

The first term on the right of the expression accounts for the effect of the Laplace pressure, while the remaining term is associated with the surface tension effect of the SALTs on the bubble interface. Where RT is the curvature radius in the transverse direction and can be calculated by

2 RT = W /8h + h/2 (6) using the circular segment assumption, as proposed by Wu et al. [6]. A high agreement between this extended model and the experiments was unexpectedly found using the time-averaged (t > 6 ms) values of h. More precisely, the bubble spreading velocity in regime (IIa) predicted by this expression is 0.76 m/s and 0.51 m/s for W = 1 mm and 2 mm, respectively, and the corresponding experimental results are 0.77 m/s and 0.53 m/s, with the relative deviation below 5%. This agreement demonstrates that the combined eﬀect of the Laplace pressure and the surface tension on the two narrow SALTs prevails over other driving forces for the bubble spreading in regime (IIa).

3.3. Bubble Rupture on the SALTs With the help of the anisotropic superaerophilicity of SALT, the bubble ruptures as it spreads on the SALTs (W = 2–5 mm) is observed first, and two sub-bubbles with similar sizes and velocities but in the opposite directions along the SALT were generated, as shown in Figures5 and7. Note that the bubble interface necking at W = 1 mm cannot be defined as a rupture, due to the gas layer between Water 2020, 12, 798 10 of 14 their two humps too thick to be distinguished from the humps (Figure7(a2–a4)). Compared to the SALTs, SALSs cannot result in the rupture of the flattened bubbles. It is interesting to note that the migrationWater velocity2020, 12, 798 of the two ruptured bubbles is higher (>0.3 m/s) than that of the moving10 of 14 contact lines (Figuretheir two7(b1–e1)), humps too and thick their to transport be distinguished distance from can the be ~10mmhumps (Figure in our 7a2–a4). experiments. Compared This to migration the capacitySALTs, of the SALSs ruptured cannot bubbles result in provides the rupture a potential of the flattened solution bubbles. for the It horizontally is interesting directionalto note that transportthe of the bubblemigration in velocity aqueous of environments.the two ruptured Ma bubbles et al. is recently higher (>0.3 proposed m/s) than this that interesting of the moving topic contact [19], using the geometrylines (Figure gradient 7b1–e1), of and the their SALS transport to transport distance the can bubble be ~10mm horizontally. in our experiments. Once the This two migration sub-bubble humpscapacity established of the as ruptured a result ofbubbles the interface provides necking a potential before solution rupture, for a the high horizontally degree of symmetrydirectional in the transport of the bubble in aqueous environments. Ma et al. recently proposed this interesting topic two ruptured bubbles, including the migration velocity and bubble geometry, can be found during this [19], using the geometry gradient of the SALS to transport the bubble horizontally. Once the two sub‐ wholebubble dynamical humps process established (Figures as 5a andresult7). of Additionally, the interface thenecking decrease before in rupture,W accelerates a high degree the necking of of the initialsymmetry bubble, in the such two as ruptured 2 ms after bubbles, puncture including for W the= migration2 mm but velocity 5ms afterand bubble puncture geometry, for W can= 5 mm. The SALTsbe found of W during= 1 and this 2 whole mm induce dynamical thicker process bubbles (Figures (with 5 and a larger7). Additionally, height of the 0.5 decrease mm–0.6 in mm) W than that ataccelerates 3 mm W the necking5 mm do of (0.2the initial mm

1mm 10(a) W= (a1) (a2) t = 4.17ms r Regime(Ⅰ) (Ⅱa)

1 (a3) t = 6.17ms /mm r

0.1 (a4) t = 8.17ms

0.01 0.1 1 10 t /ms

(b) 2mm (b1) (b2) t = 4.72ms 10 W= r rs Regime(Ⅰ) (Ⅱa) t = 8.72ms 1 (b3) /mm r

(b4)t = 12.72ms 0.1

0.01 0.1 1 10 t /ms

3mm (c1) 10(c) W= (c2) t = 5.61ms r rs Regime(Ⅰ) (Ⅱb) 1 (c3) t = 7.61ms /mm r

(Ⅲ) (Ⅳ)

0.1 (c4) t = 9.61ms

0.01 0.1 1 10 t /ms Figure 7. Cont.

