Microdroplets Impinging on Freely Suspended Smectic Films: Three

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Microdroplets Impinging on Freely Suspended Smectic Films: Three Impact Regimes Sarah Dölle* and Ralf Stannarius* Otto von Guericke University Magdeburg, Department of Nonlinear Phenomena, PB 4120, 39016 Magdeburg, Germany ABSTRACT: We employ high-speed video imaging to study microdroplets of a few picoliters volume impacting freely suspended smectic liquid-crystal films. Depending on the impact parameters, in particular, droplet velocity and mass, three different regimes are observed such as trapping, rebounding, and tunneling. Fast droplets penetrate the films completely. After they have passed the film, they are coated with a layer of film material while the original smectic film remains intact. Droplets in a certain intermediate velocity range bounce back from the film. After impact, the film deforms and hurls the droplet back, depleting a substantial share of the initial kinetic energy. Slow droplets are caught and embedded in the film. During impact and tunneling, an appreciable amount of kinetic energy is lost. The energy is partially dissipated during droplet impact and during subsequent mechanical vibrations and oscillations of the film and the droplet. The tunneling process of high-speed droplets can be exploited to prepare smectic shells of well-defined sizes that enclose picoliters of an immiscible liquid.

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INTRODUCTION Droplets impinging on various types of surfaces have been studied for more than a century. A particularly fascinating introduction into the phenomenon of droplet impact was published at the end of the 19th century by Worthington.1 Flash photography had already captured important features of impact and splashing. Stroboscopic techniques2 were a big step toward dynamic observations. Since then, considerable progress in high-speed video imaging enabled the recording, characterizing, and modeling of droplet dynamics. Therefore, interest in detailed studies of droplet impingement was boosted, and different targets such as solid substrates,3−13 solid substrates covered by thin liquid films,14−18 and surfaces of bulk liquids19−28 were investigated. The observed dynamic phenomena are manifold and, despite a profound experimental data basis, not fully understood. The dynamics appears to be quite simple at first glance, but it involves a number of complex phenomena. Apart from the fundamental relevance of the physics of droplet impact, there is considerable interest in the context of applications, for example, in surface treatment, spray cooling, or raindrop-repellent fabrics. The efficiency of fuel injection or surface coating depends on droplet impact phenomena. In coating processes or inkjet printing, the surface area covered by a droplet is essential. Recently, the progress of inkjet printing techniques in diverse fields, including microchips and bioprinting, has produced technological interest in detailed investigations of impact processes of micrometer-sized droplets on various surfaces. However, complex splashing and wetting behavior has been studied, mainly for macroscopic droplets29 on solid or liquid surfaces. © XXXX American Chemical Society

In this study, we will focus on picoliter droplets impacting liquid freely suspended films (fsf) of submicrometer thickness. Interest in those investigations is diverse. The very impact scenario itself is in general completely different from impacts on solid substrates or deep liquid pools. Thin films react elastically. Therefore, they absorb the kinetic energy of the projectile, which may be a desired effect in applications.18 Splashing is absent at impact on our films. It was shown that droplets may bounce on films after impact30 or tunnel through them. DoQuang et al.31 suggested the use of the tunneling process to wrap microdroplets of the dispenser liquid with a thin cover of the immiscible film fluid. Thus, the droplet can be used as a carrier for sensitive biological film material, or one can use the wrapped droplets as a carrier for drugs or in sensitive biological assays. We will demonstrate a similar process below. Additionally, the embedding of droplets in films of immiscible fluid material can be of interest.32 Such droplets may serve as markers or probes to visualize flow fields, or they may be used to prepare quasi two-dimensional colloids in the film plane.33 Previous investigations using thin films as targets were performed on thin soap films and oily ink films.30,31,34,35 Even the interactions of liquid jets with freely suspended films have been studied experimentally.36 In contrast to these previous studies, we prepare fsf from a smectic liquid-crystalline material. Smectic liquid crystals are characterized by a layered arrangement of rod-shaped molecules, so-called mesogens. One material chosen here is in the smectic A (SmA) phase, where Received: March 2, 2015 Revised: May 26, 2015

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DOI: 10.1021/acs.langmuir.5b00756 Langmuir XXXX, XXX, XXX−XXX

