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Water droplet impact on elastic superhydrophobic surfaces
AbstractWater droplet impact on surfaces is a ubiquitous phenomenon in nature and industry, where the time of contact between droplet and surface influences the transfer of mass, momentum and energy. To manipulate and reduce the contact time of impacting droplets, previous publications report tailoring of surface microstructures that influence the droplet surface interface. Here we show that surface elasticity also affects droplet impact, where a droplet impacting an elastic superhydrophobic surface can lead to a two fold reduction in contact time compared to equivalent rigid surfaces. Using high speed imaging, we investigated the impact dynamics on elastic nanostructured superhydrophobic substrates having membrane and cantilever designs with stiffness 0.5 7630N/m. Upon impact, the droplet excites the substrate to oscillate, while during liquid retraction, the substrate imparts vertical momentum back to the droplet with a springboard effect, causing early droplet lift off with reduced contact time. Through detailed experimental and theoretical analysis, we show that this novel springboarding phenomenon is achieved for a specific range of Weber numbers (We >40) and droplet Froude numbers during spreading (Fr >1). The observation of the substrate elasticity mediated droplet springboard effect provides new insight into droplet impact physics.IntroductionDynamics of droplet impact are important in many natural processes1,2 and industrial applications, including anti icing3,4, spray cooling5,6, pesticide and herbicide delivery7,8, and ink jet printing9. Droplet impact is governed by the complex flow physics arising within the deforming droplet, manifesting itself in the form of droplet lateral spreading and recoil. As the droplet impacts the surface, its kinetic energy is re directed in the lateral direction, flattening the droplet and converting the kinetic energy into surface energy. On low friction surfaces, this kinetic to surface energy conversion process is very efficient, resulting in minimal energy dissipation due to viscous effects10. Once all of the kinetic energy has been converted to surface energy of the flattened droplet, the reverse surface to kinetic energy conversion process initiates, resulting in droplet retraction and lift off in the vertical direction. The total contact time from initial impact to lift off, tc, influences the mass, momentum, and energy exchange between the droplet and the solid. Hence, achieving control of the contact time through manipulation of the internal flow physics dictates the transport processes occurring at the liquid solid interface.The contact time of water impact on a plane, rigid superhydrophobic surface is governed by the droplet size. Upon impact, the droplet spreads, reaches a maximum diameter, fully retracts, and vertically lifts off the surface11,10. For Weber numbers We=(v2D0)/ >1, where , D0, v and are the droplet density, initial diameter, impact speed, and surface tension, respectively, the droplet undergoes elastic impact. By balancing the droplet impact inertia (D0/tc2) with capillarity (/D02), the contact time scales as tc(D03/)1/2, and is independent of the impact speed12,13. Consequently, the only way to adjust the contact time on a plane, rigid, single length scale superhydrophobic surface is by controlling the droplet diameter.One approach to reduce the contact time is to use a surface with hierarchical superhydrophobic surface features. Droplets impacting miniature superhydrophobic ridges can break impact symmetry and decrease the contact hermes kelly clutch Knockoff time, by influencing droplet deformation near the miniature features and initiating early de wetting1,14. The same effect can be induced using a curved surface, when the curvature is on the order of the droplet diameter15. Also, during droplet recoil on hierarchical superhydrophobic posts, the surface to kinetic energy conversion can be enhanced by storing surface energy in the liquid between the miniature posts during impact, and recovering this energy during rebound16,17. For high speed impacts (We >12), droplets lift off near their maximum spreading diameter in a pancake like shape, reducing their contact time by a factor of 4. These previous approaches require fabrication of miniature features on the impacted surface, and that the impacting droplet is precisely aligned with these features. These surface structuring approaches rely on the droplet to be the energy storage mechanism (surface energy) during impact and recoil. Taking inspiration from nature (leaves) and human technology (springboards), we study droplet impact dynamics on elastic superhydrophobic substrates as a passive mechanism for controlling and reducing contact time. We hypothesize that droplets impacting elastic surfaces might exhibit distinct dynamics, resulting in energy storage and recovery not just within the droplet but also within