Supporting information: Morphing and vectoring impacting droplets by means of wettability-engineered surfaces Thomas M. Schutzius 1,2 Gustav Graeber 3 Mohamed Elsharkawy 1 James Oreluk 4 Constantine M. Megaridis 1, October 9, 2014 1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607, United States 2. Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, 8092 Zurich, Switzerland 3. Department of Mechanical Engineering, RWTH Aachen, 52072 Aachen, Germany 4. Department of Mechanical Engineering, University of California, Berkeley, CA 94720, United States *Corresponding author: email: cmm@uic.edu; phone: 1-312-996-3436; fax: 1-312-413-0447 1
S1 Fabrication of Wettability Patterns synthesis uncoated SiC PMC-HFS coated SiC 1 x inkjet pattern 4 x inkjet pattern ( a ) ( b ) ( c ) ( d) ( e ) ( f ) ( g ) ( h) high-zoom low-zoom (i) ( j ) ( k ) ( l) Figure S1: (a-d) Schematic sequence demonstrating the wettability patterned coating synthesis process; SEM micrographs of the wettability patterned coating before and after each processing step at: (e-h) low, and (i-l) high magnification. Scale bar in (e-h) represents 50 µm; Scale bar in (i-l) denotes 10 µm. Figure S1 presents a schematic sequence demonstrating the procedure for preparing wettability patterned coatings (a-d) as well as the corresponding scanning electron micrographs of the coatings after each processing step at low- (e-h) and high-magnification (i-l). To illustrate why printing four times on the same spot is required, Figure S1 (g) and (k) show the wettability patterned coating with only one layer of ink (magenta color). It is apparent that only parts of the nanostructure are covered with ink. The final wettability patterned coating, with four layers of ink, is shown in Figure S1 (h) and (l). Most of the nanostructure is covered with the ink, while maintaining a high-degree of surface micro-texture, giving rise to the extremely low value of θr. S2 Experimental Setup for Droplet Impact Visualization Figure S2 shows a schematic and image of the setup utilized for characterizing the dynamic wetting behavior of water droplet impact on wettability engineered surfaces. 2
a 1 L 5 3 6 2 4 Figure S2: (a) Schematic of the experimental setup. 1) drop generator; 2) high speed camera; 3) cool light source; 4) floating table; 5) sample; 6) platform. L represents the distance from the needle tip to the sample surface. (b) Image of the setup utilized for droplet vectoring characterization. S3 Wettability Pattern Characterization Prior to considering droplet impact on wettability patterned surfaces, it is instructive to study the intricacies of drop impact on superhydrophobic surfaces (no wettable domains present). While most superhydrophobic surfaces have the ability to shed sessile droplets from inclined samples (i.e., self-cleaning property) where droplets reside in the so-called Cassie-Baxter 1 wetting state not all such surfaces can facilitate rebound of impacting droplets. Droplets that are not repelled by superhydrophobic surfaces are said to undergo impalement which can be understood as a transition to the so-called Wenzel wetting state. 2 Deng et al. 3 presented design criteria for resisting impalement of impinging droplets with speeds O(1)-O(10) m s 1 ; their conclusion was that such superhydrophobic surfaces should have 100 nm (hydrophobic) surface texture features (e.g., pores, etc.), since the pressure required to impale the surface asperities is the Laplace pressure corresponding to the maximum deformation of the water-air interface bridging such surface textures. For porous texture, the capillary pressure can be calculated as p c = 2σ lv cosθ a /r pore, where θ a is the advancing contact angle on a flat surface and r pore is the radius of the surface pore; therefore, the smaller r pore is, the more likely a superhydrophobic surface is to resist impalement. In the case of this study, hydrophobic silica nanoparticles, coated with a fluoropolymer, were utilized to generate the required hydrophobic nano-scale surface texture in order to resist liquid impalement. To generate hierarchical micro-to-nano surface structures which are well known for their role in enhancing hydrophobicity the PMC-HFS composite coating was deposited onto a flexible micro-textured SiC substrate (see Figure S1 for micrographs). The PMC-HFS composite coating applied onto the SiC substrate displayed the following wetting characteristics: θa = 166± 1 and θr = 155±6 (see Table 2). Water droplets had a high degree of mobility, and the coating was able to resist water impalement even for U y,0 >3.5 m s 1, making the coating well suited for a droplet impact study. Once the superhydrophobic composite coating was formed, inkjet printing of standard color and black inks onto 3