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films are bulged by a subtle overpressure in the capillary. The curvature of the spherical-cap-shaped films is adjusted by controlling the air volume in the capillary with an attached syringe. On the length scale of the droplet impact zone, this curvature is negligibly small. (The radius of curvature is slightly larger than 2 mm.) That means that in the analysis of droplet impact data, curvature can be neglected and the films behave similarly to planar films. For the observation, a high-speed camera, Phantom V611, is combined with a long-range microscope, Questar QM 100. The recording rates of the camera are chosen between 4000 frames per second (fps) and 400 kfps. Droplets are shot onto the film by a microdroplet-dispenser, MJATP-01 from MicroFab Technologies. The dispenser has a nozzle diameter of about 40 μm, which essentially determines the droplet sizes. With a proper voltage pulse program, the piezoelectric nozzle deforms to create the droplet. We vary the voltage between 20 and 45 V in order to control the droplet ejection speed in a range between about 0.8 and 7 m/s. The dispenser nozzle is placed approximately 0.5 mm above the film surface. Figure 1 shows a sketch of the

the long axis of the mesogens is preferentially arranged normal to the layer plane without any long-range positional order within the layer. In the layer plane, this smectic phase resembles an isotropic liquid in two dimensions. The other material shows a smectic C (SmC) phase, and the layered structure is similar to the SmA phase but the average long axes of the mesogens are slightly tilted with respect to the layer normal. The described internal structures favor the formation of stable fsf, formed by a well-defined, well-ordered stack of molecular layers. There is a clear advantage to using smectic films instead of soap films in our experiments: they are not sensitive to drainage, and they can be drawn with uniform thicknesses and well-defined internal order. The molecular layer structure stabilizes them against film thickness fluctuations and rupture. In equilibrium, their thickness is homogeneous up to single molecular layers. There are still many open questions concerning the actual impact scenario in these systems, and analytical model calculations or numerical simulations do not describe the problem satisfactory. The reason is the complexity of the multifluid dynamics in this case, including translational kinetics of the projectile, the vibrations of the film, air flow, and droplet oscillations. By means of high-speed imaging and long-range microscopy, we can observe some of these fast phenomena experimentally. In a preceding study,32 we have shown that three impact scenarios can be distinguished. Slow droplets are trapped and gradually embedded in the smectic film. The phases of this process were already discussed in detail.32 At high impact speeds, the droplets tunnel the film, whereas at intermediate speeds we find bouncing. The details of those phenomena are described and analyzed below. As mentioned above, a potential application for the tunneling of microdroplets through smectic films is the preparation of smectic shells that separate two immiscible liquids. Such shells have been obtained previously37−41 by cooling nematic shells that were produced with a microfluidics technique.42

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Figure 1. Experimental setup for the observation of droplet impact on a smectic fsf. The film is bulged by a slight excess pressure in the capillary. The radius of curvature (>2 mm) is large compared to the length scales related to the impact. experimental setup. In most situations, a single droplet can be shot at a time. Sometimes we find smaller satellite droplets following the first droplet with a delay of 20 to 30 μs. The droplets decelerate in air because of air friction, and the asymptotic velocity of a droplet falling under its own weight is a few cm/s. However, the time constant for this deceleration is in the millisecond range, far beyond the time frame of our experiments. Within the period of interactions with the films on the order of 100 μs, the droplet deceleration by air drag can be neglected as well as gravitational acceleration. We determine the droplet velocities immediately before impact. The actual ejection speed from the dispenser may be somewhat higher, but this is not relevant here.

EXPERIMENTAL SECTION

Materials. Experiments were carried out with two different smectic materials. Most investigations were performed with a room-temperature smectic C mixture, here referred to as PP, containing equal amounts of 2-(4-n-hexyloxyphenyl)-5-n-octypyrimidine and 5-n-decyl2-(4-n-octyloxyphenyl)pyrimidine. The mesomorphism is smectic C 52 °C smectic A 68 °C nematic 72 °C isotropic. The second material is room-temperature smectic A substance 4-octyl-4′-cyanobiphenyl (8CB), with phase sequence smectic A 33.8 °C nematic 40.8 °C isotropic. This is a commercial, well-characterized standard compound. All mesogens were purchased from Synthon Chemicals. The surface tension of 8CB (SmA) with respect to air43 is σ = 0.0278 N/m, and for the PP mixture (SmC)44 it is 0.02245 N/m. We estimate that the shear viscosity for both materials is on the order of 0.05 Pa s, as in comparable smectic materials.45 The droplet material is an aqueous solution with a certain amount of 5% ethylene glycol. Ethylene glycol was purchased from Merck with a purity of at least 99%. The addition of ethylene glycol to water prohibits the fast evaporation of the droplet during shooting, impact, and potential embedding of the droplets in the smectic film. The material is immiscible with the liquid crystals used. Its density is 1 g/ cm3, its dynamic viscosity is about 1.46 mPa s, and the surface tension is approximately 0.066 N/m.46 Method. The smectic film is manually drawn on the opening of a glass capillary (inner diameter 4 mm) by means of a sharp metal edge. This is a standard technique for producing freely suspended smectic films. A small amount of smectic material is spread on the capillary opening, and by drawing the edge across this opening, the film forms. We observe the films in a viewing direction parallel to their surface. In order to achieve such a side view without obscuring film holders, the

