Bimodal dynamics of viscous pearls

Significance

Viscous drops, by definition, are slow, but they can become much quicker if placed on super-repellent materials, which minimize their contact with the substrate. We show that such drops actually exhibit two distinct modes of motion—the one expected in a situation of high repellency and a super-fast mode, quicker by a factor of typically 50. This exceptional speed arises from the spontaneous formation of a thin dynamical film of air beneath the drop, which lubricates the contact and makes the velocity independent of the viscosity. Hence, thick liquids like honey can glide as quick as water. Once in this state, drops can even fly on ordinary hydrophilic surfaces, on which they would rather stick without levitation.

Abstract

Droplets on super-repellent materials adopt the shape of pearls, which makes them highly mobile, owing to the conjunction of low contact line pinning with small dynamical friction. This property is especially valuable when drops are viscous, a case where we expect super-repellency to minimize the friction associated with viscosity. Here, we report that viscous droplets on highly repellent inclines can have two modes of descent, depending on the way they are deposited: either they run at the fast speed expected for pearls or they are 30 to 60 times quicker, which defines a super-fast regime of motion. We show that this effect relies on the tenuousness of the contact with the substrate. Consequently, this contact can be dynamically “erased” by the insertion of a cushion of air, which makes droplets glide at a speed both high and independent of their viscosity. We characterize these lubricating films (thickness and onset of appearance) and finally show that super-fast pearls initiated on a superhydrophobic (SH) surface can maintain their velocity and shape even on a hydrophilic solid.

The most striking property in a nonwetting (or super-repellent) situation is the spectacular mobility it provides to drops, especially when they are viscous (1). Since liquids at such scales are usually sluggish, this is valuable for applications, but it is also interesting because the residual friction existing on these systems is not fully understood (2). Nonwetting substrates are obtained by texturing solids with a hydrophobic microroughness. This makes them superhydrophobic (SH) (3, 4), since drops then only contact the top of the texture and thus adopt the shape of pearls. Hence, nonwetting relies on texture, which modifies the boundary conditions at interfaces in a way that often remains to be clarified (5). Yet, the main cause of mobility is known: While “usual” drops are slowed down by their contact line (6), nonwetting ones minimize both the role of these lines (6) and the contact with the substrate (7), leading to a decrease of viscous friction by a factor of order 100 as compared to lenticular drops (8).

In this paper, we examine pearls moving on inclines and focus on the case of viscous pearls for which mobility is even more desired. Our main result is the bimodal character of the dynamics: Depending on the detail of the drop deposition, pearls are observed to be either fast (as expected from their shape), or super-fast, that is, about 50 times quicker. We discuss the origin of this phenomenon and describe the dynamics in both regimes and the transition between them.

The substrates in our experiments are glass or aluminum plates treated with a commercial solution of silica hydrophobic nanobeads (30 nm in size) dispersed in isopropanol (Glaco Mirror Coat Zero). After drying of the solvent, the solid is covered by a rough, porous layer a few hundred nanometers-thick that provides super-hydrophobicity (SI Appendix, Fig. S1). The ease of application and good reproducibility make the coating suitable for extended surfaces (2.5 m). Drops are made from water–glycerol mixtures with surface tension γ ≈ 63 mN/m and density ρ ≈ 1,200 kg/m³, whose viscosity η is mainly varied between 100 and 1,200 mPa s, according to the content of glycerol. Their volume Ω is between 0.2 μL and 15 μL, which yields drop radii R always smaller than the capillary length a = (γ/ρg)^1/2 ≈ 2.3 mm. The resulting quasi-spherical drops are deposited onto the substrate inclined by an angle α ranging from 4° to 25° and their trajectory recorded from the side with a high-speed camera operating at 100 to 10,000 frames per second, using backlighting to enhance the contrast.