the elastic surface. By studying droplet impact on superhydrophobic elastic polymer sheets, we show that droplets can undergo springboarding and reduce contact times by a factor of 2 when compared to rigid superhydrophobic surfaces. Further experimental observation and theoretical analysis elucidates a surface mediated energy storage mechanism arising from the coupling of the substrate elastic response to impact, and the droplet internal flow dynamics. In contrast to previous studies, we show that droplet dynamics can be altered and contact times reduced by introducing a second energy storage mechanism during impact elastic energy of the substrate in addition to surface energy of the droplet. We present new fundamental knowledge of droplet impact physics and provide a starting point for more advanced approaches to enhance the performance of droplet based applications by using substrate elasticity to achieve enhanced thermal, mass, or momentum transport.ResultsImpact DynamicsWe first considered droplet impact on stiff and elastic nanostructured superhydrophobic surfaces. The elastic and rigid surfaces were created by coating polymer sheets of thickness hs=10 500m and a glass slide, respectively, with a commercial nanoparticle spray to render them superhydrophobic, resulting in apparent advancing/receding contact angles of 1644/1593 (see Methods for details). Prior to droplet impact testing, the superhydrophobic coating was characterized for its morphology and wetting characteristics. Figure 1a,b show optical and scanning electron microscopy (SEM) images of the superhydrophobic surfaces. Individual nanoparticles with diameters d 30nm (Fig. 1b) formed macroscopic clusters (Fig. 1a), leading to random, hierarchical surface structures with an overall roughness of r7.5, where r is the ratio of the total surface area to the projected area, and an effective solid liquid fraction of f0.05 (for more information on surface roughness, see Supplementary Information, section S.3). Droplet impact on the elastic surfaces differed greatly from impact on the rigid superhydrophobic surface.Figure 1: Surface characterization and dynamic behavior of water droplet impact on rigid and elastic superhydrophobic surfaces.(a) SEM micrographs showing the macroscale roughness of the NeverWet superhydrophobic coating due to particle clustering. (b) High resolution SEM micrograph showing individual nanoparticles. Inset: water droplet on a NeverWet coated glass slide (scale bar 1mm). The advancing and receding contact angles were 1644 and 1593, respectively. (c) High speed images showing a low velocity droplet (v=0.68m/s) impacting a rigid superhydrophobic surface, and following the classical model of spreading, retraction and lift off at the theoretical contact time tc,th=2.6 (D03/8)1/2. (d) Droplet impact on a rigid superhydrophobic surface at higher impact speeds (v=1.58m/s), showing breakup and splashing. (e) Droplet impact on an elastic superhydrophobic surface at higher impact speeds (v=1.57m/s), showing substrate oscillation, and early lift off of the droplet in a pancake shape at reduced contact times (tc tc,th=6.3ms).Figure 1c shows a droplet with D0=1.48mm impacting the rigid superhydrophobic sample at a speed of v=0.68m/s, corresponding to We=9.6 and Oh=0.0031 ( where is the droplet dynamic viscosity). As expected, impact causes the droplet to spread laterally, undergo kinetic to surface energy conversion due to additional surface area creation, and reach a maximum diameter Dmax at the spreading time t=tspr. The droplet then undergoes the reverse process and retracts due to surface to kinetic energy conversion and finally lifts off the surface at the theoretical contact time tc=tc,th=2.6 (D03/8)1/210,11,12,13. At higher impact speeds, as shown in Fig. breaks up into a core droplet and several satellite droplets after reaching its maximum spreading diameter. The remaining core of the droplet detaches from the substrate at tc=tc,th. Interestingly, when the droplet impacts the elastic surface, as shown in Fig. 1e with a droplet with D0=1.50mm and v=1.57m/s (We=51.2), splashing is eliminated by the droplet edge detachment from the surface. Before the droplet can fully retract, the entire droplet has lifted off the surface in a spread (or pancake) shape at a contact time 21% shorter than the theoretical contact time on a rigid superhydrophobic surface.Energy Conversion During ImpactInspired by this unique observation, we hypothesize that substrate elasticity enables a new energy conversion mechanism to come into play during droplet impact. On the elastic surface, two distinct post impact energy conversion mechanisms exist: kinetic to surface within the droplet and kinetic to elastic between the droplet and the elastic substrate. If tailored correctly, the elasticity of the substrate can be designed such that the two fundamental energy conversion mechanisms have disparate timescales, allowing for faster vertical momentum transfer from the elastic to kinetic energy conversion