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DROPLET IMPACT REGIMES Generally, the drop impact can be classified according to the Weber (We) and Ohnesorge (Oh) numbers.47 We=Sρv 2 /σ describes the ratio between kinetic and capillary forces, with surface tension σ, density ϱ, impact velocity v, and S being a characteristic length equal to the drop diameter ddroplet. It determines the driving force of the impact. The Ohnesorge number Oh=η /(ρσ S)1/2 = (We)1/2 /Re describes the ratio of viscous (viscosity η) and inertial forces, identifying the dominating resistance. In our experiments, We is between 1 and 100, which means that the kinetic impact energy is dominant at least for the high-speed impact regime described below. Slow droplets with We on the order of 1 will be trapped in the films, while for fast droplets the capillary forces of the film have only small decelerating effects. The Ohnesorge number has to be discussed in the relevant context. If one is interested in the deformations of the microdroplet, then one needs to insert droplet viscosities, surface tensions, and sizes. B

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Figure 2. Three scenarios after droplet impact (water with 5% ethylene glycol) on smectic fsf of the PP mixture. The initial film positions are indicated by white arrows: (a) droplet embedding, impact velocity 0.8 m/s, frame rate 18 kfps, (b) bouncing, impact velocity 4.8 m/s, frame rate 48 kfps, and (c) tunneling, impact velocity 5.3 m/s, frame rate 60 kfps. The fast droplet penetrates the film and leaves with a velocity of about 1.7 m/s. The film closes again so that a successively smaller droplet is trapped. Image sizes are 346 μm × 93 μm. The large droplets have ∼42 μm diameter, and the two smaller ones have between 27 and 33 μm diameter.

For the ethylene glycol/water mixture, one finds Oh ≈ 0.028. The droplet exhibits inviscid behavior, and weakly damped oscillations occur. If one considers the film deformations, one needs to insert the smectic shear viscosity and the approximate radius of the film deflections; the respective Ohnesorge number is slightly less that 1. Film deflections are rapidly damped by viscous dissipation. For monodisperse droplets, the crucial parameter for the dynamics is the impact speed. We find three different regimes depending on the velocity of the particles. Droplets with low impact velocities are trapped in the film. When their surface tension is larger than that of the liquid crystal, they do not spread but are locally integrated into the film. Their shape consists of two spherical caps symmetrical to the film plane.32

From their equilibrium shapes that are asymptotically reached, one can extract surface and interface tension data.48 For the PP mixture and droplets of 42 μm diameter, this scenario was found when the droplet speed was below ∼5.15 m/s. This corresponds to Weber numbers below ∼47. Smectic A films of 8CB trapped particles of that size at impact velocities up to ∼5.5 m/s, this velocity corresponds to the same We. Note that our definition of We differs from that of Gilet30 by a factor 2; they found a transition from bouncing to passing droplets shot onto soap films at We ≈ 16. In a small range around 5 m/s, droplets can bounce back from the PP film (same for 8CB at the limit velocity). If the impact velocity exceeds this limit velocity, then droplets tunnel through the films. Figure 2 shows the three impact scenarios, C

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Langmuir the images are cut out of sequences recorded with 180 kfps (a) and 240 kfps (b,c). In some experiments, satellite droplets appeared ∼20 μs after the first one (b, c). In Figure 2c, it is evident that these droplets are trapped in the film after the first one has passed the film, thus proving that the film remains intact after the passage of the tunneling droplet. In Figure 3, the

Figure 4. Oscillations of a PP film after a droplet is caught and embedded. The impact speed is 4.4 m/s, impact occurs at time t = 63 μs, and the droplet diameter is 42 μm. The data points mark the film displacement in the direction of the shot, relative to the equilibrium film. The solid line is a fit to an exponentially damped sine function with frequency 5.7 kHz and damping rate τ = 0.1 ms. Figure 3. Typical trajectories of the droplets (42 μm diameter) for three different impact velocities. The spatial coordinate gives the distance from the initially undeformed film. The origin of the time axis was chosen arbitrarily.

extracted positions of the centers of mass of the large droplets are shown for the three impact regimes. At slow impact speeds, the process of embedding droplets in the film is interesting for the study of wetting processes and interface dynamics.32 Here, we focus on the latter two scenarios, bouncing and tunneling. In these regimes, the initial kinetic energy is larger than the dissipated part and the droplet retains some excess energy to leave the film.

Figure 5. Droplet with 4.8 m/s impact speed and satellite droplet with the same velocity bouncing back from a film. The satellite droplet excites oscillations of the primary droplet so that the droplet can leave the smectic film when it has a prolate shape and a short contact line with the film. The images are background subtracted. The image size is 170 μm × 170 μm. The time in each frame is given in microseconds, with respect to the first contact of the droplet with the film.

