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Control of Droplet Impact through Magnetic Actuation of Surface Microstructures

Control of Droplet Impact through Magnetic Actuation of Surface Microstructures IntroductionThe collision of a droplet with a surface is an important phenomenon that is the subject of numerous theoretical and experimental investigations that attempt to determine the relationships between the various possible outcomes of impact and the properties of the surface and the droplet. The droplet may bounce off the surface, be deposited on the surface, or splash.[1] Each of these outcomes is useful for different potential breakthrough applications in the fields of thermal management,[2,3] energy harvesting,[4,5] microfluidics,[6–8] spraying,[9,10] and printing[11–13] technologies.The outcome of the impact on a flat (non‐structured) surface is mainly influenced by the characteristic slope of the roughness of the surface and the relationship between the kinetic energy, capillary energy, and viscous dissipation during spreading.[14,15] Two dimensionless parameters are used for scaling drop impacts. The Weber number (We=ρV02R/γ$We = \rho V_0^2R{\rm{/}}\gamma $) describes the ratio between the kinetic and the surface energy of the droplet, while the Reynolds number (Re = ρV0R/μ) describes the ratio between the kinetic and viscous dissipation effects. Here, ρ is the density of the liquid, V0 is the impact velocity of the droplet, R is its radius, γ is surface tension, and µ is the viscosity. At low impact velocity, the kinetic energy is mainly transformed into surface energy and at high impact velocities, the viscous energy dissipation dominates. In addition, the dynamic wetting of the surface is of great importance, as it influences the absorption of kinetic energy during the spreading and contraction of the droplet over the surface.[16–18] Wetting is mainly influenced by the chemical composition of the surface and its microtopography.[19,20] It is known that hydrophobic surfaces become superhydrophobic and hydrophilic surfaces convert into superhydrophilic if they possess a microstructure in the form of a matrix of columns, holes, lamellae, or increased roughness.The dynamics of droplet impact have been studied on flat surfaces with different wetting properties,[21–26] on curved surfaces,[27] and on microstructured surfaces.[19,28–34] One of the most important phenomena studied on microstructured surfaces is the penetration of the droplet through the pillars or lamellae and the resulting transition from the Cassie–Baxter state to the Wenzel state leading to droplet deposition.[32,35] In these studies, mainly pillared microstructures are investigated experimentally, as well as in numerical simulations.[20,33,34,36]Intensive research has recently been carried out on bioinspired tunable surfaces in which the wettability and other properties of the surface can be altered by external stimuli such as light, an electric field, or a magnetic field.[6,37–43] The usage of a DC magnetic field is particularly attractive, as it enables wireless manipulation and is biocompatible. Of particular interest in this category are magnetoactive elastomers (MAE), multifunctional composite materials which consist of micro‐ or nanometer‐sized magnetic particles embedded into a soft elastomeric matrix.[44] Under the influence of a magnetic field, their elastic moduli and surface roughness can change by several orders of magnitude[45,46] due to the phenomenon of the restructuring of magnetic filler particles. In a recent study, Kriegl et al.[42] showed that in a moderate magnetic field (<400 mT), the contact angle of MAE for water increases above the limit of superhydrophobicity. In another study, Kravanja et al.[6] demonstrated a laser micromachining method that allows the fabrication of different types of microstructures in MAE, which are then activated by changing the orientation of the applied magnetic field. If a magnetic field is parallel to the surface, the lamellar microstructures are flattened (bent) to the surface, resulting in a significantly increased slip angle of the droplet. With a lamellar structured magnetoactive surface, Qian et al.[47] demonstrated the possibility of expelling droplets that are already attached to the surface away from the microstructured MAE surface. Peng et al.[48] demonstrated magnetically induced fog harvesting by the fabrication of cactus‐inspired spine structures and magnetically responsive flexible conical arrays. A Janus‐type high‐aspect‐ratio magnetically responsive microplates array was fabricated and the demonstration of reversible switching of surface wettability using a magnetic field is shown in ref. [49].Hitherto, the majority of works on control of the droplet impact on a solid surface considered passive methods such as surface texturing, superhydrophobic treatments, and lubricant infusion.[50] Only a few works have considered active (requiring applied power) methods for controlling the droplet impact dynamics.[50] The reported active methods employed electric fields,[51,52] mechanical,[53] and ultrasonic[54,55] vibrations, as well as surface acoustic waves.[50] A combination of passive surface treatment and active methods may be advantageous for the optimum control of droplet impact on solid surfaces.[50] In particular, the active methods would enable the on‐demand control of the droplet impact. The possibility of using magnetic fields for the control of droplet impact on solid surfaces remains practically unexplored yet. Ahmed et al.[56] studied theoretically and experimentally the effects of an applied external magnetic field on the maximum spreading of a ferrofluid droplet impacting a non‐magnetic solid substrate. To the best of our knowledge, the effect of the magnetic field on the impact of non‐magnetic (ethanol) droplets on magneto‐sensitive surfaces has been presented so far only in ref. [43]. It was shown that, due to the magnetic field‐induced hardening of the material and the associated increased surface roughness, both driven by the restructuring of the magnetic filler, the splashing of droplets occurs at lower We numbers. However, the results were demonstrated only for a bulk (nominally flat, non‐structured) MAE surface. Similar controlling of water droplet splashing and bouncing was shown by using the dielectrowetting principle, where an electric potential of ≈1 kV affected the dynamic contact angle.[52]This paper investigates the capability of using microstructured MAE‐based surfaces to effectively manipulate and control the droplet impact by an external magnetic field. Presented is a systematic study of the impact behavior of water droplets on a microstructured MAE surface exposed to a magnetic field oriented either parallel or perpendicular to the surface. It is shown that the application of a magnetic field and modification of its direction with respect to the surface significantly change the surface topography and wettability, which consequently affects the behavior of the droplet during and after the impact. The magnetic control of droplet impact is by far more efficient than that reported in ref. [43]. Because a permanent magnet is used, our approach does not require a permanent power supply for maintaining the particular dynamics of the droplet impact as in the case of surface acoustic waves.[50] The power supply would be only required to move the magnet into a new position. Besides this, since the microstructured surface used in our study has the form of thin micro‐lamellae, a profound anisotropy of the droplet propagation during the impact is observed.ResultsFigure 1a shows the fabrication of lamellar microstructure in a 0.3 mm thick MAE layer on top of copper foil using the laser micromachining technique.