than from the classical surface to kinetic mechanism within the droplet, and thus early droplet lift off from the surface.In order to systematically study the effect of substrate elasticity on contact times, we conducted droplet impact experiments on elastic surfaces with varying stiffness (0.5k D0 v We Oh1, such that viscous forces were negligible when compared to capillary or inertial forces. Figure 2 summarizes the contact times for droplet impact on fixed fixed substrates (a, b, c) and cantilever style substrates (d, e, f). For substrate stiffness 20k vc, contact times were reduced when compared to impact on a rigid superhydrophobic surface (k=7630N/m). For low impact speeds (v Supplementary Video S1). For 0.2v vc, substrate mounting and stiffness had no effect on the droplet contact time (see Supplementary Video S2 and Video S3), which was in excellent agreement with the inertial capillary scaled contact time, tc=tc,th. For v > vc, splashing occurred for substrates having k k >150N/m (see Supplementary Video S4), while on substrates having moderate stiffness (20k Supplementary Video S5). The experiments were terminated once splashing occurred. Our data shows that droplet contact times can be halved when compared to droplet impact at lower impact speeds and on rigid superhydrophobic substrates. The reduction in contact time was observed on both fixed fixed and cantilever style substrates and was found to weakly depend on the axial impact location of the droplet due to an increase in substrate stiffness with decreasing distance to the mount (see Supplementary Information, section S.4). It is important to note that the stiffness of the substrate did not directly influence the slope and magnitude of the decrease in contact times. Furthermore, droplet spreading times were not affected by the substrate elasticity and remained constant for all substrate mounting and elasticities, in agreement with previous studies (see Supplementary Information, section S.5)1,17.Figure 2Contact times for impacting droplets for fixed fixed (a c) and cantilever (d f) style mounted substrates as a function of impact speed and substrate stiffness for the three droplet diameter ranges. The critical impact speed, vc (also see Supplementary Information, section S.5), is marked with a dashed line. For impact speeds, v >vc, the contact time decreased as a result of the 'springboard' effect where the droplet lifted off the surface prior to fully retracting. Measurements were terminated once splashing occurred. Error bars are smaller than the symbol sizes and are not shown. In (b), droplets impacting the substrate with stiffness k=63N/m did so off center from the axis, inducing a torsion of the substrate rather than an oscillation, and eliminating the possibility for contact time reduction.In addition to contact time reduction, Fig. droplet breakup and creation of satellite droplets, occurs at higher impact speeds on grace kelly bag hermes cheap elastic substrates than on rigid substrates, which has been reported previously for ethanol droplets impacting a circular membrane18. In the present study, the increase in the splashing threshold speed on fixed fixed substrates was observed for substrate stiffness up to 130N/m. The elasticity of the substrate enables kinetic to elastic energy conversion between the droplet and the substrate at early stages of impact. Hence, not as much energy is left over for kinetic to surface energy conversion, resulting in a decreased spreading inertia and increased critical splashing speed18. For all droplet sizes, splashing initiated at higher impact speeds on fixed fixed hermes kelly sizes imitation when compared to the cantilever style substrates due to more efficient kinetic to elastic energy conversion on the former mounting configuration.Mechanism of Elasticity Mediated Contact Time ReductionIn order to better understand the physical mechanism of contact time reduction, we measured the dynamics of the elastic substrate during impact and developed a simple oscillator model of substrate motion. For the fixed fixed and the cantilever substrates, the eigenfrequencies f0 can be computed as and , respectively, where ms, L, , E, and I are the mass, length, Poisson's ratio (PMMA=0.38), Young's modulus (EPMMA=3 GPa), and area moment of inertia (I=whs3/12) of the substrate, where w is the width and hs the thickness of the substrate. Table 1 lists the calculated and observed eigenfrequencies of the substrates, which are in excellent agreement, giving us confidence in the validity of the harmonic oscillator approximation. Upon impact, the droplet exerts a force on the substrate, which causes the substrate to oscillate. The upward motion of the substrate during oscillation governs the contact time reduction of an impacting droplet, acting to accelerate the flattened droplet (Dmax) in the vertical direction against gravity. The added upward force from the elastic substrate causes the droplet to detach before fully undergoing surface to kinetic energy