Water 2020, 12, 798 11 of 14 Water 2020, 12, 798 11 of 14

4mm (d1) 10(d) W= (d2) t = 7.14ms r rs Regime(Ⅰ) (Ⅱ) 1 (d3) t = 9.14ms /mm r

0.1 (Ⅲ) (Ⅳ) (d4) t = 11.14ms

0.01 0.1 1 10 t /ms

(e) 5mm (e1) (e2) 10 W= t = 6.67ms r rs Regime(Ⅰ) (Ⅱ) t = 8.67ms 1 (e3) /mm r

(Ⅲ) (Ⅳ) 0.1 (e4) t = 10.67ms

0.01 0.1 1 10 t /ms

(f) Superaerophilic Slide(f1) (f2) 10 t = 2.05ms r (f3) Regime(Ⅰ) (Ⅱ) t = 4.05ms 1 (f4) /mm (Ⅲ) (Ⅳ) r t = 6.05ms (f5)

0.1 t = 8.05ms (f6) 0.01 0.1 1 10 t /ms t = 10.05ms FigureFigure 7. Interface 7. Interface evolution evolution of bubbles of bubbles spreading spreading on on SALTs SALTs and and SALS. SALS. (a ()–(a)–(e)e) Correspond Correspond toto thethe SALT widthsSALT ranged widths from ranged 1 mm from to 1 5 mm mm, to and5 mm, (f and) corresponds (f) corresponds to theto the SALS. SALS. The The leftleft subfigures subfigures (a1 ()–a1)–(f1) (f1) illustrate the contact size r (blue square) and the center‐to‐center distance rs (pink circle) between illustrate the contact size r (blue square) and the center-to-center distance rs (pink circle) between the rupturedthe ruptured bubbles bubbles as a as function a function of oft. t The. The right right subfiguressubfigures (except (except (a1 ()–(a1f1)–())f1 show)) show the sequence the sequence of of snapshots (side view) of a bubble spreading (or rupture) on the SALTs and SALS, and their spans snapshots (side view) of a bubble spreading (or rupture) on the SALTs and SALS, and their spans correspond to the areas marked in dark pink in the left subfigures. The areas marked in light blue correspondindicate to the the transitional areas marked regime in (regime dark pink (III)) inof the contact left subfigures. propagation. The Vertical areas orange marked lines in mark light blue indicatethe the boundaries transitional of the regime dynamical (regime subregimes, (III)) of which the contact are labeled propagation. at the corresponding Vertical orange subregimes. lines mark the boundaries of the dynamical subregimes, which are labeled at the corresponding subregimes. To further understand the ruptured bubble motion, the center‐to‐center distance rs(t) between Tothe further ruptured understand bubbles was the plotted ruptured as a function bubble of motion, t simultaneously, the center-to-center compared to the distance contact rsizes(t) r between(t), the rupturedin Figure bubbles 7 For the was wider plotted SALTs as of a 3 function mm ≤ W ≤ of5t mm,simultaneously, the bubble interface compared necking to theapproximately contact size r(t), in Figurehappened7 For the around wider the SALTs transitional of 3 regime mm (regime(III)),W 5 mm, and the the bubble increase interface in W decreased necking the approximately time gap ≤ ≤ happenedbetween around the necking the transitional and the regime(III) regime (regime(III)), and postponed and the the necking. increase Like in r(Wt)‐t decreasedcurves during the time regime(III), the more apparent fluctuations of rs(t) take place lagging behind that of r(t), and it can be gap between the necking and the regime(III) and postponed the necking. Like r(t)-t curves during smoothed as the SALT width decreased from 5 mm to 3 mm and almost disappeared at W = 2 mm regime(III),(no similar the more fluctuation apparent for r( fluctuationst)‐t curves). This of correlationrs(t) take placesuggested lagging that the behind fluctuation that of onr r((tt),)‐t and curves it can be smoothedmay as induce the SALT that on width rs(t)‐ decreasedt curves, and from the 5 fluctuation mm to 3 mm is strengthened and almost disappearedafter the propagation. at W = 2 As mm (no similaranalyzed fluctuation in Section for r(t )-3.2,t curves). a thicker Thisair film correlation retained on suggested the narrower that SALTs the fluctuation (such as W on = 2r (mmt)-t curvesand 3 may inducemm) that would on rs( tproduce)-t curves, a stronger and the Laplace fluctuation pressure, is because strengthened of their afterhigher the transverse propagation. bending, As to analyzed resist in Section 3.2, a thicker air film retained on the narrower SALTs (such as W = 2 mm and 3 mm) would produce a stronger Laplace pressure, because of their higher transverse bending, to resist the interface necking. As a result, the r(t) and rs(t) change curves show a sharper fluctuation on them at the wider Water 2020, 12, 798 12 of 14

SALTs (W = 4 mm and 5 mm) and SALS, compared to that at other, narrow SALTs. Furthermore, the transitional regime can be expanded as the SALTs narrow (Figure7), for the same reason.