Fig. 1A shows an example of a viscous pearl (η = 450 mPa s, Ω = 15 μL) running down an incline with α = 7°. Owing to the viscous nature of the liquid, the drop reaches after a few centimeters a constant velocity (constant distance between successive images in the chronophotograph), found here to be V ≈ 3 cm/s, as also seen in Movie S1. However, placing the same drop on the same incline can lead to extremely different dynamics, as seen in Fig. 1B and Movie S1. Then, the terminal speed is 134 cm/s, a value about 40 times larger than in Fig. 1A. This regime is observed if the drop is deposited with a tangential velocity above 10 cm/s, which happens after gently blowing on the drop or, in a more controlled way, by launching the drop from a ramp with a higher, adjustable tilt that fixes this initial velocity. Importantly, the resulting terminal speed is the same whatever the technique used to trigger this regime. Hence, the motion of viscous pearls is bimodal, a unique feature in wetting dynamics, with a steady speed that depends on the history of the drop deposition.

Fig. 1.

Bimodal dynamics of viscous pearls. (A) Chronophotographs of a viscous pearl (η = 450 mPa s, Ω = 15 μL) on an SH plate tilted by α = 7°, with an interframe time of 23 ms. Top image: The drop has been gently deposited and it moves down at a constant velocity V ≈ 3 cm/s. Bottom image: We blow on the drop after its deposition, which triggers a super-fast regime with a terminal velocity V ≈ 134 cm/s. (B) Terminal velocity V of pearls (η = 450 mPa s, Ω = 15 μL) as a function of the tilt α. All experiments lie on two branches, corresponding to the fast regime (red diamonds) and to the super-fast regime (blue circles). Red dots and blue dashes, respectively, show the Mahadevan–Pomeau (MP) and aerodynamic laws discussed in the text. (C) Chronophotograph of a viscous pearl (η = 100 mPa s, Ω = 15 μL) on a parabolic SH plate, with an interframe time of 50 ms. (D) Instantaneous speed U of the pearl in C as a function of the tilt angle α. When reaching U ≈ 15 cm/s, the drop abruptly transitions from the first mode (red diamonds) to the second one (blue circles).

The phenomenon is robust and we could evidence it at various tilts α, as reported in Fig. 1B where we plot the terminal velocity V of a viscous pearl with Ω = 15 μL and η = 450 mPa s as a function of α (4° < α < 25°). Depending on the way the drop is “prepared,” the data split into two independent branches that correspond to the “fast” (red data) and “super-fast” (blue data) regimes in Fig. 1 A and B. In both cases, V increases with α, but differently: While the speed is linear in slope in the fast regime, the curve becomes concave in the super-fast one. In addition, the two branches are fully separated whatever the angle, with a typical ratio of 30 to 60 between the two speeds at a given α.

This first experiment suggests the existence of a dynamic transition induced by the pearl velocity, which can be tested. We construct a parabolic concave SH track where the tilt α linearly increases with the distance from the origin (Fig. 1C). As shown in Fig. 1D and Movie S2, the instantaneous speed U of a gently deposited drop (Ω = 15 μL, η = 100 mPa s) first grows linearly with α, as reported for the fast regime in Fig. 1B. However, it suddenly accelerates at a critical velocity V_c of approximately 15 cm/s, demonstrating the dynamic nature of the transition to the super-fast regime. Once this regime has emerged, it is observed regardless of the angle.

The contrast between the two regimes extends beyond mobility alone. By tracking an air bubble inside the drop, the internal flow is found to be rotational in the first regime (Movies S1 and S3) and mainly translational in the second one (Movie S4). When the liquid viscosity is reduced by a factor 2.2, from 450 to 200 mPa s, the terminal velocity increases by the same factor in the fast case (Movie S3) while it remains unchanged in the super-fast one (Movie S4).