conversion. During early departure, the droplet remains in a spread, pancake like shape (see Supplementary Videos S5). We refer to this early lift off mechanism as the springboard effect, or springboarding, taking inspiration from a springboard where the vertical acceleration of an elastic membrane or spring (elastic to kinetic energy exchange) helps a jumper to rebound. It is important to note that although analogous droplet springboarding, or trampolining has been observed on suspended soap films19, the springboard effect shown here differs fundamentally from evaporation induced droplet trampolining20. The droplet images in Fig. 3a illustrate the coupling between the oscillation of an elastic substrate in the fixed fixed configuration (k=107N/m) and droplet lift off in the pancake shape. After reaching the maximum spreading diameter (3), the edges of the droplet detach (4) near a minimum substrate position. The subsequent upward motion of the substrate supports the detachment of the center of the droplet and results in early droplet lift off (5). Figure 3b,c show the cantilever style substrate responses for k=29.8N/m and k=2.2N/m, respectively. While for the high stiffness cantilever (k=29.8N/m), droplet lift off did not occur in the pancake shape, yet contact time reduction was observed. However, droplet impact on the low stiffness substrate (k=2.2N/m) did not have a reduced contact time. Furthermore, while the stiffer cantilever oscillated at its natural eigenfrequency (f0=112Hz), the softer substrate showed an additional higher order oscillation (f0=11 and f1=68Hz). The time scales of droplet spreading and recoil (10ms) were much shorter than the first order oscillation timescale (100ms) for the low stiffness substrate, resulting in the inability to accelerate the droplet upwards (see Supplementary Video S6), and enabling full droplet recoil before lift off with similar contact times as those on a rigid superhydrophobic surface21,22. To enable contact time reduction, our results show that the substrate oscillation and droplet impact timescales must be on the same order of magnitude.Figure 3: Substrate response and droplet shapes after droplet impact (scale bar 1mm for all inset images).(a) Fixed fixed substrate with k=107N/m, D0=2.2mm and f0=325Hz. Inset: Time lapse images of the droplet impact. The substrate starts a harmonic oscillation at its natural frequency shortly after droplet impact. The droplet spreads, and lifts off the surface in a pancake shape (springboard effect). (b) Cantilever substrate with k=29.8N/m and D0=2.1mm. The substrate oscillates at its natural frequency, f0=112Hz. Inset: Time lapse images of the droplet impact showing that droplet lift off does not occur in a pancake shape, but is distinct from the retraction behavior on a rigid substrate. (c) Cantilever substrate with k=2.2N/m and D0=2.4mm. The substrate is so elastic that the droplet impact activates substrate oscillations with both the natural (f0=11Hz) and higher order frequencies (f1=68Hz). Even more elastic substrates exhibit even higher order modes, f2=178Hz (not shown). Inset: Time lapse images of the droplet impact showing spreading, retraction, and lift off behavior similar to that on rigid superhydrophobic surfaces.An additional mechanism for contact time reduction can be found by studying the droplet dynamics at high impact speeds. We first determined the critical speed for the onset of contact time reduction, vc, which was a function of the initial droplet diameter (Fig. 2). As shown in Figs 1e and 3a, and explained above, early lift off initiates at the edge of the droplet, analogous to the initial phase of droplet breakup during splashing. When splashing occurs, viscous drag decelerates the rim of the spreading droplet while the edges deform hermes kelly clutch copy upwards and away from the surface. splashing23,24,25. For splashing to occur, the splash parameter, K=WeRe1/2, where the droplet Reynolds number is Re=D0v/, must be greater than a critical parameter Kc. The critical parameter depends on the substrate roughness, and can be approximated as, Kc3,600 for the substrates used in this study26,27,28. During droplet bouncing in the present experiments, droplets initiate their lift off at the edges of the droplet at maximum spreading, as can be seen in Figs 1e and 3a; a behavior similar to the first step during splashing (also see Supplementary Video S5). During spreading, the leading edge of the radial liquid flows over a small layer of air beneath it which provides lift to the advancing contact line29. The lift force created by the spreading rim acts against gravity and facilitates the subsequent substrate oscillation driven lift off of the entire droplet. We can thus link the critical splashing parameter to the onset of contact time reduction to obtain vc=2.1/D00.6, where D0 is the droplet diameter in units of millimeters, and vc is the critical droplet impact speed in units of meters per second. For a detailed derivation of the critical impact speed, including a di