4. Conclusions

Anisotropic spreading of bubbles (deq = 2 mm) on superaerophilic straight trajectories (SALTs) of different widths (0.5 mm W 5 mm) beneath a slide in water was experimentally studied using a ≤ ≤ high-speed shadowgraphy system, and the superaerophilic surface SALS and SALTs were constructed using spray coating with a silica nanoparticle solution. With the constant initial gap between the bubbles and the slide d0 = 4 mm, the bouncing mostly happened as the bubble contacted the SALTs, except for non-bouncing at W = 4 mm. The bouncing probability of SALTs is significantly higher than that in the previous study [15]. It was found that SALT widths and bounce times hardly affect the evolution of d(t). After the repeated bouncing, the bubble becomes flattened and stops on the wall for a short while (~ O (101) ms), and then the thin film between the bubble interface and SALT (or SALS) would be punctured to trigger the rapid spreading process. Two essential mechanisms are found to be responsible for the anisotropic spreading on the narrow SALTs (W = 1 mm and 2 mm) and the wide SALTs (3 mm W 5 mm), as characterized by the different evolution of the contact lines ≤ ≤ and quantified using the r(t)-t curves. In addition to the three dynamical stages as proposed by De 1/3 1/2 Maleprade et al. for SALS [15](r(t) t at r < 0.4deq, r(t) t at 0.4deq < r(t) < a, and r(t) t at r(t) > a ∝ ∝ ∝ corresponding to the major driving forces of the SALT tension effect, Laplace pressure, and hydrostatic pressure, respectively), we identified a short transitional regime (regime (III) at r~a = 2.5 mm), which was missing in the previous study, for SALS and the wider SALTs (W = 3 mm–5 mm). We further model the contact size in regime (IV) as a linear function of time to demonstrate the surface tension effect of SALTs prevailing over the hydrostatic pressure. Compared to the wide SALTs, the enhanced constraint effect of the narrow SALTs (W = 1 mm and 2 mm) on the bubble interface in the transverse direction results in a novel evolution mechanism composed of only two subregimes. The former subregime is similar to that at 3 mm W 5 mm, while the latter one shows a linear relation between contact size ≤ ≤ and time. A simple model has been developed to depict this linear relation in regime (IIa) concerning the combined effect of the surface tension effect of the SALT and Laplace pressure. This model and our experiments are in nice agreement. Further, we first observed that the initial flattened bubble ruptured into two sub-bubbles with similar sizes and migration velocities in opposite directions during its anisotropic spreading on the SALTs at 2 mm W 5 mm. The ruptured sub-bubble pair are highly symmetric around the puncture ≤ ≤ center, concerning the bubble geometry and velocity. The bubble rupture can be attributed to the strong anisotropic-superaerophilicity of the SALT and seems to be related to the apparent fluctuations on the change curves of r(t) and rs(t). It is interesting to find that the decrease in W will smooth these fluctuations, owing to the stronger Laplace pressure generated by the smaller curvature radius of the remaining air film on the narrower SALTs to better withstand the interface necking caused by the hydrostatic effect. It is unavoidable to arrange some engineering structures horizontally in the aqueous environments, such as the electrodes of fuel cells and the heat exchangers, where the bubble accumulation on the horizontal surfaces are usually undesired. In contrast, underwater vehicles or ships covered by a thin plastron of air can achieve lower hydrodynamic resistance [25,26]. Through SALTs, the bubble can be directionally transported at a velocity of about 0.4 0.1 m/s for a medium ± distance, and the gas film can be effectively constrained into the designated surface area of these engineering structures on demand.

Author Contributions: Conceptualization, C.T.; methodology, Q.Y., Y.Y., Y.W., S.Y., P.D., and C.T.; formal analysis, Z.Y., R.J., and X.L.; investigation, Y.C., Z.Y., R.J., and X.L.; writing—original draft preparation, C.T., Y.C., and Q.Y.; and writing—review and editing, C.T. and F.B.; All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Water 2020, 12, 798 13 of 14

Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grants No. 11972334, No. 11672284, No. 11632016, No. 11872217, and No.51871206) and the National Key R&D Program of China (Grant no.2017YFB0603701). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