[6] Since the ablation threshold of MAE is significantly lower than the ablation threshold of Cu, which is attributed to the lower evaporation temperature and thermal conductivity of PDMS, the height of the lamellae h was determined by the thickness of the MAE layer. Moreover, the cross‐section of the lamellae was almost completely rectangular (see Figure 1e). To study droplet impacts, we fabricated a lamellar microstructure with dimensions w = 25 µm, l = 275 µm, and h = 300 µm. The ratio between the height h of the lamellae and their mutual spacing l was chosen so that the lamellae did not overlap when they were laid parallel with the surface (see Figure 1d,f).1Figurea) Laser fabrication process of a lamellar microstructure with characteristic dimensions. b) Schematic representation of the relative positions of the sample and the magnet to ensure proper orientation of the magnetic field. c) Edge‐on orientation of lamellae is obtained in the absence of a magnetic field or if the field is oriented perpendicular to the MAE surface (β = 0°). d) Face‐on orientation of lamellae is obtained when a magnetic field is oriented parallel to the MAE surface (β = 90°). OCT images of e) edge‐on and f) face‐on oriented lamellae. β denotes the angle between the magnetic field and the normal vector to the MAE surface.The orientation of lamellae was actuated by changing the orientation of the magnetic field by the movement of the sample according to the permanent magnet (see Figure 1b). In the edge‐on orientation of lamellae (Figure 1c,e), the magnet was centered below the observed surface. In face‐on orientation (β = 0°), the sample was moved to the side so that the observed surface coincided with the region in which the magnetic field was parallel to the surface (β = 90°) (see Figure 1d,e).The impact experiments were performed with water droplets of diameter D0 = 2.7 ± 0.1 mm released from the height z in the range of 5–500 mm which resulted in impact speeds ranging from 0.31 < V0 < 3.1 m s−1, Weber number range 1.9 < We < 187 and Reynolds number range 966 < Re < 9660. The Ohnesorge number (Oh=µ/ρRγ$Oh = \mu {\rm{/}}\sqrt {\rho R\gamma } $) was constant for all experiments and equal to Oh = 0.0028. We investigated droplet collisions with four different MAE surfaces: i) an unprocessed flat MAE surface; a surface with edge‐on oriented lamellae ii) in the absence of magnetic field (B = 0) and iii) exposed to magnetic field B = 247 mT (shown on Figure 1e); and iv) a surface with face‐on oriented lamellae exposed to B = 140 mT (shown on Figure 1f). For ii–iv we used the same sample, changing only the magnitude and orientation of the magnetic field.Figure 2 shows how the impact outcome depends on the type of surface and the We number. If the droplet is completely bounced off the surface after the impact, we labeled the impact as “Rebound.” If at least part of the droplet remained attached to the surface after initial contact, we referred to the impact as “Deposition/Penetration.” In the case of an edge‐on lamellar surface, this was the case when the droplet surface was pinned by the lamellar structure and consequently, the liquid could advance to the bottom of the channels between the lamellas and stick there. However, in the case of a flat MAE surface, the term “deposition” is more commonly used when the droplet does not rebound from the surface anymore. In the case of faster impacts (larger We numbers), a splash began to form, which was visible as a disintegration of the water disk into individual droplets that spread out. The splash first appeared in the direction parallel to the lamellar structure, which is labeled as “Parallel splash,” and later, that is, at larger We numbers, it proceeded in all directions, which is labeled “Circular splash.”2FigureImpact outcomes of water droplets on different types of MAE surfaces. Black marks represent We number of transitions between different outcomes. See Supporting Information for typical videos.Figure 3 shows selected successive images of impacts at low velocities (We = 10). On the flat surface and face‐on oriented lamellae, the droplet sticks to the surface after the impact, while in contrast, on the surface with edge‐on oriented lamellae (bottom row), the droplet bounces off completely.3FigureSelected images of impacts on a flat surface (top row), face‐on lamellae (middle row), and edge‐on lamellae (bottom row) at low speeds (V0 = 0.72 m s−1, We = 10, Re = 2240). See Supporting Information for entire video sequences.Figure 4 shows droplet collisions at intermediate velocities (We = 44), for which the resistance to the droplet spreading is somehow lower on a surface with face‐on oriented lamellae (second row) than on an unprocessed flat surface (top row). This is particularly evident in the contraction phase, where a narrow elongated cylindrical shape is formed for face‐on lamellae and a wider hemispherical shape is formed on a flat surface (see images at 20 ms).4FigureSelected images of impacts on a flat surface (top row), face‐on lamellae (middle row), and edge‐on lamellae (bottom row) at intermediate speeds (V0 = 1.52 m s−1, We = 44, Re = 4690). See Supporting Information for entire video sequences.Figure 5 shows the dynamic properties of droplet impacts on individual surfaces, for water spreading perpendicular (⊥) and parallel to the lamellas (║), respectively. Figure 5b shows the time dependence of the contact diameter of the droplet (D) at low velocities (We = 10). In the first part of the expansion, the droplet spreads on the face‐on oriented lamellae (red curve) as fast as on the flat surface (black curve). The maximum diameter (Dmax) is similar in both cases. However, in the contraction phase, the droplet shrinks faster on the face‐on oriented lamellae, especially in the direction perpendicular to the lamellae (solid red curve). In this direction, the spreading of the droplet stops completely after about 7 ms. In the direction parallel to the lamellae, the width of the contact area of the droplet continues to decrease during the entire observed time interval.5FigureWater spreading dynamics during droplet impacts on different surfaces: flat (black crosses), face‐on lamellae (β = 90°, red circles), and edge‐on lamellae (β = 0°, blue diamonds). a) Sketch of measured diameter D and velocity V of the contact line between droplet and surface. b) Variation of contact diameter D overtime at low impact speed (V0 = 0.72 m s−1, We = 10, Re = 2240). c) Ratio between maximal contact diameter (Dmax) and initial droplet diameter (D0) as a function of We number. d) Ratio between maximal spreading velocity (Vmax) and the droplet impact speed (V0) as a function of We number. In all graphs “⊥” and “║” stands for water spreading perpendicular and parallel to the lamellas, respectively.On edge‐on oriented lamellae, the expansion and contraction of the droplet even more strongly depend on the direction of observation. The maximum width of droplet expansion in the transverse direction to the lamellae (⊥) is about 20% smaller than along the lamellae (║). Moreover, the maximum width is reached slightly earlier, indicating slower propagation in the ⊥ direction. This results in smaller energy dissipation which shifts the rebound/penetration transition to higher impact velocities. This difference in spreading diameters and velocities can be clearly seen in Figure 5c,d, which shows the ratio between maximal contact diameter (Dmax) and initial droplet diameter (D0) and the ratio between maximal spreading velocity (Vmax) and the droplet impact speed (V0) as a function of the We number, respectively. The solid and dashed curves in Figure 5c represent an approximation with a polynomial of order 4, while the curves in Figure 5d represent the approximation with the power function, which are used as guides to the eye.As it is evident from the obtained results on water spreading dynamics, an important property that influences the impact behavior is surface wettability, which is the measure of a droplet's ability to interact with the surface.[21,57] To qualitatively resolve this property, we measured a dynamic contact angle between the droplet and the surface in the initial phase of expansion (within 1.5 ms after impact), namely the advancing contact angle θadv (see Figure 6a), and after it starts contracting back, that is, the receding contact angle θrec (see Figure 6b). Due to the extremely fast nature of the splashing process, these contact angles could only be measured at low‐impact velocities (We = 10). As the dynamic contact angles are not constant during spreading between neighboring lamellae, we report an average value. The differences between different surfaces are obvious. Advancing and receding contact angles are the smallest for flat unprocessed MAE surfaces. Slightly larger are their values for face‐on oriented lamellae, for which the receding angle measured along lamellae (║ direction) is significantly larger (114 ± 9°) than in ⊥ direction (82 ± 6°). The highest advancing and receding contact angles were measured for edge‐on oriented lamellar surface, showing superhydrophobic behavior. Additionally, we calculated contact angle hysteresis (θadv − θrec), which is a measure of how much energy is dissipated during droplet impact.