AbstractWater droplet impact on surfaces is a ubiquitous phenomenon in nature and industry, where the time of contact between droplet and surface influences the transfer of mass, momentum and energy. To manipulate and reduce the contact time of impacting droplets, previous publications report tailoring of surface microstructures that influence the droplet surface interface. Here we show that surface elasticity also affects droplet impact, where a droplet impacting an elastic superhydrophobic surface can lead to a two fold reduction in contact time compared to equivalent rigid surfaces. Using high speed imaging, we investigated the impact dynamics on elastic nanostructured superhydrophobic substrates having membrane and cantilever designs with stiffness 0.5 7630N/m. Upon impact, the droplet excites the substrate to oscillate, while during liquid retraction, the substrate imparts vertical momentum back to the droplet with a springboard effect, causing early droplet lift off with reduced contact time. Through detailed experimental and theoretical analysis, we show that this novel springboarding phenomenon is achieved for a specific range of Weber numbers (We >40) and droplet Froude numbers during spreading (Fr >1). The observation of the substrate elasticity mediated droplet springboard effect provides new insight into droplet impact physics.IntroductionDynamics of droplet impact are important in many natural processes1,2 and industrial applications, including anti icing3,4, spray cooling5,6, pesticide and herbicide delivery7,8, and ink jet printing9. Droplet impact is governed by the complex flow physics arising within the deforming droplet, manifesting itself in the form of droplet lateral spreading and recoil. As the droplet impacts the surface, its kinetic energy is re directed in the lateral direction, flattening the droplet and converting the kinetic energy into surface energy. On low friction surfaces, this kinetic to surface energy conversion process is very efficient, resulting in minimal energy dissipation due to viscous effects10. Once all of the kinetic energy has been converted to surface energy of the flattened droplet, the reverse surface to kinetic energy conversion process initiates, resulting in droplet retraction and lift off in the vertical direction. The total contact time from initial impact to lift off, tc, influences the mass, momentum, and energy exchange between the droplet and the solid. Hence, achieving control of the contact time through manipulation of the internal flow physics dictates the transport processes occurring at the liquid solid interface.The contact time of water impact on a plane, rigid superhydrophobic surface is governed by the droplet size. Upon impact, the droplet spreads, reaches a maximum diameter, fully retracts, and vertically lifts off the surface11,10. For Weber numbers We=(v2D0)/ >1, where , D0, v and are the droplet density, initial diameter, impact speed, and surface tension, respectively, the droplet undergoes elastic impact. By balancing the droplet impact inertia (D0/tc2) with capillarity (/D02), the contact time scales as tc(D03/)1/2, and is independent of the impact speed12,13. Consequently, the only way to adjust the contact time on a plane, rigid, single length scale superhydrophobic surface is by controlling the droplet diameter.One approach to reduce the contact time is to use a surface with hierarchical superhydrophobic surface features. Droplets impacting miniature superhydrophobic ridges can break impact symmetry and decrease the contact hermes kelly clutch Knockoff time, by influencing droplet deformation near the miniature features and initiating early de wetting1,14. The same effect can be induced using a curved surface, when the curvature is on the order of the droplet diameter15. Also, during droplet recoil on hierarchical superhydrophobic posts, the surface to kinetic energy conversion can be enhanced by storing surface energy in the liquid between the miniature posts during impact, and recovering this energy during rebound16,17. For high speed impacts (We >12), droplets lift off near their maximum spreading diameter in a pancake like shape, reducing their contact time by a factor of 4. These previous approaches require fabrication of miniature features on the impacted surface, and that the impacting droplet is precisely aligned with these features. These surface structuring approaches rely on the droplet to be the energy storage mechanism (surface energy) during impact and recoil. Taking inspiration from nature (leaves) and human technology (springboards), we study droplet impact dynamics on elastic superhydrophobic substrates as a passive mechanism for controlling and reducing contact time. We hypothesize that droplets impacting elastic surfaces might exhibit distinct dynamics, resulting in energy storage and recovery not just within the droplet but also within the elastic surface. By studying droplet impact on superhydrophobic elastic polymer