the coating modified its surface energy not surface texture in a spatially specific manner. Since the coating was inherently non-wettable, initially it did display repellency towards the impinging liquid inks; however, as multiple printing steps were performed on the same region, the surface progressively displayed a higher degree of printing uniformity. The ink patterned regions on the PMC-HFS composite coating displayed the following wetting characteristics: θ a = 93±5 and θ r 0 (Table 2). While θ a is actually high enough to deem this ink coating hydrophobic, the extremely low value for θ r indicates that for receding contact line conditions which are of great importance for droplet rebound situations this coating behaves as if it were hydrophilic. In addition, the ink-coated regions act to pin, or arrest the motion of the contact line due to its high contact angle hysteresis, θ = θ a θ r. Such behavior can be quite useful for constraining droplet motion during dynamic fluid events, as will be shown later. S4 Droplet Impact on Hydrophilic Rings: The Effect of Radius Figure S3 presents seven image sequences of droplets impacting with a constant value of We = 80 onto surfaces with different wettability. In (a) and (b) the wettability of the surface is isotropic (superhydrophobic and hydrophilic, respectively). In (c)-(g) the wettability is anisotropic (hydrophilic rings on a superhydrophobic background). The radial thickness of the rings is held constant, while their radius is varied. It is clear that in the early stages of droplet impact, the wettability of the surface does not have a large effect on the dynamics (e.g., spreading diameter); however, the receding dynamics and the outcome of the impact event are greatly affected by the wettability of the surface. 4
before impact impact max. spreading receding outcome -1.33 ms 0 ms 2.33 ms 4.66 ms 32.00 ms (a) -1.66 ms 0 ms 2.33 ms 4.66 ms 31.66 ms (b) -4.66 ms 0 ms 2.33 ms 4.33 ms 16.66 ms (c) -3.00 ms 0 ms 2.33 ms 4.66 ms 23.33 ms (d) -5.00 ms 0 ms 2.33 ms 4.33 ms 12.00 ms (e) -5.00 ms 0 ms 2.33 ms 4.33 ms 5.00 ms (f) -2.33 ms 0 ms 2.33 ms 4.33 ms 5.00 ms (g) Figure S3: Drop impact with We = 80 on: (a) superhydrophobic paper, (b) entirely patterned hydrophilic paper; hydrophilic ring pattern on hydrophobic background with outer ring diameter r o = (c) 0.5 mm, (d) 1 mm, (e) 1.5 mm, (f) 2 mm, (g) 2.5 mm, and w o =0.2 mm. The scale bar in (a) indicates 2 mm. The black arrow in (g) indicates when a penetrating hole has formed in the middle of the liquid lens. 5
top view a b rosin( ϕ) dβ c arc r o dα d side view r osin( ϕ ) z z z x β x r o α x 2ϕ droplet x arc θ* r,pho θ* r,phi Figure S4: (a)-(d) Schematics showing the parameters required to compute the force due to surface tension acting on the water droplet during the retraction (restitution) phase of droplet impact from the top and side-view perspective. θr,pho and θ r,phi denote the receding contact angles on the phobic and philic portions of the surface, respectively (sideview). In (a), the yellow arrows indicate forces which are acting in the z-direction and cancel each other out; therefore, they have no bearing on dynamics along the x-direction. (b) and (c) Show the geometrical parameters relevant to the forces acting on the phobic and philic sides, respectively. S5 Droplet Vectoring: Force Calculation The force exerted in the lateral direction (parallel to the surface) during the retraction phase of the droplet is due to the surface tension. More specifically, it is the result of a large difference in the dynamic (receding) contact angles on the philic (θr,phi ) and phobic (θ r,pho ) regions of the surface. Figure S4 shows these angles schematically (side-view). The hydrophilic arc (in red, or purple when covered with water) is a semi-circle symmetric around the x-axis. The droplet impacts orthogonally to the x z plane, and makes first contact with the geometric center of the arc. We make the following assumptions to develop the model for the unbalanced surface tension force acting in the x-direction: (i) θ r,phi and θr,pho are constant and do not vary along the contact line; (ii) the