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TRAPPING When the droplet hits the film at low speed, it is caught and all initial kinetic energy is lost, partially dissipated immediately at impact and partially transformed into droplet and film deformations. The film with the trapped droplet performs damped oscillations toward its equilibrium shape. Figure 4 shows an example of a film hit by a droplet at a velocity of 4.4 m/s. The film oscillates with a frequency of about 6 kHz, and the oscillations are damped within a few hundred milliseconds. Further details of the trapping and embedding processes of lowspeed droplets into smectic films can be found in an earlier study.32

films this gives 5.9 μN. In fact, the droplet flattens after the collision with the satellite (equatorial diameter ≈ 46 μm at time 48.6 μs), which increases the contact line and thus the capillary force limit of the film to ∼7 μN. The impactor remains above the film and bounces back. As a consequence of their coalescence, the droplets perform damped oscillations with a frequency of about 35 kHz. While the film bends upward, the droplet reaches a prolate oscillation phase, with ∼35 μm diameter at the equator. The capillary forces of the film (maximal at 5.4 μN) are not sufficient to hold it, and the droplet can leave the film. It is hurled back with a velocity of approximately 1 m/s. It loses approximately 95% of its initial kinetic energy to film deformation and impact losses. Because this process depends crucially on details of the collisions and shape transformations of the rebound droplet, the rebound velocities are not very well defined, and values scatter between almost zero and 3 m/s. It is evident in Figure 3 that the backward velocity of the droplet decreases considerably (here, from v0 ≈ 2 m/s to the final v∞ = 0.96 m/s) when the droplet detaches from the film. This is marked with an arrow in the figure. The retardation can be attributed to a kinetic energy loss of mdroplet(v02 − v∞2)/2 when work is performed against capillary forces between the film and the droplet. The kinetic energy loss for this droplet is 60 pJ, i.e., approximately 80%. The surface energy necessary to

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REBOUND The phenomenon of rebounding drops is observed frequently in a narrow velocity range. It often occurs when the first droplet is hit by a successive satellite droplet shortly before or after it bounces on the film. Such an event is seen in Figure 2b in the fifth image. In detail, the bouncing process is seen in Figure 5. We propose the following explanation: The droplet does not have enough energy to pass the film. The film remains intact below the droplet. The maximum force of the film to hold the droplet can be roughly estimated, for a spherical droplet, as 2πddropletσ, where σ is the smectic surface tension. This force is calculated under the assumption that the film is in contact with the droplet at the equator and starts as a vertical tube near the droplet (43 μs image in Figure 5). For 42 μm droplets on a PP D

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8CB (open circles). Slower droplets are either trapped or they rebound (crosses). The droplets tunneling the film slow down considerably. The dashed line marks the complete loss of kinetic energy, ΔE = Ein. Most of the droplets with energies in the vicinity of the threshold are found to be very close below that line, and they lose the major part of their kinetic energy. Some droplets with higher impact speeds preserve larger shares of their kinetic energy, but the minimal energy loss for tunneling droplets is ET. The general observation is that the droplets do not lose a fixed amount of energy when they tunnel the film. In that case, the loss curve in Figure 6 would be a horizontal line, but the droplets dispense the major part of their kinetic energy in all experiments, independently of their impact speed. There is a trend toward a larger kinetic energy of the passing droplet with larger Weber numbers; see the end of the section. Several contributions to the energy loss ΔE can be distinguished. Some kinetic energy is dissipated immediately at impact. Another part is dissipated during droplet oscillations. Then, energy is needed to deflect the film. There is also work done against air during film deflection.32 As shown above, the tunneling droplet also loses energy when it detaches from the film. First, we estimate the energy for the deflection of the film, which remains in the film after tunneling/rebound. Figure 7

detach the droplet can be crudely estimated from (π/4) ddroplet2(σfilm + σdroplet). Inserting the respective surface tensions for both the film and droplet, one obtains a surface energy in good agreement with the kinetic energy loss during detachment. We derive the following interpretation for the bouncing phenomenon: The droplets that are hurled back do not possess enough kinetic energy to penetrate the film, and the film tension holds the droplet at the moment when the film reaches its maximum downward deformation. When the film swings back, the droplet adopts a more prolate extension during its shape oscillations. It may leave the film in the backward direction if its kinetic energy exceeds the above-estimated surface energy for detachment. The necessary energy to detach originates from the oscillation energy of the droplet that adds to the translational energy. In most cases but not all, the oscillations were amplified by the impact of a small, secondary droplet, while the first droplet was in contact with the film. In all these experiments, the original films retain their thickness. The reason is obviously that both the formation of “holes” of depleted layers49 and the formation of “islands” of excess layers44 are comparably slow processes on the time scale of the droplet impact phenomena.