The origin of these two distinct dynamics can be attributed to the nature of the contact between the liquid and its substrate. 1) If the liquid meets the top of the solid roughness, Mahadevan and Pomeau assumed no-slip at the contact and the rotation of these nonwetting drops at small Reynolds numbers Re = ρRV/η (7), a condition always fulfilled in the “fast” regime (Re < 0.7). In such a viscous regime, we expect linearity between the velocity and the driving force (Fig. 1C, red dots) and between the velocity and the inverse of the viscosity (Movie S3). 2) In contrast, a velocity independent of η implies that the solid/liquid contact has been “erased,” which happens if a drop dynamically levitates above its substrate, as reported for water on SH solids (9). The friction law becomes of a different nature so that the speed has no reason to remain linear in slope (dashes in Fig. 1B). Since the viscous globules just glide on air, we expect pure translation and, of course, much higher velocities—such as reported in other cases where contact lines disappear in favor of air films (Leidenfrost situation, drops on moving plates, etc.) (10,11, 12). At first glance, it may also be seen as analogous to the oleoplanning observed for drops on materials lubricated with oil (13). However, oleoplanning is a monomodal mode of motion, which besides produces much smaller speeds due to a much larger dissipation.

The nature of the solid/pearl contact can be examined by looking at drops from below, using transparent Glaco-treated glass. Interferometry with a monochromatic source provides an image of the contact and thin film interferences if an air film is present (9, 10). In the latter case, spectroscopic reflectometry is used to measure its absolute thickness (13, 14). These techniques are thus relevant for distinguishing wetting from levitation. Viscous drops (η = 450 mPa s, Ω = 15 μL) trapped by a needle placed at their north pole are dragged at a constant velocity, while we film the reflection of the light illuminating the drop from below. As shown in Fig. 2A and Movie S5, the interference pattern markedly evolves when the speed varies between 1 and 30 cm/s. At low speed, the image is heterogeneous and it reveals a Cassie state, where the liquid sits on a patchwork of solid and air. Interestingly, this Cassie state is itself dynamic: As the drop moves quicker, the proportion of air in the patchwork increases, showing that the liquid tends to detach from its substrate in a continuous manner toward levitation. This transition occurs around 12 cm/s where fringes reveal that the air film becomes quasi-continuous, except a few local contacts with the solid—a situation that leads to full levitation at higher speed, with more and more fringes that reveal a thickening of the air film with the speed.

Fig. 2.

Air film below a drop moving on an SH solid. (A) Illuminating from below a transparent SH plate provides an interference pattern that depends on the drop speed V. Starting from a Cassie heterogeneous state at low speed, the air below the drop invades the contact zone around V_c = 12 cm/s; this cushion then thickens with the drop speed. (B) Thickness h of the air cushion deduced from the optical measurements, as a function of the drop speed V in the regime of levitation (V > V_c). Coordinates are logarithmic and dots show the slope 2/3. The drop radius is R = 1.5 mm, and its viscosity is η = 450 mPa s. (C) Film thickness h as a function of the drop radius R at fixed velocity (V = 16 cm/s). The thickness increases linearly with R before saturating when R exceeds ~2 mm.

These observations provide a rationale for the bimodal dynamics of pearls on SH solids. 1) Either the liquid partially contacts the solid (Cassie state), and the no-slip condition at this interface applies at the scale of millimetric drops, with viscous dissipation at the solid/liquid contact. This defines the viscous regime. 2) Or a continuous film of air gets dynamically inserted between the pearl and its substrate, and the resulting lubrication deeply modifies the boundary condition at this interface: A large slip becomes possible and viscous drops fly above the solid. This defines the aerodynamic regime.