droplet contact line recedes along the hydrophilic arc with a linear angular velocity in time (t); (iii) time zero (t r = 0) begins when the contact lines begin to recede (i.e., retraction or restitution phase). With these assumptions, we can express the differential of the lateral force as df σ = σr o ( cosθ r,phi cosαdα cosθ r,pho sinφ cosβ dβ), (S1) where α and β are angles in the azimuthal direction and r o is the outer radius of the hydrophilic arc (see Figure S4 top-view). To rectify the total surface tension force along the x-direction, we must integrate this differential in the azimuthal direction (α and β ). As observed experimentally, the droplet is continuously de-wetting the hydrophilic arc in time, so φ = φ(t r )=(π/2)(1 (t r /τ r )), where τ r is the total time of the retraction phase (see Figure S4 top-view). Thus the total lateral force can be written as 6
r (ms) 25 20 15 10 5 0 K( D 3 0 /8 )0.5 K=3.1 /8 )0.5 ( D 3 0 0 20 40 60 80 100 We Figure S5: Plot of the retraction contact time with the solid surface for droplet impact on hydrophilic arcs on superhydrophobic background. The outer arc radius r o was adjusted to match the value of the maximum spreading radius (D max /2). Note that the values are relatively close for a certain range of We (indicated by shaded blue region). The horizontal dotted line indicates the inertial-capillary time scale ( ρd 3 0 /8σ), while the dashed line indicates the same time scale multiplied by a constant pre-factor (K). F σ = σr o (cosθ r,phi φ φ cosαdα cosθ r,pho sinφ π/2 π/2 ) cosβ dβ, (S2) where φ is the maximum angle in the azimuthal direction where the droplet is still contacting the hydrophilic arc. After integration, we obtain F σ = 2σr o ( cosθ r,phi cosθ r,pho) sinφ. (S3) Recalling that φ(t r )=(π/2)(1 (t r /τ r )) and substituting yields [ ( F σ = 2σr o cosθ r,phi cosθr,pho ) π sin 2 ( 1 t )] r. (S4) τ r The retraction contact time (τ r ) of the droplet for impact on hydrophilic arc patterns on superhydrophobic surfaces is plotted in Figure S5. When the impact conditions are in the inertial regime (We>> 1), then the retraction time-scale (τ r ) can be estimated by balancing surface tension with inertia, 4 e.g., inertial dewetting of thin films. The result is τ r D max U ret 2 ρd 3 ] 1 0 π [1 cos(θ 8σ r,pho ) ρd 3 0 K 8σ (S5) U ret is the retraction velocity of the contact line, D max is the maximum spreading diameter of the droplet, and ρ is the density of the liquid, and K is a constant which is determined experimentally (see Figure S5; K = 3.1). By integrating Equation S4 in time, one can obtain the change in momentum ( P) due to the contact angle hysteresis force as 7
P= τr 0 [ [ ( ( 2σr o cosθ r,phi cosθr,pho ) π sin 1 t )]] r dt r = m(u x,2 U x,1 ), 2 τ r (S6) where U x the velocity of the droplet in the x direction and m=ρ(π/6)d 3 0 is the mass of the droplet. The subscripts 1 and 2 indicate when the receding phase begins and ends, respectively. The assumptions are: (i) τ r K ρd 3 0 /8σ 4 (see Figure S5) and (ii) r o D 0 We 0.25 /2 5 (inviscid droplet). To satisfy (ii), the outer radius of the hydrophilic arc should be adjusted depending on We. Since U x,1 = 0 (velocity is zero when receding begins), we can divide both sides of Equation S6 by U y,0 (droplet impact velocity) and define the horizontal restitution coefficient (ε x ). After integrating, we see that ε x = U ( )( ) x,2 6 1 ( = U y,0 ρπd 3 σd 0 We 0.25) ( cosθ 0 U r,phi cosθ ) [ ( 2τ r r,pho y,0 π cos π(τr t r ) 2τ r Combining assumption (i) with Equation S7, and recalling the definition of We=ρU 2 y,0 D 0/σ, yields )] τr 0. (S7) ε x = 3 2 π 2 K( cosθr,phi ) cosθ r,pho We 0.25. (S8) Therefore, this theory suggests that for drop impact events on hydrophilic arcs with diameter 2r o D max, ε x has a We 0.25 dependence. S6 Ring Inner Radius for Optimal Liquid Distribution in an Annulus By designing patterns that can precisely guide the final conformation of the droplet, it may be possible to prevent unwanted discharge. Since r o is pre-defined by the maximum lateral spread of the liquid, volume analysis can be utilized to compute the second relevant wettability pattern parameter r i. As an example, consider the volume of a liquid annulus with θ = 90, which can be estimated by the half volume of a torus with the same outer and inner radii. The half volume is V t,1/2 = π 2 R t r 2 t, (S9) where R t is the torus radius and r t the radius of its cross section. For the