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TUNNELING In this section, we focus on standard droplets with a 42 μm diameter. (A few experiments are available for droplets with other sizes, and they will be mentioned at the end of this section.) The two interesting aspects are the details of the geometry and the energy balance during the penetration of the film. We refer to this process as tunneling here, even though it is evident that it is in fact a wrapping of the droplet into film material after impact and a subsequent detachment from the recovered film. The original film thickness remains the same after the droplet has penetrated the film. Material is supplied from the meniscus to replace the amount of material that encloses the droplet after penetration. Figure 6 shows the energy loss of droplets with different impact energies. For complete penetration of the film, the kinetic droplet energy has to be larger than a minimal tunneling energy of ET = 0.51 nJ for PP (solid circles) and 0.58 nJ for

Figure 7. Deflection of the smectic PP film immediately before the detachment of a tunneling droplet. The dashed line indicates the film profile. An empirical fit function of the form ∝exp(−r/r0) was employed to approximate the deformation.

shows the cross section at the instant of maximum film deformation in a tunneling process. The droplet equator has already passed the film. A satisfactory fit is found with the empirical function h0 − h(r) = a exp(−r/r0) and parameters a = 80 μm and r0 = 55 μm (r is the lateral distance from the point of impact). The film area thereby increases by ΔA ≈ 3300 μm2. The bending rigidity of the smectic film is negligible, as are elastic distortions of the director, thus the energy for this deformation is essentially the excess surface energy ΔEs = 2σΔA ≈ 0.15 nJ. This energy is subsequently dissipated in damped film oscillations (Figure 4). Another share of the initial kinetic energy is transformed into damped droplet oscillations after impact and subsequently dissipated by them. This term can also be estimated from the experiment. The measured frequency of the ground mode of droplet oscillations (from prolate to oblate) is ω2/(2π) ≈ 35 kHz. (There is a misprint in our ref 32 which gives an incorrect oscillation frequency.) This is in good agreement with Lamb’s formula50 predicting the angular frequencies of the nth eigenmodes of the droplet oscillation (spherical harmonics),

Figure 6. Energy loss of tunneling droplets through PP (solid circles) and 8CB (open circles) films for different impact energies. The two arrows indicate the limiting energies for the tunneling of 42 μm droplets for PP (left) and 8CB (right), respectively. Crosses mark rebound droplets of PP. The dashed line indicates the complete loss of kinetic energy. Data from three experiments with tunneling droplets of other sizes are added (open squares).

ωn = E

8n(n − 1)(n + 2)σ ρ ddroplet 3

(1) DOI: 10.1021/acs.langmuir.5b00756 Langmuir XXXX, XXX, XXX−XXX

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Langmuir Here σ is the surface tension, ρ is the mass density of the droplet material, and ddroplet is the diameter of a sphere with the same volume. The second eigenmode dominates the abovementioned oblate−prolate shape transformation. The oscillation amplitude r̂ depends upon the impact speed vin: for vin = 5 m/s, it is r̂ ≈ 4 μm, roughly one-fifth of the droplet radius, and it increases with higher impact speeds. A crude estimate of the initial energy in the droplet oscillations is Eosc ≈ mdroplet (ω2r̂2)/6, which is less than 0.01 nJ. Subtracting all these contributions from the initial E0, we conclude that the major part of the energy is directly dissipated during the impact and during the detachment of the tunneling droplet. The dispenser allows us to produce only one droplet size, but a few droplets with different radii were occasionally observed. Smaller droplets obviously need lower energies to penetrate the film (Figure 6), and their energy loss is lower. Their Weber numbers (57 for the 29 μm droplet, 75 for the 35 μm droplet) are well above the critical value. The same applies for the 51 μm droplet (We = 90).

droplet coated with smectic material that is immersed in a shallow water layer on a glass plate.

Figure 9. Ethylene glycol droplets coated with smectic film after passing the fsf and hitting a shallow water layer on a glass substrate. The images were taken with crossed polarizers; the image size is 88 μm × 88 μm. The left droplet is an intact sphere with a diameter of approximately 40 μm. The right droplet obviously burst, and it forms a hemisphere on the glass substrate. At its base, focal conic textures are seen. Compared to smectic and nematic shells prepared by microfluidic techniques, considerably smaller shells are achieved with this preparation method. The thickness of the coating is determined by the thickness of the smectic fsf.