[58] In Figure 6c, one can notice that contact angle hysteresis is the highest for the flat MAE surface (93 ± 7°). For face‐on oriented lamellae it is slightly smaller (62 ± 8° for ⊥ and 32 ± 10° for ║ direction), while for edge‐on lamellae the hysteresis is the smallest (6 ± 6° for ⊥ and 11 ± 7° for ║ direction). This explains the absence of droplet rebound on the untreated (flat) surface and face‐on oriented lamellae.6FigureDynamic contact angles for different types of surfaces at low impact speeds (We ≈ 10). a) Advancing contact angle (θadv) is measured when the droplet is in the initial phase of spreading (within 1.5 ms after the impact) over the surface, b) Receding contact angle (θrec) is measured when the droplet starts contracting, and c) contact angle hysteresis represents the difference θadv − θrec. In all graphs “⊥” and “∥” stands for water spreading perpendicular and parallel to the lamellas respectively. Results are presented as the mean value ± standard deviation (n = 5).DiscussionOur observations demonstrate that lamellar structured MAE surface can be strongly manipulated by changing magnetic field orientation. With this functional principle, the lamellae can be oriented either edge‐on or face‐on with respect to the surface. Depending on their orientation, the outcome of the water droplet impacts significantly changes. At low impact velocities (We < 13 ± 3), the impact outcome changes from the rebound to penetration/deposition, as the orientation of the lamellae changes from edge‐on to face‐on. Another obvious difference between the two orientations of lamellae is the limiting velocity of the droplet at which splashing occurs, leading to the formation of a large number of secondary microdroplets. For the edge‐on orientation of the lamellae, splashing occurs at We > 32 ± 3, while for the face‐on orientation, splashing occurs only at We > 52 ± 4. Since We number depends on the square of the droplet velocity, this means that the ratio of the associated critical velocities is about 1:3. This provides a possibility of using such surfaces to trap or deflect water droplets on demand, simply by changing the magnetic field.The transition from the rebound to the adhesion of the droplets at low‐impact velocities is mainly influenced by the wettability of the surface. For face‐on oriented lamellae, the wetted surface behaves similarly to the unprocessed flat surface, thus the Wenzel regime[59] is established even at the minimum impact velocity of the droplets. On the other hand, for edge‐on oriented lamellae, the Cassie–Baxter contact regime is established,[60] in which only the tips of the lamellae are wetted. Consequently, for face‐on oriented lamellae and unprocessed flat surfaces, the contact angle hysteresis is relatively large (62 ± 8° for face‐on oriented lamellae and 93 ± 7° for the flat surface), so the droplets stick to the surface (see Figure 3). In contrast, for edge‐on oriented lamellae, the advancing and receding contact angles are about 150°, indicating the superhydrophobic properties of this surface. Therefore, the adhesion is so low that the droplet can bounce elastically off the surface at moderately low impact speeds (We < 13 ±3 ).The results of droplet spreading on the flat surface are similar to the results in ref. [15], where they developed universal rescaling of the maximum spreading ratio (Dmax/D0) over the wide range of impact velocities. Figure S1, Supporting Information, shows that for the flat surface, (Dmax/D0) is a linear function of We1/2 in the entire range of We numbers. This is true also for structured surfaces at low impact velocities. However, Figure S3, Supporting Information, demonstrates that for the edge‐on lamellae in the perpendicular direction, the maximum spreading ratio is significantly lower than that for the flat surface. This happens when the droplet starts to penetrate through the lamellae (We > 13). Figure S2, Supporting Information, presents the dependences of (Dmax/D0) on Reynold's number for all cases.There are two major mechanisms of reduction in spreading velocity in case of edge‐on oriented lamellae. For ║‐direction, the contact line between the water and the MAE surface advances continuously. However, when a droplet penetrates through lamellae, the liquid flow inside the grooves reduces the spreading velocity due to the viscous dissipation of kinetic energy. In the ⊥‐direction, the contact line experiences landscape inhomogeneity imposed by the neighboring lamellae, giving rise to a stick‐slip‐like motion.[20] A similar observation was reported for a hydrophobic grooved surface made of stainless steel.[34]Besides the contact angle hysteresis, the velocity of the contraction phase is also important. As evident from Figure 5b, the lowest (almost zero) contraction velocity appears on a flat surface and the face‐on lamellae in a perpendicular direction. The rebound newer happened on these two surfaces. Contrary, a much higher contraction velocity (≈0.4 m s−1) appears in both directions of edge‐on lamellae, where rebound was detected up to We < 13.When the droplet, due to its high velocity and inertia, wets the entire surface with the edge‐on oriented lamellae, including the bottom of the grooves between the lamellae, the penetration regime begins. The associated wetting state transition from the Cassie state to the Wenzel state was previously observed experimentally[31,61,62] and numerically.[33] In this state, part of the water remains trapped between the lamellae, while part is rebounded in the form of medium‐sized droplets (see Figure 4 and Supporting Information Videos). It was shown that critical velocity can be estimated from the condition that the dynamic pressure (ρV2) needs to exceed a critical Laplace pressure (γh/l2) associated with the drop deformation inside the textured material[31]1Vpinning=γh/ρl2\[\begin{array}{*{20}{c}}{{V_{{\rm{pinning}}}} = \sqrt {\gamma h{\rm{/}}\rho {l^2}} }\end{array}\]where h and l are the height and mutual distance of the structural elements, γ is liquid–vapor surface tension, and ρ is liquid density. By applying geometrical values for our edge‐on (h = 300 µm, l = 275 µm) and face‐on lamellae (h = 30 µm, l = 275 µm), the critical velocities are 0.53 and 0.17 m s−1, respectively, and corresponding critical We numbers are 5.4 and 0.45. This is in good agreement with our results (see Figure 2), which showed that on face‐on lamellae, the penetration and corresponding deposition occurred at a We number smaller than our minimal measured value (We > 1.4), while the pining on edge‐on lamellae occurred at We > 13 ± 3. Numerical simulations presented in ref. [36] show that pining occurs already in the rebound phase, which could explain the mismatch between predicted and observed critical We numbers.In the penetration regime, when the water fills a significant part of the grooves between the lamellae, it begins to spread in an anisotropic way, with a higher advancing velocity along the lamellae and a much lower velocity transverse to the lamellae. As can be seen from Figure 5d, the ratio between the two propagation velocities at high impact speed (We > 33 ± 3) is about 3:2. Due to the channeling of the water between the lamellae, the detachment of the water jets first causes splashing in the direction of the lamellae (║ direction). Similar production of small droplets during the drop impact process was observed earlier on a grooved steel surface of similar size.[34] Interestingly, we observed that a parallel splash also occurs with face‐on oriented lamellae (see Figure 2), but at much higher We numbers (We > 52 ± 4). We attribute this to the fact that the face‐on oriented lamellae do not touch each other perfectly but form a slightly rippled structure that also possesses anisotropic properties. The latter is also evidenced by the results of measurements of dynamic contact angles (see Figure 6, red columns). Similarly, different velocities of water spreading parallel (║) and perpendicular (⊥) to the direction of lamellae were also observed (see Figure 5), with the most striking difference appearing for the edge‐on oriented lamellae (blue points).At the highest investigated We numbers (We > 79 ± 7 for face‐on oriented lamellae and We > 112 ± 10 for edge‐on oriented lamellae), a circular splash occurs. The reason for a higher critical velocity associated with this type of impact outcome for the edge‐on oriented lamellae is primarily the anisotropic expansion of the liquid that channels most of the droplet's kinetic energy along the lamellae. Therefore, the water velocity in the direction perpendicular to the lamellae is significantly lower (see Figure 5d). However, this does not fully explain the higher critical circular splashing velocity for edge‐on oriented lamellae. One would expect that structural anisotropy increases the propagation velocity along the lamellae, but from Figure 5d, it can be seen that this spreading velocity is even lower than for flat surfaces and face‐on oriented lamellae. When the liquid flows inside the grooves between the lamellae, there is an increased dissipation of kinetic energy due to the increased contact area between the liquid and the surface, which leads to a slower spreading of the droplet and subsequently circular splashing appears at larger We numbers. A similar conclusion was pointed out in a previous study[36] by showing that significant dissipation of kinetic energy of droplets occurs when the droplet first encounters the surface, and even more importantly, during the penetration through the inter‐ridge valleys.A recent study by Garcia et al.