Above the threshold of levitation, the multiwavelength interference pattern gives access to the absolute value of the thickness h of the air film (Fig. 2B). As could be expected from Fig. 2A, h is in the micrometric range and it increases with V. We view the film formation as a Landau-Levich-Derjaguin (LLD) situation (15), that generally describes how an interface moving at a constant velocity relative to a solid detaches from it. The thickness h of the deposited film (here, made of air) results from a balance between viscous forces η _aV and surface tensionγ. In this frame, h increases with the capillary number Ca = η _aV/γ defined with the viscosity η _a of air, and with the radius of curvature of the interface “far” from the film, which is here the radius R of the pearl for R < a (15, 16). Drawn with dots in Fig. 2B, the LLD law, h ~ R Ca^2/3, convincingly fits the data, with a numerical coefficient of 1.1, of order unity, as expected for this law. Due to the small viscosity of air (η_a ≈ 18 µPa s), capillary numbers remain smaller than 10^-3 whatever the slope, that is, within the range of validity of the LLD law. In addition, the measured thicknesses (a few micrometers) are larger than the nanometric roughness of the solid, so that this roughness does not induce corrections to the law. We finally test how the air thickness depends on the drop radius at fixed velocity (V = 16 cm/s). As seen in Fig. 2C, h is linear in R, in accord with the LLD scaling. However, it saturates at “large” R, which we interpret as a consequence of gravity. When R approaches the capillary length a, the radius of curvature at the drop base scales as a, which provides a thickness h ~ a Ca^2/3 independent of R. Hence, we expect (and measure) films always thinner than 10 µm, a magnitude that explains that side views of moving drops at a large scale (such as displayed in Fig. 1A) do not directly evidence the presence of such thin films.

Trying to understand the threshold of levitation, we might first anticipate air entrainment at any velocity, as predicted from the LLD law if we assume that pearls have an advancing angle of π (17). However, the solid is rough at a scale δ, so that air can be entrained within the roughness. Expressed differently, a continuous film of air will only form if we have h > δ. Plugging the thickness δ in the LLD law yields a threshold velocity V_c ∼ (γ/η_a) (δ/R)^3/2. The Glaco layer exhibits “defects” with a micrometric height, as evidenced in Fig. 2A. For δ ≈ 1 µm, the formula predicts a critical velocity V_c on the order of 10 cm/s, in good agreement with what we see in Fig. 1D. Consequently, V_c should depend on the samples, owing to the fluctuations of δ. More generally, V_c marks the transition between the viscous and aerodynamic regimes. If the drop speed exceeds V_c, it will fly aerodynamically and reach the corresponding terminal speed. Conversely, if the drop moves slower than V_c throughout the motion, it will stay in the viscous regime with a steady velocity smaller by nearly two orders of magnitude.

After clarifying the boundary conditions specific to each regime, we turn to the description of both motions. The viscous dynamics of a small nonwetting drop (radius R < a) was modeled by Mahadevan and Pomeau (MP) (7). First, the pearl weight slightly flattens its base, whose size l_o ∼ R²/a is fixed by balancing Laplace and hydrostatic pressures. Second, a moving viscous drop undergoes a solid-body rotation, except in the l_o-region where dissipation takes place with a power scaling as η(V/R)²l_o³. Equating it with the gravitational power ρgR³Vα gives the MP terminal velocity, V ∼ (γα/η) (a/R) (7, 18), provided the speed is small enough to keep the contact l_o quasi-static. This law (dots in Figs. 1B and 3A) accurately captures the data in the fast regime, where we vary both the tilt of the substrate and the liquid viscosity. It also predicts an unusual dependence of V on R, that stems from the quadratic dependency of l_o in R (7, 18, 19). As reported in Fig. 3B, V indeed decreases hyperbolically with R, in good agreement with the MP model (dots) drawn with a numerical factor of 1. This shows that pearls, even at a small scale, are nonwetting enough to avoid a wetting-driven contact with the substrate that would lead to a more classical behavior (increase of the speed with R). This high degree of repellency can be qualitatively understood by noticing in Fig. 2A (first and second photo) that the Cassie state is itself dynamical, so as to increase contact angles and generate gravity-driven contacts even at small R.

Fig. 3.