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COATING AND DETACHMENT Details of the detachment of a droplet after tunneling are shown in Figure 8. Most importantly, the film does not rupture

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DISCUSSION AND SUMMARY We have presented a method that uses freely suspended smectic films as targets for droplets of a ethylene glycol/water mixture. The tunneling mechanism and energy balances have been analyzed in detail. Some observations made in the smectic films are comparable to earlier soap film experiments by Gilet et al.30 These authors studied the shooting of droplets on target films which were made of the same materials as the droplets. As in their work, we find embedding, bouncing, and tunneling scenarios, depending upon the impact parameters. The Weber number for the transition to the tunneling regime is roughly in the same range. The main difference in our experiment compared to the soap film study is the coating of the tunneling droplet by the uniform smectic film. The smectic film retains its thickness after droplet interactions. When the droplet is coated by the smectic film, the material loss near the impact area is replenished by the supply of the smectic substance from the film meniscus. We conclude from the unchanged thickness of the target film that the film around the droplet also retains its original thickness (except in a micrometer range near the pinchoff region) so that the thickness of the coating can be controlled to a certain extent by the target film thickness. This coating effect can be exploited for the preparation of smectic shells that are filled with an immiscible liquid. In order to verify this, we have shot coated droplets onto millimetersized sessile water/surfactant drops on a glass substrate, where the smectic-film-coated droplets immerged. The target drop or any pool of target liquid can be used to collect and store large numbers of coated droplets for further experiments, processing, or analysis. Such smectic shells can be used to study director textures on curved surfaces in the same way as in earlier work on nematic37−42,51 and smectic shells.37−41,52 Moreover, one can use these shells to transport reagents in an aqueous environment. Heating them into the nematic phase is a way to subsequently open such shells and release the internal fluid, or to coalesce them. Other droplet volumes can be prepared with different dispenser nozzle diameters, which are commercially

Figure 8. Detachment of a droplet after tunneling. The time is given in microseconds, relative to the first image in the sequence. The film first contracts to a narrow hose within ∼10 μs. This hose elongates when the droplet flies on and finally breaks. Thereafter, both remaining parts of the broken connection contract axially. The width of each image is 82.5 μm.

during impact. It embeds the droplet during penetration. After the droplet has passed the film plane, the film closes behind the droplet and forms a thin hose with a radius on the order of 1 μm. This hose expands with increasing distance between droplet and film. After a few dozen microseconds, the connection pinches off and the two tubular ends contract in the axial direction until they disappear within less that 100 μs. The droplet is then coated with an ordered smectic film of welldefined thickness. It also contains a small air bubble from the air contained in the hose, but this detail is not resolved in the optical images. One can estimate from the geometry seen in the images that the air volume entrapped is much smaller than the amount of smectic film wrapped around the droplet, not to speak of the droplet volume. As mentioned above, the film thickness of the recovering target film is uninfluenced by the passage of the droplet. Therefore, we have reason to assume that the film coating the droplet has the same thickness as the latter. When the coated droplets are shot on a liquid pool or, for example, onto large sessile water drops on a glass substrate, they survive the impact on the water surface and are immersed as shells of smectic-filmcoated dispenser liquid. Figure 9 (left) shows an image of a F