sheets, we show that droplets can undergo springboarding and reduce contact times by a factor of 2 when compared to rigid superhydrophobic surfaces. Further experimental observation and theoretical analysis elucidates a surface mediated energy storage mechanism arising from the coupling of the substrate elastic response to impact, and the droplet internal flow dynamics. In contrast to previous studies, we show that droplet dynamics can be altered and contact times reduced by introducing a second energy storage mechanism during impact elastic energy of the substrate in addition to surface energy of the droplet. We present new fundamental knowledge of droplet impact physics and provide a starting point for more advanced approaches to enhance the performance of droplet based applications by using substrate elasticity to achieve enhanced thermal, mass, or momentum transport.ResultsImpact DynamicsWe first considered droplet impact on stiff and elastic nanostructured superhydrophobic surfaces. The elastic and rigid surfaces were created by coating polymer sheets of thickness hs=10 500m and a glass slide, respectively, with a commercial nanoparticle spray to render them superhydrophobic, resulting in apparent advancing/receding contact angles of 1644/1593 (see Methods for details). Prior to droplet impact testing, the superhydrophobic coating was characterized for its morphology and wetting characteristics. Figure 1a,b show optical and scanning electron microscopy (SEM) images of the superhydrophobic surfaces. Individual nanoparticles with diameters d 30nm (Fig. 1b) formed macroscopic clusters (Fig. 1a), leading to random, hierarchical surface structures with an overall roughness of r7.5, where r is the ratio of the total surface area to the projected area, and an effective solid liquid fraction of f0.05 (for more information on surface roughness, see Supplementary Information, section S.3). Droplet impact on the elastic surfaces differed greatly from impact on the rigid superhydrophobic surface.Figure 1: Surface characterization and dynamic behavior of water droplet impact on rigid and elastic superhydrophobic surfaces.(a) SEM micrographs showing the macroscale roughness of the NeverWet superhydrophobic coating due to particle clustering. (b) High resolution SEM micrograph showing individual nanoparticles. Inset: water droplet on a NeverWet coated glass slide (scale bar 1mm). The advancing and receding contact angles were 1644 and 1593, respectively. (c) High speed images showing a low velocity droplet (v=0.68m/s) impacting a rigid superhydrophobic surface, and following the classical model of spreading, retraction and lift off at the theoretical contact time tc,th=2.6 (D03/8)1/2. (d) Droplet impact on a rigid superhydrophobic surface at higher impact speeds (v=1.58m/s), showing breakup and splashing. (e) Droplet impact on an elastic superhydrophobic surface at higher impact speeds (v=1.57m/s), showing substrate oscillation, and early lift off of the droplet in a pancake shape at reduced contact times (tc tc,th=6.3ms).Figure 1c shows a droplet with D0=1.48mm impacting the rigid superhydrophobic sample at a speed of v=0.68m/s, corresponding to We=9.6 and Oh=0.0031 ( where is the droplet dynamic viscosity). As expected, impact causes the droplet to spread laterally, undergo kinetic to surface energy conversion due to additional surface area creation, and reach a maximum diameter Dmax at the spreading time t=tspr. The droplet then undergoes the reverse process and retracts due to surface to kinetic energy conversion and finally lifts off the surface at the theoretical contact time tc=tc,th=2.6 (D03/8)1/210,11,12,13. At higher impact speeds, as shown in Fig. breaks up into a core droplet and several satellite droplets after reaching its maximum spreading diameter. The remaining core of the droplet detaches from the substrate at tc=tc,th. Interestingly, when the droplet impacts the elastic surface, as shown in Fig. 1e with a droplet with D0=1.50mm and v=1.57m/s (We=51.2), splashing is eliminated by the droplet edge detachment from the surface. Before the droplet can fully retract, the entire droplet has lifted off the surface in a spread (or pancake) shape at a contact time 21% shorter than the theoretical contact time on a rigid superhydrophobic surface.Energy Conversion During ImpactInspired by this unique observation, we hypothesize that substrate elasticity enables a new energy conversion mechanism to come into play during droplet impact. On the elastic surface, two distinct post impact energy conversion mechanisms exist: kinetic to surface within the droplet and kinetic to elastic between the droplet and the elastic substrate. If tailored correctly, the elasticity of the substrate can be designed such that the two fundamental energy conversion mechanisms have disparate timescales, allowing for faster vertical momentum transfer from the elastic to kinetic energy conversion than from the classical surface to kinetic mechanism within the droplet, and