The two dynamics of viscous pearls. (A) In the viscous regime, the terminal velocity V of a pearl (viscosity η, Ω = 15 μL) increases linearly with the tilt angle α of its substrate and it decreases hyperbolically with η, in accord with the MP law shown with dots and a prefactor of 1.1. (B) The velocity also varies as the inverse of the pearl radius R, as seen here for η = 450 mPa s and α = 7°, as predicted by the MP law drawn with a prefactor of 1. (C) In the aerodynamic regime, the curve V(α) becomes concave, and the velocity unsensitive to the liquid viscosity (data for Ω = 15 μL with η = 450 mPa s and η = 1 mPa s). Dashes show the aerodynamic law discussed in the text (V ~ α^2/3) and drawn with a prefactor of 0.22. (D) The velocity is also linear in radius R, as shown here for η = 1 mPa s and α = 10°, in agreement with the aerodynamic law drawn with a prefactor of 0.23.

In the aerodynamic regime, the air cushion erases the no-slip condition at the subjacent interface and viscous effects become marginal. This is evidenced in Movie S4, where two droplets exhibit the same terminal velocity despite viscosities differing by a factor of order 2. Fig. 3C extends this observation by comparing the terminal velocity V of water and water/glycerol mixture 450 times more viscous. Whatever the tilt, both pearls have identical velocities, confirming that dissipation in the super-fast regime does not occur within the liquid, but rather in the surrounding air. Denoting the density of air as ρ_a, the Reynolds number in air, Re_a = ρ_aRV/ η _a, is typically 150, a value where dissipation is primarily located in the boundary layer around the drop (skin friction) (20). Its thickness δ scales as R/Re_a^1/2, which yields a friction ρ_aV²R²/Re_a^1/2. Balancing it with the gravitational force ρgR³α gives the terminal velocity in the aerodynamic regime: V ∼ R (ρ²g²α²/ρ_aη_a)^1/3 (20). This law predicts that V varies as α^2/3, in accord with Figs. 1B and 3C, and as R, which we test in Fig. 3D with water drops, this regime being independent of the liquid viscosity. Data confirm this linear dependency (Fig. 3D), a behavior markedly different from that in the viscous regime (Fig. 3B). The numerical coefficient used for the different fits is around 0.23, a value smaller than 0.35, the coefficient measured for a sphere freely moving in air (21, 22). This difference is likely to arise from the presence of a solid close to the moving quasi-sphere whose effect is known to increase the friction (20, 23), and thus to decrease the velocity.

These descriptions have interesting consequences, and we discuss three of them.

• 1)Once levitating, a pearl should become insensitive to the nature of its substrate. In Fig. 4A and Movie S6, we compare the dynamics of viscous drops on two plates tilted by 7°. In the first chronophotograph, the drop aerodynamically flies on an SH solid at a terminal velocity V ≈ 135 cm/s. In the second image, the SH plate upstream becomes not Glaco-treated downstream, where motion is recorded: Even if the pearl is on hydrophilic steel, it moves with a spherical shape at V ≈ 131 cm/s, a dynamic hardly distinguishable from the first one. Once a drop enters the aerodynamic regime, its motion is independent of the substrate wettability—which can be exploited to make viscous drops super-fast on “regular” solids.
• 2)If an SH tilted plate becomes horizontal (Fig. 4B and Movie S7), drops gradually decelerate until they stop in about 20 cm with a nearly unchanged shape (top image). The first stage of the deceleration is similar on hydrophilic steel (bottom image), but the arrest is now abrupt: when the velocity reaches ~30 cm/s, the air film is thin enough (~3 µm) to induce a contact with the wettable solid, which stops the pearl and transforms it into a lens.
• 3)Nonwetting states can be also generated by coating the liquid with a hydrophobic micropowder that insulates it from its substrate, producing a quasi-spherical “liquid marble” (19). In order to be mechanically resistant, these marbles are generally made with grains with a size of a few tens of micrometers. Comparing the movement of viscous marbles with that of pearls running down super-repellent inclines leads to interesting differences, despite an apparent similarity in the degree of repellency. As shown in Fig. 4C, the continuous air cushion forming with pearls above a velocity of ~10 cm/s (left image) is not observed with marbles (right image). Instead, the contact elongates when increasing the speed (Movie S8), a consequence of viscous effects that remain dominant in the absence of levitation. As discussed earlier, the thickness h of the air cushion below a pearl is in the range of 1 to 10 µm, a distance significantly smaller than the grain size of 40 µm used in our experiment, so that air below such marbles can circulate without detaching the liquid. Unlike pearls that accelerate as soon as they levitate, marbles consequently remain in the MP regime, as shown in Fig. 4D for slopes between 5° and 20°. This remains true whatever the concentration Φ of grains at the surface, varied here between 30 and 80%, where the latter concentration roughly corresponds to the saturation of the interface. Hence, even if viscous marbles are ideally nonwetting, they cannot be as fast as viscous pearls—they just, classically, move with unimodal dynamics.