[63] on droplet splashing on rough surfaces revealed that the critical We number is highly dependent on the ratio between the thickness of the water lamella Ht and the characteristic size of surface roughness ε. When ε > Ht, which is the case for our edge‐on and face‐on surfaces, the droplet disintegrates because of local jets forming inside the surface grooves of size ε. According to their model, which compares the spreading velocity with the wetting velocity, we obtain the equivalent roughness ε equal to 13 µm for flat, 55 µm for face‐on, and 140 µm for edge‐on surface, when splashing actually occurred. This is in good agreement with our actual geometry, however, further study is needed to theoretically describe the splashing criteria, since their model is suited for randomly rough surfaces with Young's angle smaller than 90°, which is not the case for PDMS (≈110°).In analyzing video sequences of the impacts, we paid particular attention to the possible buckling of the lamellae during the impact of the droplet. Slender structures, such as lamellae, can buckle under excessive compressive loading, which can locally lead to the transformation of the surface from an edge‐on to a face‐on lamellar orientation. By careful reviewing of the recorded sequences, we did not observe any such phenomenon in any velocity interval. This is also supported by the comparison between the impact behavior of the edge‐on oriented lamellae in the absence and the presence of a magnetic field (see Figure 2, the third and fourth column). Due to the magnetorheological effect, the stiffness of lamellae in the presence of a magnetic field is expected to be much higher, however, the transitions between different types of impact outcomes occur at very similar We numbers. This observation demonstrates that droplet impact properties of micro‐structured MAE surfaces can be strongly modified by simply switching on or off a magnetic field in a direction parallel to the surface.We assume that by optimizing the lamella geometry, it is possible to additionally extend the interval of We numbers in which we can switch between rebound, deposition, and splashing. Equation (1) shows that the critical speed of deposition decreases with the distance between the lamellae and increases with the height of the lamellae. Thus, by decreasing the interlamellar separation, the rebound area could be considerably increased in the case of an edge‐on orientation. Further development of microstructuring technology, use of finer magnetic particles, and optimization of laser processing by using shorter pulses and better‐focusing optics could provide advancements. We also assume that thinner lamellae will better approximate a flat surface in the face‐on orientation. This may minimize the velocity range in which parallel splashes occur. Consequently, the critical velocities for splash formation on edge‐on and face‐on surfaces would also be pushed further apart.ConclusionAn effective methodology for in situ control of droplet impact by remote tuning of the surface topography of microstructured MAEs with a magnetic field is demonstrated in this work. Laser micromachining was used to create a lamellar microstructure that can be controlled by a magnetic field. We show that changing the direction of the magnetic field with respect to the surface transforms the orientation of lamellas from an “edge‐on” state to a “face‐on” state. By this, the critical velocities of droplet deposition and splashing can be significantly altered. Switching between rebound and deposition regimes was observed up to We = 13 ± 3 and switching between deposition and splashing was detected for We in the range 32–52. Since the geometry of the laser‐fabricated microstructures can be highly complex and can be selectively applied to a specific surface area of the processed component, the described technology has great potential for applications in soft robotics, microfluidics, and advanced thermal management.Experimental SectionFabrication of Lamellar MAE SurfacesSpecimens were prepared by applying a 0.3 mm thick layer of uncured MAE onto a 0.2 mm thick copper (Cu) base plate. The MAE was a hybrid material composed of 75 wt% (≈27 vol%) carbonyl iron powder (CIP; type SQ, mean particle size d50 of 4.5 µm, no coating; BASF SE, Ludwigshafen am Rhein, Germany) embedded in a soft PDMS matrix. The material preparation is described in detail in refs. [64, 65]. The viscous mixture was spread onto the Cu plate by means of a doctor blade coater for precise thickness control of the MAE film.[42] The specimen was then cured for 1 h at 80 °C followed by 24 h at 60 °C. The effective shear modulus G′ of the resulting MAE material was ≈28 kPa.The samples were then cut into 30 × 30 mm tiles, on which a lamellar microstructure was fabricated using the laser micromachining technique.[6] For this purpose, a pulsed laser source (SPI Lasers UK Ltd., G4 pulsed fiber laser) with an average power of 20 W, a wavelength of 1064 nm, a pulse duration of 12 ns, and a pulse repetition rate of 30 kHz was used. Using a laser scanning head (manufacturer Raylase, model SE‐II), the laser beam was guided along a preprogrammed trajectory and focused through an f‐theta lens (f = 56 mm) so that the focal diameter was 13.2 µm (measured at 1/e2 maximum intensity). The scanning speed was 500 mm s−1, and the distance between adjacent lines within each groove was 15 µm. Surface topography of the fabricated microstructures was imaged by optical coherence tomography (OCT) system (Telesto TEL221, Thorlabs Inc., Newton, NJ, USA), and processed with ThorImageOCT software (Thorlabs Inc., Newton, NJ, USA).Observation of Droplet ImpactsDroplet impacts on the microstructured MAE surface were observed using the experimental system shown in Figure 7 at a constant ambient temperature of 23 ± 1 °C and humidity of 50 ± 10%. Droplets were generated by a microliter syringe pump (Dual Syringe Pump, Ossila Ltd., Sheffield S4 7WB, UK) filled with deionized water (specific electrical conductivity σ ≈ 3 µS cm−1) and connected to a stainless‐steel needle (diameter of 0.6 mm) placed at a variable height above the center of the sample surface. Height z is the distance between the MAE surface and the bottom of the droplet just before its release. The collisions were observed with a high‐speed camera (Photron, Fastcam Nova S16, type 1100K‐M‐64GB) and a high‐brightness LED light (EFFI Spot, EFFILUX, Les Ulis, France) placed on the opposite side. Due to the anisotropy of the surface structure, the collisions were monitored from two sides: in the so‐called front view, the droplet was spreading on the surface in the direction perpendicular to the lamellae (⊥ orientation) while in the side view, it was spreading in the direction along the lamellae (║ orientation). In this way, the anisotropy of the spreading dynamics during the collision could be observed but had to subsequently drop two drops to record the videos from both sides (see Supporting Information for typical examples). The high‐speed camera recorded 30 000 frames per second. With a macro lens (Sigma, 180 mm F2.8 APO MACRO EX), the optical magnification was 1:1 and the resolution on the object side was 20 µm.7FigureExperimental setup for observing droplet impacts on MAE surface with a high‐speed camera. The sketch shows schematically two positions of the camera for the observation of impacts from the side and the front view.The recorded video sequences were processed with a custom LabView program, which extracts the width D of the droplet's contact area and the contact angle θ from each image. The velocity of contact line V was calculated as the time derivative of D, and the maximal velocity Vmax was calculated as the average velocity during the first millisecond of the collision. Dynamic contact angles were extracted during the expansion and contraction phases as advancing θadv and receding θrec angles, respectively. The first represents an average value within 1.5 ms after the impact, while the second represents an average value within 1.5 ms after the start of the contraction phase.Statistical AnalysisThe transitions between different impact outcomes (such as the transition from the rebound to deposition, or deposition to parallel splash) were modeled using logistic regression,[66] which gave the probability of the outcome. Measurements of impact outcomes on every surface type were repeated two times at 38 different heights. Intervals of different impact regimes were estimated as a 50% probability of certain regime, while the confidence interval corresponds to a 15–85% probability. See Supporting Information (Section: 2. Probability estimation for impact outcomes) for details. The results of dynamic contact angles are presented as the mean value ± standard deviation. The number of repeated measurements was n = 5.AcknowledgementsThe authors acknowledge financial support by the Slovenian Research Agency (ARRS) in the framework of the research programs P1‐0192‐Light and Matter and P2‐0392‐Optodynamics, and research project J1‐3006. The work of R.K. and M.S. was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 437391117. The authors are grateful to the Students’ Union of OTH Regensburg for providing funds for the high‐speed camera and the OCT imaging system.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are openly available in Mendeley at https://doi.org/10.17632/s34pwpv4dr.1.A. L. Yarin, Annu. Rev. Fluid Mech. 2006, 38, 159.M. Jiang, Y. Wang, F. Liu, H. Du, Y. Li, H. Zhang, S. To, S. Wang, C. Pan, J. Yu, D. Quéré, Z. Wang, Nature 2022, 601, 568.C. Josserand, S. T. Thoroddsen, Annu. Rev. 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Control of Droplet Impact through Magnetic Actuation of Surface Microstructures