thus early droplet lift off from the surface.In order to systematically study the effect of substrate elasticity on contact times, we conducted droplet impact experiments on elastic surfaces with varying stiffness (0.5k D0 v We Oh1, such that viscous forces were negligible when compared to capillary or inertial forces. Figure 2 summarizes the contact times for droplet impact on fixed fixed substrates (a, b, c) and cantilever style substrates (d, e, f). For substrate stiffness 20k vc, contact times were reduced when compared to impact on a rigid superhydrophobic surface (k=7630N/m). For low impact speeds (v Supplementary Video S1). For 0.2v vc, substrate mounting and stiffness had no effect on the droplet contact time (see Supplementary Video S2 and Video S3), which was in excellent agreement with the inertial capillary scaled contact time, tc=tc,th. For v > vc, splashing occurred for substrates having k k >150N/m (see Supplementary Video S4), while on substrates having moderate stiffness (20k Supplementary Video S5). The experiments were terminated once splashing occurred. Our data shows that droplet contact times can be halved when compared to droplet impact at lower impact speeds and on rigid superhydrophobic substrates. The reduction in contact time was observed on both fixed fixed and cantilever style substrates and was found to weakly depend on the axial impact location of the droplet due to an increase in substrate stiffness with decreasing distance to the mount (see Supplementary Information, section S.4). It is important to note that the stiffness of the substrate did not directly influence the slope and magnitude of the decrease in contact times. Furthermore, droplet spreading times were not affected by the substrate elasticity and remained constant for all substrate mounting and elasticities, in agreement with previous studies (see Supplementary Information, section S.5)1,17.Figure 2Contact times for impacting droplets for fixed fixed (a c) and cantilever (d f) style mounted substrates as a function of impact speed and substrate stiffness for the three droplet diameter ranges. The critical impact speed, vc (also see Supplementary Information, section S.5), is marked with a dashed line. For impact speeds, v >vc, the contact time decreased as a result of the 'springboard' effect where the droplet lifted off the surface prior to fully retracting. Measurements were terminated once splashing occurred. Error bars are smaller than the symbol sizes and are not shown. In (b), droplets impacting the substrate with stiffness k=63N/m did so off center from the axis, inducing a torsion of the substrate rather than an oscillation, and eliminating the possibility for contact time reduction.In addition to contact time reduction, Fig. droplet breakup and creation of satellite droplets, occurs at higher impact speeds on grace kelly bag hermes cheap elastic substrates than on rigid substrates, which has been reported previously for ethanol droplets impacting a circular membrane18. In the present study, the increase in the splashing threshold speed on fixed fixed substrates was observed for substrate stiffness up to 130N/m. The elasticity of the substrate enables kinetic to elastic energy conversion between the droplet and the substrate at early stages of impact. Hence, not as much energy is left over for kinetic to surface energy conversion, resulting in a decreased spreading inertia and increased critical splashing speed18. For all droplet sizes, splashing initiated at higher impact speeds on fixed fixed hermes kelly sizes imitation when compared to the cantilever style substrates due to more efficient kinetic to elastic energy conversion on the former mounting configuration.Mechanism of Elasticity Mediated Contact Time ReductionIn order to better understand the physical mechanism of contact time reduction, we measured the dynamics of the elastic substrate during impact and developed a simple oscillator model of substrate motion. For the fixed fixed and the cantilever substrates, the eigenfrequencies f0 can be computed as and , respectively, where ms, L, , E, and I are the mass, length, Poisson's ratio (PMMA=0.38), Young's modulus (EPMMA=3 GPa), and area moment of inertia (I=whs3/12) of the substrate, where w is the width and hs the thickness of the substrate. Table 1 lists the calculated and observed eigenfrequencies of the substrates, which are in excellent agreement, giving us confidence in the validity of the harmonic oscillator approximation. Upon impact, the droplet exerts a force on the substrate, which causes the substrate to oscillate. The upward motion of the substrate during oscillation governs the contact time reduction of an impacting droplet, acting to accelerate the flattened droplet (Dmax) in the vertical direction against gravity. The added upward force from the elastic substrate causes the droplet to detach before fully undergoing surface to kinetic energy conversion. During early departure, the droplet remains in a spread, pancake