Fig. 4.

Robustness of the aerodynamic regime. (A) Chronophotographs of viscous droplets (η = 450 mPa s, Ω = 15 μL) sliding down a plate inclined by 7° in the super-fast regime. Photos are captured every 20 ms. In the top image (blue), the plate is fully SH and the pearl reaches a terminal velocity V ≈ 135 cm/s. In the bottom image (gray), the same droplet is released on an SH incline that becomes hydrophilic (bare steel) after one meter, where photos are made (same rate). The absence of SH coating does not disrupt the super-fast regime (V ≈ 131 cm/s). (B) Chronophotographs of the same droplets decelerating on a horizontal plate (α = 0°), with photos every 20 ms. On the SH surface (blue), the droplet slows down smoothly from 50 cm/s to 0 cm/s, and it maintains its spherical shape. On the hydrophilic surface (gray), the trajectory is similar down to 30 cm/s, velocity at which the drop abruptly stops and becomes lenticular. (C) Interference patterns beneath a viscous pearl (Left) and a viscous marble (Right) (η = 450 mPa s, Ω = 15 μL), recorded at different velocities. For the pearl, the Cassie state at small V transitions into levitation at large V, as already seen in Fig. 2A. In contrast, no levitation is observed with the marble, where the grain layer (approximately 40 μm thick) allows the circulation of air below the liquid and thus prevents the formation of a continuous air cushion. (D) Instantaneous drop velocity U as a function of a for pearls and marbles (η = 130 mPa s, Ω = 15 μL) running down the parabolic substrate shown in Fig. 1C. While the pearl velocity markedly increases above a critical angle (as in Fig. 1D), the marble velocity follows the MP law (dots) at all tested slopes, whatever the surface coverage Φ by grains varied between 30 and 80%.

At larger driving forces, that is, at larger α, the difference between pearls and marbles will be of a different nature. While we mainly expect pearls to glide on air cushions, fast revolving marbles are then known to generate eccentric shapes such as peanuts and donuts that result from their fast centrifugation (19). Therefore, a valuable consequence of the bimodal dynamics of pearls is their ability to keep their shape roughly unchanged—a way to maintain their integrity despite the velocity.

Materials and Methods

SH Coating of the Incline.

5 cm-wide, 2.5 m-long aluminum strips were sequentially cleaned with acetone and isopropanol, coated with a solution of hydrophobic nanobeads (Glaco Mirror Coat Zero) and dried vertically. The SH treated substrates were then mounted on a thick, bare aluminum substrate used as a support for the incline.

Interferometry Measurements.