present pattern, R t = (r o + r i )/2 and r t = (r o r i )/2. Substituting in Equation S9, and considering that V t,1/2 = 4.7 4.8µL (i.e., initial drop volume; D 0 2.1 mm) and r o = 2.5 mm, we obtain r i = 1.53 mm for the inner ring radius for optimal liquid distribution in the annulus. The actual value of r i found in practice to consistently produce a symmetric liquid annulus was below the above analytical value, which can be viewed as an upper bound for this quantity. Figure 5 presents a drop impact sequence that forms a liquid annulus without any mass loss; r i for this functioning wettability pattern was 1.35 mm, which represents a 12% decrease compared with the r i value obtained from the idealized torus, a reasonable deviation in-line 8
with the present analysis. S7 Penetrating Hole Formed at the Wettability Transition Line side-view w o r hole h h top-view o r 2r h 2r o Figure S6: Schematic depicting a non-axisymmetric penetrating hole in a liquid spherical lens on a single ring wettability pattern with outer radius r o and width w o. The hole has a height h h and a radius r h, and its centerline is positioned at r=r o w o r h. For a more detailed analysis of hole formation in liquid lenses at wettability transitions, refer to Kim et al. 6 A brief discussion of their analysis is given here for completeness. Figure S6 is a schematic depicting a non-axisymmetric penetrating hole formed in a liquid spherical lens resting centrally over a non-wettable disk surrounded by a wettable ring. Previous analysis showed that for contact lines advancing on a superhydrophobic surface, if their velocities exceed a critical value ( 0.01-0.1 m s 1 for water) as in this study contact lines can become roughened and entrain air bubbles up to the point where they meet the hydrophilic annulus. 6 At the Cassie-Baxter to Wenzel transition line, the entrained air bubbles following the liquid flow suddenly become trapped. 6 In the analysis by Kim et al., the first observable penetrating holes which formed due to the presence of large underlying air pockets had radii 90µm. We hypothesize that by increasing the value of w o, one can make it energetically unfavorable for such holes to form/grow. To confirm this, Equation S12 (see Section S9 for derivation) can be employed to calculate whether or not a penetrating hole is energetically favorable or not; however, since in this case the hole radius r h is fixed, and the volume of the hole is small compared with the liquid lens (i.e., does not affect the radius of curvature, r curv ; 9
0.009 0.006 E ( J) 0.003 0.000-0.003 0.0 0.2 0.4 0.6 0.8 1.0 w o (mm) Figure S7: Plot of E (calculated from Equation S11) vs. w o for D 0 = 2.1 mm, r o = 2.5mm, and r h = 0.05mm; no inner ring is considered in this case. V h /V 0 = 0.0005), h h can be found from h h = rcurv (r 2 o w o r h ) 2 r curv + h max, (S10) where h max is the maximum height of the liquid lens. 6 With this, Equation S12 (see Section S9) can be recast as a function of w o [ ( ] E = E 2 E 1 = σ lv 2πr h rcurv (r 2 o w o r h ) 2 r curv + h max ) πr 2 h(1 cosθcb). (S11) Figure S7 presents a plot of E vs. w o for the following conditions: r h = 0.09 mm, D 0 2.1 mm, and r o = 2.5 mm. E changes sign at w o = 0.15 mm, above which hole formation for the aforesaid conditions becomes energetically unfavorable. While w o = 0.15 mm is obviously much less than the value employed in this study, w o = 0.50 mm, the previous analysis gives justification as to why the minimum width of an annular wettability pattern for µl-sized droplets impacting with We = O(10 100) is of sub-millimetric scale. This outcome may prove useful in future design of wettability patterns for droplet impact. 10
S8 Droplet Splitting and Sampling Figure S8 presents an image sequence of a droplet impacting (We = 30) onto a superhydrophobic line of width 0.5 mm. Under these conditions, droplet splitting was not observed. 0.0ms 2.3ms 4.7ms 7.0ms 73ms Figure S8: Drop impact with We=30 on a superhydrophobic line of width 0.5 mm. The line can be seen under the spread droplet at 73ms. Figure S9 presents an image sequence of a droplet impacting with We=60 onto a superhydrophobic line of width 3 mm. Under these conditions, droplet splitting was observed, but a large volume of the liquid droplet was ejected from the surface. The line was too wide, causing the unwanted ejection. 0.0ms 2.3ms 4.6ms 7.0ms 14ms 21ms 28ms 66ms Figure S9: Drop impact with We=60 on a superhydrophobic line of width 3 mm. Note the ejected liquid at 14ms. Figure S10 presents an image sequence of a droplet impacting with We = 100 onto a angular wettability pattern designed to sample a large number of small volumes of liquid (24). 11