DOI: 10.1021/acs.langmuir.5b00756 Langmuir XXXX, XXX, XXX−XXX

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Langmuir

(17) Thoraval, M.-J.; Takehara, K.; Etoh, T. G.; Thoroddsen, S. T. Drop impact entrapment of bubble rings. J. Fluid Mech. 2013, 724, 234−258. (18) Energy absorption in a bamboo foam. Europhys. Lett. 2008, 84, 36001. (19) Single drop impact onto liquid films: Neck distortion, jetting, tiny bubbles entrainment, and crown formation. J. Fluid Mech. 1999, 385, 229. (20) Vandewalle, N.; Terwagne, D.; Mulleners, K.; Gilet, T.; Dorbolo, S. Dancing droplets onto liquid surfaces. Phys. Fluids 2012, 18, 091106. (21) Thoroddsen, S. T.; Thoraval, M.-J.; Takehara, K.; Etoh, T. G. Droplet Splashing by a Slingshot Mechanism. Phys. Rev. Lett. 2011, 106, 034501. (22) Thoroddsen, S. T.; Thoraval, M.-J.; Takehara, K.; Etoh, T. G. Micro-bubble morphologies following drop impacts onto a pool surface. J. Fluid Mech. 2012, 708, 469−479. (23) Thoraval, M.-J.; Takehara, K.; Etoh, T. G.; Popinet, S.; Ray, P.; Josserand, C.; Zaleski, S.; Thoroddsen, S. T. von Karman Vortex Street within an Impacting Drop. Phys. Rev. Lett. 2012, 108, 264506. (24) Thoraval, M. J.; Thoroddsen, S. T. Contraction of an air disk caught between two different liquids. Phys. Rev. E 2013, 88, 061001. (25) Zhang, L. V.; Toole, J.; Fezzaa, K.; Deegan, R. D. Evolution of the ejecta sheet from the impact of a drop with a deep pool. J. Fluid Mech. 2012, 690, 5. (26) Jiang, T.; Ouyang, J.; Li, X.; Ren, J.; Wang, X. Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown. J. Appl. Mech. Technol. Phys. 2013, 54, 720−728. (27) Nikolopoulos, N.; Strotos, G.; Nikas, K. S.; Gavaises, M.; Theodorakakos, A.; Marengo, M.; Cossali, G. E. Experimental Investigation of a Single Droplet Impact onto a Sessile Drop. Atomization Sprays 2010, 20, 909−922. (28) Focke, C.; Kuschel, M.; Sommerfeld, M.; Bothe, D. Collision between high and low viscosity droplets: Direct Numerical Simulations and experiments. Int. J. Multiphase Flow 2013, 56, 81−92. (29) Yarin, A. Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing···. Annu. Rev. Fluid Mech. 2006, 38, 159−192. (30) Gilet, T.; Bush, J. W. M. The fluid trampoline: droplets bouncing on a soap film. J. Fluid Mech. 2009, 625, 267. (31) Do-Quang, M.; Geyl, L.; Stemme, G.; Wijngaart, W.; Amberg, G. Fluid dynamic behavior of dispensing small droplets through a thin liquid film. Microfluid. Nanofluid. 2010, 9, 303−311. (32) Dölle, S.; Harth, K.; John, T.; Stannarius, R. Impact and Embedding of Picoliter Droplets into Freely Suspended Smectic Films. Langmuir 2014, 30, 12712. (33) Bohley, C.; Stannarius, R. Inclusions in free standing smectic liquid crystal films. Soft Matter 2008, 4, 683. (34) Courbin, L.; Stone, H. A. Impact, puncturing, and the selfhealing of soap films. Phys. Fluids 2006, 18, 091105. (35) Kim, I.; Wu, X. Tunneling of micron-sized droplets through soap films. Phys. Rev. E 2010, 82, 026313. (36) Kirstetter, G.; Raufaste, C.; Celestini, F. Jet impact on a soap film. Phys. Rev. E 2012, 86, 036303. (37) Lopez-Leon, T.; Fernandez-Nieves, A.; Nobili, M.; Blanc, C. Nematic-Smectic Transition in Spherical Shells. Phys. Rev. Lett. 2011, 106, 247802. (38) Liang, H.-L.; Rudquist, S. S. P.; Lagerwall, J. Nematic-Smectic Transition under Confinement in Liquid Crystalline Colloidal Shells. Phys. Rev. Lett. 2011, 106, 247801. (39) Liang, H.-L.; E. Enz, G. S.; Lagerwall, J. Liquid crystals in novel geometries prepared by microfluidics and electrospinning. Mol. Cryst. Liq. Cryst. 2011, 549, 69. (40) Liang, H.-L.; Zentel, R.; Rudquist, P.; Lagerwall, J. Towards tunable defect arrangements in smectic liquid crystal shells utilizing the nematic-smectic transition in hybrid-aligned geometries. Soft Matter 2012, 8, 5443. (41) Liang, H.-L.; Noh, J.; Zentel, R.; Rudquist, P.; Lagerwall, J. Tuning the defect configurations in nematic and smectic liquid crystalline shells. Philos. Trans. R. Soc. A 2013, 371, 20120258.

available in a broad size range. In general, the droplets prepared by our method can be made substantially smaller than those produced with the conventional microfluidic technique. Small droplets are required, particularly when one is interested in the effects of curvature on the textures and orientation patterns of liquid crystals.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: +49 391 *E-mail: +49 391

[email protected]. Fax: +49 391 67 18108 Tel: 67 58582 [email protected]. Fax: +49 391 67 18108 Tel: 67 58582

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are indebted to Jan Lagerwall and Alexey Eremin for stimulating discussions. DFG is acknowledged for support with project STA 425-28, and the German Aerospace Research Center DLR is acknowledged for support with project 50WM1430 (OASIS-Co).