Contact visualization was performed by reflective interference contrast microscopy (RICM) using a transparent Glaco-coated glass substrate. Interference patterns were generated using green LED illumination (λ = 530 nm) through a 2 × microscope objective and recorded with a high-speed camera coupled to an infinity-corrected tube lens. Film thicknesses were measured using white-light interferometry. An optical fiber probe (RP23, Thorlabs) was positioned beneath the transparent substrate to simultaneously deliver white light and collect the reflected signal through a multimode optical fiber connected to a spectrometer (CCS100, Thorlabs). The film thickness was then determined by analyzing the wavelength-dependent normalized intensity, in particular the positions of interference maxima and minima.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Bimodal dynamic of viscous pearls. Videos of a viscous pearl (Ω = 15 μL, η = 450 mPa.s) running down a SH plate tilted by α = 7° (with the camera tilted accordingly). The bar shows 5 mm and the movies are slowed down by a factor 5. The regime of descent is bimodal, with two possible speeds that fifer by a factor 40. a. Fast regime. The motion is steady, and it takes place at a velocity V = 3.2 cm/s. b. Super-fast regime. The drop now steadily at a speed V = 134 cm/s.

Movie S2.

Transition between fast and super-fast regimes. Viscous pearl (Ω = 15 μL, η = 100 mPa.s) running down a parabolic SH plate whose tilt α increases linearly with the travelled distance. The drop abruptly transitions into the super-fast regime after traversing about 10 cm on the parabola. The video is slowed down by a factor 2.

Movie S3.

Fast regime. Viscous pearl (Ω = 15 μL) rolling down a plate tilted by α = 7° in the fast Mahadevan-Pomeau regime (camera tilted accordingly, video slowed down 10 times). Air bubbles reveal that drops are rotating as they move. The bar shows 5 mm and movies are slowed down by a factor 5. a. η = 450 mPa.s and V = 3.2 cm/s b. η = 200 mPa.s and V = 6.5 cm/s – that is, 2.2 times larger than in the first video.

Movie S4.

Super-fast regime. Viscous pearl (Ω = 15 μL) rolling down a plate tilted by α = 7° in the superfast regime (camera tilted accordingly, video slowed down 10 times). Air bubbles reveal that drops remain roughly in translation. The bar shows 5 mm and movies are slowed down by a factor 30. a. η = 450 mPa.s and V = 134 cm/s b. η = 200 mPa.s, V = 131 cm/s – that is, similar to that with a liquid 2.2 times more viscous.

Movie S5.

Interferometry below a viscous drop. Interferometry pattern below a viscous pearl (Ω = 15 μL, η = 450 mPa.s) running at velocity V. From left to right: V = 1 cm/s, V = 4 cm/s, V = 12 cm/s, V = 16 cm/s and V = 30 cm/s. The bar shows 0.5 mm and videos are slowed down by 10, 25, 83, 125 and 250, respectively. Contact transitions from Cassie to levitating state around 12 cm/s.

Movie S6.

Generality of the super-fast regime. Viscous pearl (Ω = 15 μL, η = 450 mPa.s) running down a plate tilted by α = 7° (camera tilted accordingly). The bar shows 5 mm and movies are slowed down by 30. a. The plate is superhydrophobic and the drop reaches a steady velocity V = 134 cm/s. b. If the SH plate becomes hydrophilic (bare aluminum), the drop keeps on flying, and it moves at the same terminal velocity, V = 135 cm/s.

Movie S7.

Stop on horizontal platform. Viscous pearl (Ω = 15 μL, η = 450 mPa.s) decelerating on a horizontal plate. The bar shows 1 cm and movies are slowed down by a factor 10. a. On a superhydrophobic solid, the drop velocity decreases from 50 cm/s to 0 cm/s. b. On a hydrophilic aluminum plate, the drop velocity decreases from 50 cm/s to 30 cm/s, where it suddenly stops.

Movie S8.

Marbles. Interferometry pattern below a viscous marble (Ω = 15 μL, η = 450 mPa.s) running at velocity V = 1 cm/s on the left and V = 16 cm/s on the right. The bar shows 0.5 mm and videos are slowed down by 10 and 200, respectively.

Data, Materials, and Software Availability

All study data can be found following the link https://doi.org/10.5281/zenodo.18393248 (24) and/or in the supporting information.