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Abstract

IntroductionThe collision of a droplet with a surface is an important phenomenon that is the subject of numerous theoretical and experimental investigations that attempt to determine the relationships between the various possible outcomes of impact and the properties of the surface and the droplet. The droplet may bounce off the surface, be deposited on the surface, or splash.[1] Each of these outcomes is useful for different potential breakthrough applications in the fields of thermal management,[2,3] energy harvesting,[4,5] microfluidics,[6–8] spraying,[9,10] and printing[11–13] technologies.The outcome of the impact on a flat (non‐structured) surface is mainly influenced by the characteristic slope of the roughness of the surface and the relationship between the kinetic energy, capillary energy, and viscous dissipation during spreading.[14,15] Two dimensionless parameters are used for scaling drop impacts. The Weber number (We=ρV02R/γ$We = \rho V_0^2R{\rm{/}}\gamma $) describes the ratio between the kinetic and the surface energy of the droplet, while the Reynolds number (Re = ρV0R/μ) describes the ratio between the kinetic and viscous dissipation effects. Here, ρ is the density of the liquid, V0 is the impact velocity of the droplet, R is its radius, γ is surface tension, and µ is the viscosity. At low impact velocity, the kinetic energy is mainly transformed into surface energy and at high impact velocities, the viscous energy dissipation dominates. In addition, the dynamic wetting of the surface is of great importance, as it influences the absorption of kinetic energy during the spreading and contraction of the droplet over the surface.[16–18] Wetting is mainly influenced by the chemical composition of the surface and its microtopography.[19,20] It is known that hydrophobic surfaces become superhydrophobic and hydrophilic surfaces convert into superhydrophilic if they possess a microstructure in the form of a matrix of columns, holes, lamellae, or increased roughness.The dynamics of droplet impact have been studied on flat surfaces with different wetting properties,[21–26] on curved surfaces,[27] and on microstructured surfaces.[19,28–34] One of the most important phenomena studied on microstructured surfaces is the penetration of the droplet through the pillars or lamellae and the resulting transition from the Cassie–Baxter state to the Wenzel state leading to droplet deposition.[32,35] In these studies, mainly pillared microstructures are investigated experimentally, as well as in numerical simulations.[20,33,34,36]Intensive research has recently been carried out on bioinspired tunable surfaces in which the wettability and other properties of the surface can be altered by external stimuli such as light, an electric field, or a magnetic field.[6,37–43] The usage of a DC magnetic field is particularly attractive, as it enables wireless manipulation and is biocompatible. Of particular interest in this category are magnetoactive elastomers (MAE), multifunctional composite materials which consist of micro‐ or nanometer‐sized magnetic particles embedded into a soft elastomeric matrix.[44] Under the influence of a magnetic field, their elastic moduli and surface roughness can change by several orders of magnitude[45,46] due to the phenomenon of the restructuring of magnetic filler particles. In a recent study, Kriegl et al.[42] showed that in a moderate magnetic field (<400 mT), the contact angle of MAE for water increases above the limit of superhydrophobicity. In another study, Kravanja et al.[6] demonstrated a laser micromachining method that allows the fabrication of different types of microstructures in MAE, which are then activated by changing the orientation of the applied magnetic field. If a magnetic field is parallel to the surface, the lamellar microstructures are flattened (bent) to the surface, resulting in a significantly increased slip angle of the droplet. With a lamellar structured magnetoactive surface, Qian et al.[47] demonstrated the possibility of expelling droplets that are already attached to the surface away from the microstructured MAE surface. Peng et al.[48] demonstrated magnetically induced fog harvesting by the fabrication of cactus‐inspired spine structures and magnetically responsive flexible conical arrays. A Janus‐type high‐aspect‐ratio magnetically responsive microplates array was fabricated and the demonstration of reversible switching of surface wettability using a magnetic field is shown in ref. [49].Hitherto, the majority of works on control of the droplet impact on a solid surface considered passive methods such as surface texturing, superhydrophobic treatments, and lubricant infusion.[50] Only a few works have considered active (requiring applied power) methods for controlling the droplet impact dynamics.[50] The reported active methods employed electric fields,[51,52] mechanical,[53] and ultrasonic[54,55] vibrations, as well as surface acoustic waves.[50] A combination of passive surface treatment and active methods may be advantageous for the optimum control of droplet impact on solid surfaces.[50] In particular, the active methods would enable the on‐demand control of the droplet impact. The possibility of using magnetic fields for the control of droplet impact on solid surfaces remains practically unexplored yet. Ahmed et al.[56] studied theoretically and experimentally the effects of an applied external magnetic field on the maximum spreading of a ferrofluid droplet impacting a non‐magnetic solid substrate. To the best of our knowledge, the effect of the magnetic field on the impact of non‐magnetic (ethanol) droplets on magneto‐sensitive surfaces has been presented so far only in ref. [43]. It was shown that, due to the magnetic field‐induced hardening of the material and the associated increased surface roughness, both driven by the restructuring of the magnetic filler, the splashing of droplets occurs at lower We numbers. However, the results were demonstrated only for a bulk (nominally flat, non‐structured) MAE surface. Similar controlling of water droplet splashing and bouncing was shown by using the dielectrowetting principle, where an electric potential of ≈1 kV affected the dynamic contact angle.[52]This paper investigates the capability of using microstructured MAE‐based surfaces to effectively manipulate and control the droplet impact by an external magnetic field. Presented is a systematic study of the impact behavior of water droplets on a microstructured MAE surface exposed to a magnetic field oriented either parallel or perpendicular to the surface. It is shown that the application of a magnetic field and modification of its direction with respect to the surface significantly change the surface topography and wettability, which consequently affects the behavior of the droplet during and after the impact. The magnetic control of droplet impact is by far more efficient than that reported in ref. [43]. Because a permanent magnet is used, our approach does not require a permanent power supply for maintaining the particular dynamics of the droplet impact as in the case of surface acoustic waves.[50] The power supply would be only required to move the magnet into a new position. Besides this, since the microstructured surface used in our study has the form of thin micro‐lamellae, a profound anisotropy of the droplet propagation during the impact is observed.ResultsFigure 1a shows the fabrication of lamellar microstructure in a 0.3 mm thick MAE layer on top of copper foil using the laser micromachining technique.