like shape (see Supplementary Videos S5). We refer to this early lift off mechanism as the springboard effect, or springboarding, taking inspiration from a springboard where the vertical acceleration of an elastic membrane or spring (elastic to kinetic energy exchange) helps a jumper to rebound. It is important to note that although analogous droplet springboarding, or trampolining has been observed on suspended soap films19, the springboard effect shown here differs fundamentally from evaporation induced droplet trampolining20. The droplet images in Fig. 3a illustrate the coupling between the oscillation of an elastic substrate in the fixed fixed configuration (k=107N/m) and droplet lift off in the pancake shape. After reaching the maximum spreading diameter (3), the edges of the droplet detach (4) near a minimum substrate position. The subsequent upward motion of the substrate supports the detachment of the center of the droplet and results in early droplet lift off (5). Figure 3b,c show the cantilever style substrate responses for k=29.8N/m and k=2.2N/m, respectively. While for the high stiffness cantilever (k=29.8N/m), droplet lift off did not occur in the pancake shape, yet contact time reduction was observed. However, droplet impact on the low stiffness substrate (k=2.2N/m) did not have a reduced contact time. Furthermore, while the stiffer cantilever oscillated at its natural eigenfrequency (f0=112Hz), the softer substrate showed an additional higher order oscillation (f0=11 and f1=68Hz). The time scales of droplet spreading and recoil (10ms) were much shorter than the first order oscillation timescale (100ms) for the low stiffness substrate, resulting in the inability to accelerate the droplet upwards (see Supplementary Video S6), and enabling full droplet recoil before lift off with similar contact times as those on a rigid superhydrophobic surface21,22. To enable contact time reduction, our results show that the substrate oscillation and droplet impact timescales must be on the same order of magnitude.Figure 3: Substrate response and droplet shapes after droplet impact (scale bar 1mm for all inset images).(a) Fixed fixed substrate with k=107N/m, D0=2.2mm and f0=325Hz. Inset: Time lapse images of the droplet impact. The substrate starts a harmonic oscillation at its natural frequency shortly after droplet impact. The droplet spreads, and lifts off the surface in a pancake shape (springboard effect). (b) Cantilever substrate with k=29.8N/m and D0=2.1mm. The substrate oscillates at its natural frequency, f0=112Hz. Inset: Time lapse images of the droplet impact showing that droplet lift off does not occur in a pancake shape, but is distinct from the retraction behavior on a rigid substrate. (c) Cantilever substrate with k=2.2N/m and D0=2.4mm. The substrate is so elastic that the droplet impact activates substrate oscillations with both the natural (f0=11Hz) and higher order frequencies (f1=68Hz). Even more elastic substrates exhibit even higher order modes, f2=178Hz (not shown). Inset: Time lapse images of the droplet impact showing spreading, retraction, and lift off behavior similar to that on rigid superhydrophobic surfaces.An additional mechanism for contact time reduction can be found by studying the droplet dynamics at high impact speeds. We first determined the critical speed for the onset of contact time reduction, vc, which was a function of the initial droplet diameter (Fig. 2). As shown in Figs 1e and 3a, and explained above, early lift off initiates at the edge of the droplet, analogous to the initial phase of droplet breakup during splashing. When splashing occurs, viscous drag decelerates the rim of the spreading droplet while the edges deform hermes kelly clutch copy upwards and away from the surface. splashing23,24,25. For splashing to occur, the splash parameter, K=WeRe1/2, where the droplet Reynolds number is Re=D0v/, must be greater than a critical parameter Kc. The critical parameter depends on the substrate roughness, and can be approximated as, Kc3,600 for the substrates used in this study26,27,28. During droplet bouncing in the present experiments, droplets initiate their lift off at the edges of the droplet at maximum spreading, as can be seen in Figs 1e and 3a; a behavior similar to the first step during splashing (also see Supplementary Video S5). During spreading, the leading edge of the radial liquid flows over a small layer of air beneath it which provides lift to the advancing contact line29. The lift force created by the spreading rim acts against gravity and facilitates the subsequent substrate oscillation driven lift off of the entire droplet. We can thus link the critical splashing parameter to the onset of contact time reduction to obtain vc=2.1/D00.6, where D0 is the droplet diameter in units of millimeters, and vc is the critical droplet impact speed in units of meters per second. For a detailed derivation of the critical impact speed, including a di
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