Figure S10: Droplet impact with We = 100 on a wettability patterned surface designed to instantaneously sample numerous equal small volumes of liquid. Scale bar shown is 2 mm. The inner disk (at the point of first contact) is wettable and has a diameter of 1.05 mm. A hydrophilic line segment of 0.5 mm was rotated every 15 degrees to create the angular pattern. S9 Penetrating Hole Formation Let us now examine the penetrating hole problem. It is instructive to examine the stability of a hole at its centerline position in a liquid volume resting on a solid surface. The purpose is to see whether a nascent hole is capable of growing or not. The configuration of the liquid lens during hole formation is presented in Figure S11. The hole is assumed to be axisymmetric and has a volume of V h = πrh 2h h, where r h and h h are, respectively, the radius and height of the hole. In order to establish whether a formed hole is stable and therefore capable of growing or collapsing it is necessary to determine whether the hole is energetically favorable (in terms of free surface availability). With the maximum lens thickness being less than the capillary length, we can neglect gravitational effects and assume that the lens conforms to the shape of a spherical cap. 7 The change in energy E due to the hole formation can then be expressed as 6 E = E 2 E 1 = σ lv [ 2πrh h h πr 2 h(1 cosθ CB) ], (S12) where the apparent contact angle θcb can be defined by the Cassie-Baxter equation, for droplets in a Cassie-Baxter state, as cosθcb = 1+Φ S(cosθ e + 1), where Φ S is the liquid-solid contact area fraction (Φ S 1). 1,7 Previous analysis 6 neglected the effect that a displaced liquid volume as a result of hole formation had on the shape of the 12
side-view liquid air 2 hole = V = πr h h h h h h top-view U h 2r h 2r o Figure S11: Schematic illustrating hole formation in a thin liquid lens formed through droplet impact on a wettabilitypatterned surface. V h, h h, U h, r h, and r o represent the approximate volume of the penetrating hole, the approximate depth of the penetrating hole, the velocity of the expanding hole, the radius of the hole, and the outer lens radius, respectively. liquid lens. In the present analysis, we held V (droplet volume) constant, and therefore accounted for the change in lens shape as a result of hole formation (see Section S10 for details). The displaced liquid in the lens should act to increase the maximum height of the lens; therefore, from Equation S12 this would raise the value of E, thus making hole formation less energetically favorable. Accounting for the displaced liquid volume increased the value of r h,c by 9% when D 0 = 2.1 mm. Figure S12 presents plots of E vs. r h for three different values of D 0, and shows the transition point ( E = 0, r h = r h,c ) where hole formation becomes energetically favorable ( E < 0) for each case. For D 0 = 2.1 mm, r h,c = 0.54 mm, and as D 0 decreases so does r h,c, which is intuitive. Now that the physical requirements for hole formation in liquid lenses have been rationalized, droplet impact on a variety of increasing complex annular patterns can be considered. Figure S13 presents a 2.1 mm-diameter water droplet impacting (with We=80) on an annular pattern with r o = 2.5 mm and an increased value of w o = 0.5 mm. At t = 6 ms, the first stable hole was observed (not shown) with r h 0.49±0.06 mm, which is slightly below the critical radius estimate (r h,c = 0.54 mm) obtained with the previous analysis. In the early stages of growth, the hole expansion velocity (U h ) can be estimated by balancing surface tension forces with inertial forces. For liquid films disintegrating in open air, U h can be defined by the Taylor-Culick formula, 6,8,9 U h = 2σlv ρ h, where h is the nominal thickness of the liquid film. If one assumes that the liquid dynamics on a superhydrophobic surface (θ CB = 150 ) are similar to those in open air (θ CB = 180 ), 6 and that h h h, then 13