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REFERENCES

(1) Worthington, A. M. The Splash of a Drop; Romance of Science; S.P.C.K.: London, 1895. (2) Edgerton, H. E.; Killian, J. R., Jr. Flash! Seeing the Unseen by Ultra High-Speed Photography; Hale, Cushman & Flint: Boston, 1939. (3) Rioboo, R.; Voue, M.; Adao, H.; Conti, J.; Vaillant, A.; Seveno, D.; de Coninck, J. Drop Impact on Soft Surfaces: Beyond the Static Contact Angles. Langmuir 2010, 26, 4873−4879. (4) Driscoll, M. M.; Nagel, S. R. Ultrafast Interference Imaging of Air in Splashing Dynamics. Phys. Rev. Lett. 2011, 107, 154502. (5) de Ruiter, J.; Oh, J. M.; van den Ende, D.; Mugele, F. Dynamics of Collapse of Air Films in Drop Impact. Phys. Rev. Lett. 2012, 108, 074505. (6) Kolinski, J. M.; Rubinstein, S. M.; Mandre, S.; Brenner, M. P.; Weitz, D. A.; Mahadevan, L. Skating on a Film of Air: Drops Impacting on a Surface. Phys. Rev. Lett. 2012, 108, 074503. (7) Latka, A.; Strandburg-Peshkin, A.; Driscoll, M. M.; Stevens, C. S.; Nagel, S. R. Creation of Prompt and Thin-Sheet Splashing by Varying Surface Roughness or Increasing Air Pressure. Phys. Rev. Lett. 2012, 109, 054501. (8) Bischofberger, I.; Mauser, K. W.; Nagel, S. R. Seeing the invisibleAir vortices around a splashing drop. Phys. Fluids 2013, 25, 091110. (9) Lee, J. S.; Weon, B. M.; Je, J. H.; Fezzaa, K. How Does an Air Film Evolve into a Bubble During Drop Impact? Phys. Rev. Lett. 2013, 109, 204501. (10) Moore, M. R.; Ockendon, J. R.; Oliver, J. M. Air-cushioning in impact problems. IMA J. Appl. Math. 2013, 78, 818−838. (11) Hicks, P. D.; Purvis, R. Liquid-solid impacts with compressible gas cushioning. J. Fluid Mech. 2013, 735, 120−149. (12) Gilet, T.; Bush, J. W. M. Droplets bouncing on a wet, inclined surface. Phys. Fluids 2012, 24, 122103. (13) Koplik, J.; Zhang, R. Nanodrop impact on solid surfaces. Phys. Fluids 2013, 25, 022003. (14) Rioboo, R.; Bauthier, C.; Conti, J.; Vou, M.; de Coninck, J. Experimental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp. Fluids 2003, 35, 648−652. (15) Josserand, C.; Zaleski, S. Droplet splashing on a thin liquid film. Phys. Fluids 2003, 15, 1650−1657. (16) Pan, K.-L.; Hung, C.-Y. Droplet impact upon a wet surface with varied fluid and surface properties. J. Colloid Interface Sci. 2010, 352, 186−193. G

DOI: 10.1021/acs.langmuir.5b00756 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir (42) Fernandez-Nieves, A.; Vitelli, V.; Utada, A. S.; Link, D. R.; Marquez, M.; Nelson, D. R.; Weitz, D. A. Novel defect structures in nematic liquid crystal shells. Phys. Rev. Lett. 2007, 99, 157801. (43) Schüring, H.; Thieme, C.; Stannarius, R. Surface Tensions of Smectic Liquid Crystals. Liq. Cryst. 2001, 28, 241. (44) May, K.; Harth, K.; Trittel, T.; Stannarius, R. Dynamics of freely floating smectic bubbles. Europhys. Lett. 2012, 100, 16003. (45) Eremin, A.; Baumgarten, S.; Harth, K.; Stannarius, R.; Nguyen, Z. H.; Goldfain, A.; Park, C. S.; Maclennan, J. E.; Glaser, M. A.; Clark, N. A. Phys. Rev. Lett. 2011, 107, 268301. (46) Tsierkezos, N. G.; Molinou, I. E. Thermodynamic Properties of Water + Ethylene Glycol at 283.15, 293.15, 303.15, and 313.15 K. J. Chem. Eng. Data 1998, 43, 989−993. (47) Schiaffino, S.; Sonin, A. A. Molten droplet deposition and solidification at low Weber numbers. Phys. Fluids 1997, 9, 3172. (48) Schüring, H.; Stannarius, R. Isotropic Droplets in Thin Free Standing Smectic Films. Langmuir 2002, 18, 9735−9743. (49) Harth, K.; Stannarius, R. Deep Holes in Free-Standing Smectic C Films. Ferroelectrics 2014, 468, 92. (50) Lamb, H. Hydrodynamics; Cambridge University Press: Cambridge, 1932. (51) Liang, Q.; Ye, S. W.; Zhang, P. W.; Chen, J. Z. Y. Rigid linear particles confined on a spherical surface: Phase diagram of nematic defect states. J. Chem. Phys. 2014, 141, 244901. (52) Klein, S.; Raynes, P.; Sambles, R. New frontiers in anisotropic fluid-particle composites. Philos. Trans. R. Soc. A 2013, 371, 20120510.

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DOI: 10.1021/acs.langmuir.5b00756 Langmuir XXXX, XXX, XXX−XXX