References

1. Seymour, R.S.; Matthews, P.G. Physical gills in diving insects and spiders: Theory and experiment. J. Exp. Biol. 2013, 216, 164–170. [CrossRef][PubMed] 2. Parker, A.R.; Lawrence, C.R. Water capture by a desert beetle. Nature 2001, 414, 33. [CrossRef][PubMed] 3. Zheng, Y.; Bai, H.; Huang, Z.; Tian, X.; Nie, F.-Q.; Zhao, Y.; Zhai, J.; Jiang, L. Directional water collection on wetted spider silk. Nature 2010, 463, 640–643. [CrossRef][PubMed] 4. Kamei, J.; Saito, Y.; Yabu, H. Biomimetic ultra-bubble-repellent surfaces based on a self-organized honeycomb film. Langmuir 2014, 30, 14118–14122. [CrossRef][PubMed] 5. Yang, Q.; Li, T.; Lu, Z.; Sun, X.; Liu, J. Hierarchical construction of an ultrathin layered double hydroxide nanoarray for highly-efficient oxygen evolution reaction. Nanoscale 2014, 6, 11789–11794. [CrossRef] [PubMed] 6. Wu, C.-J.; Chang, C.-C.; Sheng, Y.-J.; Tsao, H.-K. Extraordinarily rapid rise of tiny bubbles sliding beneath superhydrophobic surfaces. Langmuir 2017, 33, 1326–1331. [CrossRef][PubMed] 7. Yu, C.; Zhu, X.; Cao, M.; Yu, C.; Li, K.; Jiang, L. Superhydrophobic helix: Controllable and directional bubble transport in an aqueous environment. J. Mater. Chem. A 2016, 4, 16865–16870. [CrossRef] 8. Huppert, H.E. The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 1982, 121, 43–58. [CrossRef] 9. Tanner, L. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D Appl. Phys. 1979, 12, 1473. [CrossRef] 10. Zenit, R.; Legendre, D. The coefficient of restitution for air bubbles colliding against solid walls in viscous liquids. Phys. Fluids 2009, 21, 083306. [CrossRef] 11. Manica, R.; Klaseboer, E.; Chan, D.Y. Force balance model for bubble rise, impact, and bounce from solid surfaces. Langmuir 2015, 31, 6763–6772. [CrossRef][PubMed] 12. Zawala, J.; Malysa, K. Influence of the impact velocity and size of the film formed on bubble coalescence time at water surface. Langmuir 2011, 27, 2250–2257. [CrossRef][PubMed] 13. Tsao, H.K.; Koch, D.L. Observations of high Reynolds number bubbles interacting with a rigid wall. Phys. Fluids 1997, 9, 44–56. [CrossRef] 14. Pelletier, E.; Béguin, C.; Étienne, S. Experiments of air bubbles impacting a rigid wall in tap water. Phys. Fluids 2015, 27, 123302. [CrossRef] 15. De Maleprade, H.; Clanet, C.; Quéré, D. Spreading of bubbles after contacting the lower side of an aerophilic slide immersed in water. Phys. Rev. Lett. 2016, 117, 094501. [CrossRef] 16. Jeong, H.; Park, H. Near-wall rising behaviour of a deformable bubble at high Reynolds number. J. Fluid Mech. 2015, 771, 564–594. [CrossRef] 17. Javadi, K.; Davoudian, S.H. Surface wettability effect on the rising of a bubble attached to a vertical wall. Int. J. Multiph. Flow 2018, 109, 178–190. [CrossRef] 18. Wang, J.; Zheng, Y.; Nie, F.-Q.; Zhai, J.; Jiang, L. Air bubble bursting effect of lotus leaf. Langmuir 2009, 25, 14129–14134. [CrossRef] 19. Ma, H.; Cao, M.; Zhang, C.; Bei, Z.; Li, K.; Yu, C.; Jiang, L. Directional and Continuous Transport of Gas Bubbles on Superaerophilic Geometry-Gradient Surfaces in Aqueous Environments. Adv. Funct. Mater. 2018, 28, 1705091. [CrossRef] 20. Levich, B.; Landau, L. Dragging of a liquid by a moving plate. Acta Physicochim. URSS 1942, 17, 42. 21. Zawala, J.; Krasowska, M.; Dabros, T.; Malysa, K. Influence of bubble kinetic energy on its bouncing during collisions with various interfaces. Can. J. Chem. Eng. 2007, 85, 669–678. [CrossRef] 22. Zawala, J.; Dabros, T. Analysis of energy balance during collision of an air bubble with a solid wall. Phys. Fluids 2013, 25, 123101. [CrossRef] 23. Sato, A.; Shirota, M.; Sanada, T.; Watanabe, M. Modeling of bouncing of a single clean bubble on a free surface. Phys. Fluids 2011, 23, 013307. [CrossRef] Water 2020, 12, 798 14 of 14

24. Culick, F. Comments on a ruptured soap ﬁlm. J. Appl. Phys. 1960, 31, 1128–1129. [CrossRef] 25. Kavalenka, M.N.; Vüllers, F.; Lischker, S.; Zeiger, C.; Hopf, A.; Röhrig, M.; Rapp, B.E.; Worgull, M.; Hölscher, H. Bioinspired air-retaining nanofur for drag reduction. ACS Appl. Mater. Interfaces 2015, 7, 10651–10655. [CrossRef] 26. Jones, P.R.; Hao, X.; Cruz-Chu, E.R.; Rykaczewski, K.; Nandy, K.; Schutzius, T.M.; Varanasi, K.K.; Megaridis, C.M.; Walther, J.H.; Koumoutsakos, P. Sustaining dry surfaces under water. Sci. Rep. 2015, 5, 12311. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).