[6] Since the ablation threshold of MAE is significantly lower than the ablation threshold of Cu, which is attributed to the lower evaporation temperature and thermal conductivity of PDMS, the height of the lamellae h was determined by the thickness of the MAE layer. Moreover, the cross‐section of the lamellae was almost completely rectangular (see Figure 1e). To study droplet impacts, we fabricated a lamellar microstructure with dimensions w = 25 µm, l = 275 µm, and h = 300 µm. The ratio between the height h of the lamellae and their mutual spacing l was chosen so that the lamellae did not overlap when they were laid parallel with the surface (see Figure 1d,f).1Figurea) Laser fabrication process of a lamellar microstructure with characteristic dimensions. b) Schematic representation of the relative positions of the sample and the magnet to ensure proper orientation of the magnetic field. c) Edge‐on orientation of lamellae is obtained in the absence of a magnetic field or if the field is oriented perpendicular to the MAE surface (β = 0°). d) Face‐on orientation of lamellae is obtained when a magnetic field is oriented parallel to the MAE surface (β = 90°). OCT images of e) edge‐on and f) face‐on oriented lamellae. β denotes the angle between the magnetic field and the normal vector to the MAE surface.The orientation of lamellae was actuated by changing the orientation of the magnetic field by the movement of the sample according to the permanent magnet (see Figure 1b). In the edge‐on orientation of lamellae (Figure 1c,e), the magnet was centered below the observed surface. In face‐on orientation (β = 0°), the sample was moved to the side so that the observed surface coincided with the region in which the magnetic field was parallel to the surface (β = 90°) (see Figure 1d,e).The impact experiments were performed with water droplets of diameter D0 = 2.7 ± 0.1 mm released from the height z in the range of 5–500 mm which resulted in impact speeds ranging from 0.31 < V0 < 3.1 m s−1, Weber number range 1.9 < We < 187 and Reynolds number range 966 < Re < 9660. The Ohnesorge number (Oh=µ/ρRγ$Oh = \mu {\rm{/}}\sqrt {\rho R\gamma } $) was constant for all experiments and equal to Oh = 0.0028. We investigated droplet collisions with four different MAE surfaces: i) an unprocessed flat MAE surface; a surface with edge‐on oriented lamellae ii) in the absence of magnetic field (B = 0) and iii) exposed to magnetic field B = 247 mT (shown on Figure 1e); and iv) a surface with face‐on oriented lamellae exposed to B = 140 mT (shown on Figure 1f). For ii–iv we used the same sample, changing only the magnitude and orientation of the magnetic field.Figure 2 shows how the impact outcome depends on the type of surface and the We number. If the droplet is completely bounced off the surface after the impact, we labeled the impact as “Rebound.” If at least part of the droplet remained attached to the surface after initial contact, we referred to the impact as “Deposition/Penetration.” In the case of an edge‐on lamellar surface, this was the case when the droplet surface was pinned by the lamellar structure and consequently, the liquid could advance to the bottom of the channels between the lamellas and stick there. However, in the case of a flat MAE surface, the term “deposition” is more commonly used when the droplet does not rebound from the surface anymore. In the case of faster impacts (larger We numbers), a splash began to form, which was visible as a disintegration of the water disk into individual droplets that spread out. The splash first appeared in the direction parallel to the lamellar structure, which is labeled as “Parallel splash,” and later, that is, at larger We numbers, it proceeded in all directions, which is labeled “Circular splash.”2FigureImpact outcomes of water droplets on different types of MAE surfaces. Black marks represent We number of transitions between different outcomes. See Supporting Information for typical videos.Figure 3 shows selected successive images of impacts at low velocities (We = 10). On the flat surface and face‐on oriented lamellae, the droplet sticks to the surface after the impact, while in contrast, on the surface with edge‐on oriented lamellae (bottom row), the droplet bounces off completely.3FigureSelected images of impacts on a flat surface (top row), face‐on lamellae (middle row), and edge‐on lamellae (bottom row) at low speeds (V0 = 0.72 m s−1, We = 10, Re = 2240). See Supporting Information for entire video sequences.Figure 4 shows droplet collisions at intermediate velocities (We = 44), for which the resistance to the droplet spreading is somehow lower on a surface with face‐on oriented lamellae (second row) than on an unprocessed flat surface (top row). This is particularly evident in the contraction phase, where a narrow elongated cylindrical shape is formed for face‐on lamellae and a wider hemispherical shape is formed on a flat surface (see images at 20 ms).4FigureSelected images of impacts on a flat surface (top row), face‐on lamellae (middle row), and edge‐on lamellae (bottom row) at intermediate speeds (V0 = 1.52 m s−1, We = 44, Re = 4690). See Supporting Information for entire video sequences.Figure 5 shows the dynamic properties of droplet impacts on individual surfaces, for water spreading perpendicular (⊥) and parallel to the lamellas (║), respectively. Figure 5b shows the time dependence of the contact diameter of the droplet (D) at low velocities (We = 10). In the first part of the expansion, the droplet spreads on the face‐on oriented lamellae (red curve) as fast as on the flat surface (black curve). The maximum diameter (Dmax) is similar in both cases. However, in the contraction phase, the droplet shrinks faster on the face‐on oriented lamellae, especially in the direction perpendicular to the lamellae (solid red curve). In this direction, the spreading of the droplet stops completely after about 7 ms. In the direction parallel to the lamellae, the width of the contact area of the droplet continues to decrease during the entire observed time interval.5FigureWater spreading dynamics during droplet impacts on different surfaces: flat (black crosses), face‐on lamellae (β = 90°, red circles), and edge‐on lamellae (β = 0°, blue diamonds). a) Sketch of measured diameter D and velocity V of the contact line between droplet and surface. b) Variation of contact diameter D overtime at low impact speed (V0 = 0.72 m s−1, We = 10, Re = 2240). c) Ratio between maximal contact diameter (Dmax) and initial droplet diameter (D0) as a function of We number. d) Ratio between maximal spreading velocity (Vmax) and the droplet impact speed (V0) as a function of We number. In all graphs “⊥” and “║” stands for water spreading perpendicular and parallel to the lamellas, respectively.On edge‐on oriented lamellae, the expansion and contraction of the droplet even more strongly depend on the direction of observation. The maximum width of droplet expansion in the transverse direction to the lamellae (⊥) is about 20% smaller than along the lamellae (║). Moreover, the maximum width is reached slightly earlier, indicating slower propagation in the ⊥ direction. This results in smaller energy dissipation which shifts the rebound/penetration transition to higher impact velocities. This difference in spreading diameters and velocities can be clearly seen in Figure 5c,d, which shows the ratio between maximal contact diameter (Dmax) and initial droplet diameter (D0) and the ratio between maximal spreading velocity (Vmax) and the droplet impact speed (V0) as a function of the We number, respectively. The solid and dashed curves in Figure 5c represent an approximation with a polynomial of order 4, while the curves in Figure 5d represent the approximation with the power function, which are used as guides to the eye.As it is evident from the obtained results on water spreading dynamics, an important property that influences the impact behavior is surface wettability, which is the measure of a droplet's ability to interact with the surface.[21,57] To qualitatively resolve this property, we measured a dynamic contact angle between the droplet and the surface in the initial phase of expansion (within 1.5 ms after impact), namely the advancing contact angle θadv (see Figure 6a), and after it starts contracting back, that is, the receding contact angle θrec (see Figure 6b). Due to the extremely fast nature of the splashing process, these contact angles could only be measured at low‐impact velocities (We = 10). As the dynamic contact angles are not constant during spreading between neighboring lamellae, we report an average value. The differences between different surfaces are obvious. Advancing and receding contact angles are the smallest for flat unprocessed MAE surfaces. Slightly larger are their values for face‐on oriented lamellae, for which the receding angle measured along lamellae (║ direction) is significantly larger (114 ± 9°) than in ⊥ direction (82 ± 6°). The highest advancing and receding contact angles were measured for edge‐on oriented lamellar surface, showing superhydrophobic behavior. Additionally, we calculated contact angle hysteresis (θadv − θrec), which is a measure of how much energy is dissipated during droplet impact.