0.05 E( J) 0.00-0.05-0.10-0.15-0.20 0.0 0.2 0.4 0.6 0.8 1.0 r (mm) h Figure S12: Plot of energy change E vs. rh for a liquid lens with a hole formed when droplets of varying initial diameter (D0 ) deposit on a ring of constant outer radius ro = 2.5 mm (Fig. S11). The liquid displaced by generating a hollow cylinder of volume Vh in the center of the lens was accounted for in this model. Curves for the following values of D0 are plotted: 2.1 mm ( ), 1.9 mm ( ), and 1.7 mm ( - - ). Uh 0.5 m s 1 a fairly fast moving contact line. In fact in this case, as in a previous report, 6 the hole expansion process eventually results in the ejection of a significant portion of the droplet volume from the annular pattern. It is interesting to note the direction of the ejected volume. In hole expansion processes that are asymmetric (i.e., off center), the droplet ejection direction is along a straight line connecting the center of the hole with the center of the ring pattern (see Figure S13). 6 While this is a repeatable process, predicting the location of where the penetrating hole forms is not, thus this pattern is not suitable for controlled propulsion of droplets in this case. 0 ms 2.33 ms 4.33 ms 4.66 ms 7.00 ms 9.33 ms 11.66 ms 14.00 ms 16.33 ms final Figure S13: Dropl impact on a hydrophilic annulus with outer radius ro = 2.5 mm and radial width wo = 0.50 mm for We = 80. The dotted line indicates an axis of symmetry (because of the impact offset) as well as the direction of the expelled liquid volume. 14
S10 Hole Formation in Liquid Lens h h (mm) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 r h (mm) Figure S14: Plot of hole height (h h ) which coincides with the maximum lens height vs. hole radius (r h ) when: ( ) volume displacement due to hole formation is accounted for, and ( ) volume displacement is neglected. The following parameters were used D o = 2.1 mm, r o = 2.5 mm. Considerations on the effect that cylindrical (axisymmetric) hole formation has on the shape of a liquid lens are given here. In order to form a cylindrical hole of volume V h = πr 2 h h h in a lens, it is necessary to displace liquid of equal volume. The volume of the lens before hole formation can be approximated by that of a spherical cap V l = πh l 6 ( 3r 2 o + h 2 ) l. (S13) E ( J) 0.05 0.00-0.05-0.10-0.15-0.20 0.0 0.2 0.4 0.6 0.8 1.0 r h (mm) Figure S15: Plot of energy change E vs. r h when: ( ) volume displacement due to hole formation is accounted for, and ( ) volume displacement is neglected. D o = 2.1 mm, r o = 2.5 mm. The volume of a lens with a hole (assuming again that the spherical cap shape is maintained) can be approximated as V l,h = πh l,h 6 ( 3r 2 o + h 2 ) l,h πhh rh, 2 (S14) 15
where h l,h is the lense height after the hole forms and displaces some of the liquid, in turn, raising the fluid level (the outer contact area remains pinned; i.e.r o = constant). Since the liquid volume is conserved (and is known), and assuming that h h h l,h, Equation S14 can be solved for h l,h for known values of r h. Figure S14 shows how h h varies with r h for the cases where the shape of the lens is or not accounted for during hole formation. For r h < 0.2 mm, neglecting the change in shape of the lens when the hole forms appears to be a good approximation; however, for r h = 0.52 mm, the hole has a measurable impact on h h (increase of 8.3%) and therefore the shape of the lens. Figure S15 shows how E (from Equation S12) is affected by accounting for the change in lens shape as a result of hole formation. The critical radius for hole formation r h,c (i.e., r h at E = 0) increased by 10% when accounting for the change in lens shape, as expected. Figure S16 presents a plot of the ratio V h /V o where V h is the hole volume, and V o the initial drop volume vs. r h. At r h = r h,c = 0.52 mm, V h V 1 0 = 0.093, which represents a non-trivial volume fraction, and acts to show the importance of accounting for changes in the lens height during hole formation. V h /V 0 ( L L -1 ) 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 1.0 r h (mm) Figure S16: Plot of V h /V o vs. r h when the change in lens shape due to volume displacement as a result of hole formation is accounted for. The following parameters were used: D o = 2.1 mm, r o = 2.5 mm. V h /V 0 is 9.3% at r h = 0.52 mm, which is the critical hole radius. 16
S11 Videos Video S1 is the full video utilized to generate the sequence in Figure 2 Video S2 is the full video utilized to generate the sequence in Figure 4 Video S3 is the full video utilized to generate the sequence in Figure 5. Video S4 is the full video utilized to generate the sequence in Figure 9. 17
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