[58] In Figure 6c, one can notice that contact angle hysteresis is the highest for the flat MAE surface (93 ± 7°). For face‐on oriented lamellae it is slightly smaller (62 ± 8° for ⊥ and 32 ± 10° for ║ direction), while for edge‐on lamellae the hysteresis is the smallest (6 ± 6° for ⊥ and 11 ± 7° for ║ direction). This explains the absence of droplet rebound on the untreated (flat) surface and face‐on oriented lamellae.6FigureDynamic contact angles for different types of surfaces at low impact speeds (We ≈ 10). a) Advancing contact angle (θadv) is measured when the droplet is in the initial phase of spreading (within 1.5 ms after the impact) over the surface, b) Receding contact angle (θrec) is measured when the droplet starts contracting, and c) contact angle hysteresis represents the difference θadv − θrec. In all graphs “⊥” and “∥” stands for water spreading perpendicular and parallel to the lamellas respectively. Results are presented as the mean value ± standard deviation (n = 5).DiscussionOur observations demonstrate that lamellar structured MAE surface can be strongly manipulated by changing magnetic field orientation. With this functional principle, the lamellae can be oriented either edge‐on or face‐on with respect to the surface. Depending on their orientation, the outcome of the water droplet impacts significantly changes. At low impact velocities (We < 13 ± 3), the impact outcome changes from the rebound to penetration/deposition, as the orientation of the lamellae changes from edge‐on to face‐on. Another obvious difference between the two orientations of lamellae is the limiting velocity of the droplet at which splashing occurs, leading to the formation of a large number of secondary microdroplets. For the edge‐on orientation of the lamellae, splashing occurs at We > 32 ± 3, while for the face‐on orientation, splashing occurs only at We > 52 ± 4. Since We number depends on the square of the droplet velocity, this means that the ratio of the associated critical velocities is about 1:3. This provides a possibility of using such surfaces to trap or deflect water droplets on demand, simply by changing the magnetic field.The transition from the rebound to the adhesion of the droplets at low‐impact velocities is mainly influenced by the wettability of the surface. For face‐on oriented lamellae, the wetted surface behaves similarly to the unprocessed flat surface, thus the Wenzel regime[59] is established even at the minimum impact velocity of the droplets. On the other hand, for edge‐on oriented lamellae, the Cassie–Baxter contact regime is established,[60] in which only the tips of the lamellae are wetted. Consequently, for face‐on oriented lamellae and unprocessed flat surfaces, the contact angle hysteresis is relatively large (62 ± 8° for face‐on oriented lamellae and 93 ± 7° for the flat surface), so the droplets stick to the surface (see Figure 3). In contrast, for edge‐on oriented lamellae, the advancing and receding contact angles are about 150°, indicating the superhydrophobic properties of this surface. Therefore, the adhesion is so low that the droplet can bounce elastically off the surface at moderately low impact speeds (We < 13 ±3 ).The results of droplet spreading on the flat surface are similar to the results in ref. [15], where they developed universal rescaling of the maximum spreading ratio (Dmax/D0) over the wide range of impact velocities. Figure S1, Supporting Information, shows that for the flat surface, (Dmax/D0) is a linear function of We1/2 in the entire range of We numbers. This is true also for structured surfaces at low impact velocities. However, Figure S3, Supporting Information, demonstrates that for the edge‐on lamellae in the perpendicular direction, the maximum spreading ratio is significantly lower than that for the flat surface. This happens when the droplet starts to penetrate through the lamellae (We > 13). Figure S2, Supporting Information, presents the dependences of (Dmax/D0) on Reynold's number for all cases.There are two major mechanisms of reduction in spreading velocity in case of edge‐on oriented lamellae. For ║‐direction, the contact line between the water and the MAE surface advances continuously. However, when a droplet penetrates through lamellae, the liquid flow inside the grooves reduces the spreading velocity due to the viscous dissipation of kinetic energy. In the ⊥‐direction, the contact line experiences landscape inhomogeneity imposed by the neighboring lamellae, giving rise to a stick‐slip‐like motion.[20] A similar observation was reported for a hydrophobic grooved surface made of stainless steel.[34]Besides the contact angle hysteresis, the velocity of the contraction phase is also important. As evident from Figure 5b, the lowest (almost zero) contraction velocity appears on a flat surface and the face‐on lamellae in a perpendicular direction. The rebound newer happened on these two surfaces. Contrary, a much higher contraction velocity (≈0.4 m s−1) appears in both directions of edge‐on lamellae, where rebound was detected up to We < 13.When the droplet, due to its high velocity and inertia, wets the entire surface with the edge‐on oriented lamellae, including the bottom of the grooves between the lamellae, the penetration regime begins. The associated wetting state transition from the Cassie state to the Wenzel state was previously observed experimentally[31,61,62] and numerically.[33] In this state, part of the water remains trapped between the lamellae, while part is rebounded in the form of medium‐sized droplets (see Figure 4 and Supporting Information Videos). It was shown that critical velocity can be estimated from the condition that the dynamic pressure (ρV2) needs to exceed a critical Laplace pressure (γh/l2) associated with the drop deformation inside the textured material[31]1Vpinning=γh/ρl2\[\begin{array}{*{20}{c}}{{V_{{\rm{pinning}}}} = \sqrt {\gamma h{\rm{/}}\rho {l^2}} }\end{array}\]where h and l are the height and mutual distance of the structural elements, γ is liquid–vapor surface tension, and ρ is liquid density. By applying geometrical values for our edge‐on (h = 300 µm, l = 275 µm) and face‐on lamellae (h = 30 µm, l = 275 µm), the critical velocities are 0.53 and 0.17 m s−1, respectively, and corresponding critical We numbers are 5.4 and 0.45. This is in good agreement with our results (see Figure 2), which showed that on face‐on lamellae, the penetration and corresponding deposition occurred at a We number smaller than our minimal measured value (We > 1.4), while the pining on edge‐on lamellae occurred at We > 13 ± 3. Numerical simulations presented in ref. [36] show that pining occurs already in the rebound phase, which could explain the mismatch between predicted and observed critical We numbers.In the penetration regime, when the water fills a significant part of the grooves between the lamellae, it begins to spread in an anisotropic way, with a higher advancing velocity along the lamellae and a much lower velocity transverse to the lamellae. As can be seen from Figure 5d, the ratio between the two propagation velocities at high impact speed (We > 33 ± 3) is about 3:2. Due to the channeling of the water between the lamellae, the detachment of the water jets first causes splashing in the direction of the lamellae (║ direction). Similar production of small droplets during the drop impact process was observed earlier on a grooved steel surface of similar size.[34] Interestingly, we observed that a parallel splash also occurs with face‐on oriented lamellae (see Figure 2), but at much higher We numbers (We > 52 ± 4). We attribute this to the fact that the face‐on oriented lamellae do not touch each other perfectly but form a slightly rippled structure that also possesses anisotropic properties. The latter is also evidenced by the results of measurements of dynamic contact angles (see Figure 6, red columns). Similarly, different velocities of water spreading parallel (║) and perpendicular (⊥) to the direction of lamellae were also observed (see Figure 5), with the most striking difference appearing for the edge‐on oriented lamellae (blue points).At the highest investigated We numbers (We > 79 ± 7 for face‐on oriented lamellae and We > 112 ± 10 for edge‐on oriented lamellae), a circular splash occurs. The reason for a higher critical velocity associated with this type of impact outcome for the edge‐on oriented lamellae is primarily the anisotropic expansion of the liquid that channels most of the droplet's kinetic energy along the lamellae. Therefore, the water velocity in the direction perpendicular to the lamellae is significantly lower (see Figure 5d). However, this does not fully explain the higher critical circular splashing velocity for edge‐on oriented lamellae. One would expect that structural anisotropy increases the propagation velocity along the lamellae, but from Figure 5d, it can be seen that this spreading velocity is even lower than for flat surfaces and face‐on oriented lamellae. When the liquid flows inside the grooves between the lamellae, there is an increased dissipation of kinetic energy due to the increased contact area between the liquid and the surface, which leads to a slower spreading of the droplet and subsequently circular splashing appears at larger We numbers. A similar conclusion was pointed out in a previous study[36] by showing that significant dissipation of kinetic energy of droplets occurs when the droplet first encounters the surface, and even more importantly, during the penetration through the inter‐ridge valleys.A recent study by Garcia et al.[63] on droplet splashing on rough surfaces revealed that the critical We number is highly dependent on the ratio between the thickness of the water lamella Ht and the characteristic size of surface roughness ε. When ε > Ht, which is the case for our edge‐on and face‐on surfaces, the droplet disintegrates because of local jets forming inside the surface grooves of size ε. According to their model, which compares the spreading velocity with the wetting velocity, we obtain the equivalent roughness ε equal to 13 µm for flat, 55 µm for face‐on, and 140 µm for edge‐on surface, when splashing actually occurred. This is in good agreement with our actual geometry, however, further study is needed to theoretically describe the splashing criteria, since their model is suited for randomly rough surfaces with Young's angle smaller than 90°, which is not the case for PDMS (≈110°).In analyzing video sequences of the impacts, we paid particular attention to the possible buckling of the lamellae during the impact of the droplet. Slender structures, such as lamellae, can buckle under excessive compressive loading, which can locally lead to the transformation of the surface from an edge‐on to a face‐on lamellar orientation. By careful reviewing of the recorded sequences, we did not observe any such phenomenon in any velocity interval. This is also supported by the comparison between the impact behavior of the edge‐on oriented lamellae in the absence and the presence of a magnetic field (see Figure 2, the third and fourth column). Due to the magnetorheological effect, the stiffness of lamellae in the presence of a magnetic field is expected to be much higher, however, the transitions between different types of impact outcomes occur at very similar We numbers. This observation demonstrates that droplet impact properties of micro‐structured MAE surfaces can be strongly modified by simply switching on or off a magnetic field in a direction parallel to the surface.We assume that by optimizing the lamella geometry, it is possible to additionally extend the interval of We numbers in which we can switch between rebound, deposition, and splashing. Equation (1) shows that the critical speed of deposition decreases with the distance between the lamellae and increases with the height of the lamellae. Thus, by decreasing the interlamellar separation, the rebound area could be considerably increased in the case of an edge‐on orientation. Further development of microstructuring technology, use of finer magnetic particles, and optimization of laser processing by using shorter pulses and better‐focusing optics could provide advancements. We also assume that thinner lamellae will better approximate a flat surface in the face‐on orientation. This may minimize the velocity range in which parallel splashes occur. Consequently, the critical velocities for splash formation on edge‐on and face‐on surfaces would also be pushed further apart.ConclusionAn effective methodology for in situ control of droplet impact by remote tuning of the surface topography of microstructured MAEs with a magnetic field is demonstrated in this work. Laser micromachining was used to create a lamellar microstructure that can be controlled by a magnetic field. We show that changing the direction of the magnetic field with respect to the surface transforms the orientation of lamellas from an “edge‐on” state to a “face‐on” state. By this, the critical velocities of droplet deposition and splashing can be significantly altered. Switching between rebound and deposition regimes was observed up to We = 13 ± 3 and switching between deposition and splashing was detected for We in the range 32–52. Since the geometry of the laser‐fabricated microstructures can be highly complex and can be selectively applied to a specific surface area of the processed component, the described technology has great potential for applications in soft robotics, microfluidics, and advanced thermal management.Experimental SectionFabrication of Lamellar MAE SurfacesSpecimens were prepared by applying a 0.3 mm thick layer of uncured MAE onto a 0.2 mm thick copper (Cu) base plate. The MAE was a hybrid material composed of 75 wt% (≈27 vol%) carbonyl iron powder (CIP; type SQ, mean particle size d50 of 4.5 µm, no coating; BASF SE, Ludwigshafen am Rhein, Germany) embedded in a soft PDMS matrix. The material preparation is described in detail in refs. [64, 65]. The viscous mixture was spread onto the Cu plate by means of a doctor blade coater for precise thickness control of the MAE film.[42] The specimen was then cured for 1 h at 80 °C followed by 24 h at 60 °C. The effective shear modulus G′ of the resulting MAE material was ≈28 kPa.The samples were then cut into 30 × 30 mm tiles, on which a lamellar microstructure was fabricated using the laser micromachining technique.[6] For this purpose, a pulsed laser source (SPI Lasers UK Ltd., G4 pulsed fiber laser) with an average power of 20 W, a wavelength of 1064 nm, a pulse duration of 12 ns, and a pulse repetition rate of 30 kHz was used. Using a laser scanning head (manufacturer Raylase, model SE‐II), the laser beam was guided along a preprogrammed trajectory and focused through an f‐theta lens (f = 56 mm) so that the focal diameter was 13.2 µm (measured at 1/e2 maximum intensity). The scanning speed was 500 mm s−1, and the distance between adjacent lines within each groove was 15 µm. Surface topography of the fabricated microstructures was imaged by optical coherence tomography (OCT) system (Telesto TEL221, Thorlabs Inc., Newton, NJ, USA), and processed with ThorImageOCT software (Thorlabs Inc., Newton, NJ, USA).Observation of Droplet ImpactsDroplet impacts on the microstructured MAE surface were observed using the experimental system shown in Figure 7 at a constant ambient temperature of 23 ± 1 °C and humidity of 50 ± 10%. Droplets were generated by a microliter syringe pump (Dual Syringe Pump, Ossila Ltd., Sheffield S4 7WB, UK) filled with deionized water (specific electrical conductivity σ ≈ 3 µS cm−1) and connected to a stainless‐steel needle (diameter of 0.6 mm) placed at a variable height above the center of the sample surface. Height z is the distance between the MAE surface and the bottom of the droplet just before its release. The collisions were observed with a high‐speed camera (Photron, Fastcam Nova S16, type 1100K‐M‐64GB) and a high‐brightness LED light (EFFI Spot, EFFILUX, Les Ulis, France) placed on the opposite side. Due to the anisotropy of the surface structure, the collisions were monitored from two sides: in the so‐called front view, the droplet was spreading on the surface in the direction perpendicular to the lamellae (⊥ orientation) while in the side view, it was spreading in the direction along the lamellae (║ orientation). In this way, the anisotropy of the spreading dynamics during the collision could be observed but had to subsequently drop two drops to record the videos from both sides (see Supporting Information for typical examples). The high‐speed camera recorded 30 000 frames per second. With a macro lens (Sigma, 180 mm F2.8 APO MACRO EX), the optical magnification was 1:1 and the resolution on the object side was 20 µm.7FigureExperimental setup for observing droplet impacts on MAE surface with a high‐speed camera. The sketch shows schematically two positions of the camera for the observation of impacts from the side and the front view.The recorded video sequences were processed with a custom LabView program, which extracts the width D of the droplet's contact area and the contact angle θ from each image. The velocity of contact line V was calculated as the time derivative of D, and the maximal velocity Vmax was calculated as the average velocity during the first millisecond of the collision. Dynamic contact angles were extracted during the expansion and contraction phases as advancing θadv and receding θrec angles, respectively. The first represents an average value within 1.5 ms after the impact, while the second represents an average value within 1.5 ms after the start of the contraction phase.Statistical AnalysisThe transitions between different impact outcomes (such as the transition from the rebound to deposition, or deposition to parallel splash) were modeled using logistic regression,[66] which gave the probability of the outcome. Measurements of impact outcomes on every surface type were repeated two times at 38 different heights. Intervals of different impact regimes were estimated as a 50% probability of certain regime, while the confidence interval corresponds to a 15–85% probability. See Supporting Information (Section: 2. Probability estimation for impact outcomes) for details. The results of dynamic contact angles are presented as the mean value ± standard deviation. 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Journal

Advanced Materials Interfaces – Wiley

Published: Apr 1, 2023

Keywords: laser micromachining; magnetically responsive structure; magnetoactive elastomer; tunable droplet impact; tunable wettability

References

  • Wetting and Spreading Dynamics
    Starov, V. M.; Velarde, M. G.
  • Stimuli‐Responsive Dewetting/Wetting Smart Surfaces and Interfaces
    Hozumi, A.; Jiang, L.; Lee, H.; Shimomura, M.
  • Encyclopedia of Materials: Plastics and Polymers
    Sarkar, M.; Hasanuzzaman, M.; Gulshan, F.; Rashid, A.
  • Applied Logistic Regression
    Hosmer, D. W.; Lemeshow, S.