SUPPLEMENTARY MATERIAL
Flat-bottomed oblate spheroid model
The stretched sessile droplet on superhydrophobic surfaces can be modeled using a flatbottomed oblate spheroid as shown in Fig. S1(a). Based on this model, the surface area of a sessile
droplet can be formulated, where the height (c+d), the width (a), and the radius of the contact area
(rc) of a stretched sessile droplet are the major parameters basically given by measurement. Because
a and c satisfy a complete oblate spheroid (x2/a2+y2/c2=1) and the droplet volume should be
conserved, c=αR and a  R
 , where R is the radius of the equivalent sphere to the complete
oblate spheroid (0<α≤1). However, due to the flat bottom, the vertical radius of the lower part, d, is
shorter than c; d=δc, 0<δ≤1. Then, rc  a 1   2 , and  Y  tan 1   (1   2 ) /  2 are derived
based on α and δ.
In addition, R and Ro, which are unequal, can be related by the volume conservation; Ro is
the radius of the initial spherical droplet.
R3
4
2  3   3
Ro
(S1)
The free surface contacting with air can be divided into a cap surface (Sc) and a side-wall surface
(Ss). Then, the entire surface area (So) of a stretched sessile droplet becomes the sum of the free
surface and the bottom surface (Sb).
1


S c  R 2  
sinh 1 ( ) 




S s  R 2   

(S2)
 2  1  1 sinh 1 ( ) 

1

(S3)
1  2 

S b  R 2 
  

S o  R 2   (2   2 )  2  1  

(S4)
 2  1  1 sinh 1 ( )  sinh 1 ( )

where,  
1
3

(S5)
1
So, So can be rewritten by substituting R with Ro.
S o  4Ro2 f ( ,  )
2
1
3 
, where f ( , )   
(2   2 )  2  1  
3  
 4  6  2  
(S6)
 2  1  1 sinh 1 ( )  sinh 1 ( )

.
The actual shape of a maximally stretched sessile droplet in dynamic condition (Fig. S1(b))
seems to increasingly deviate from an oblate spheroid, as higher electric potentials are applied,
presumably due to the wavy oscillation of the surface. To evaluate the accuracy of the oblate
spheroid model, the surface areas calculated based on the Eq. (S6) were compared with those of
actual droplets shown in Fig. S1(b) measured through the image processing. As shown in Fig. 1(c),
the surface areas calculated by the flat-bottomed oblate spheroid model show fairly acceptable
accuracies, when compared with the measured ones. And interestingly, the deviation does not
increase as droplets are stretched up to f=1.4.
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FIG. S1. The oblate spheroid model for the analyses of the surface energy stored on the surface of a
stretched sessile droplet. (a) Schematic of a stretched droplet, where each parameter is determined
based on the oblate spheroid model; Ro: the radius of the spherical droplet, csp: the geometric center
of the spherical droplet, cm: the mass center of the stretched sessile droplet, cob: the geometric center
of the complete oblate spheroid, H: the distance between csp and the center of the airborne droplet,
Hm: the distance between cm and the center of the airborne droplet (jumping height), hc: the distance
from the bottom to cm, λ: the distance between cob and cm, a: the horizontal radius of the oblate
spheroid, c: the vertical radius of the oblate spheroid, d: the distance from the bottom to cob, rc: the
radius of the contact area, θ: the contact angle. (b) Stretched droplets by electrowetting are
demonstrated according to the applied potentials that change the wettability and the wetting area.
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Surfactant materials and surface tension
We explored the effect of surface tension on the droplet jumping phenomenon. To decrease
the surface tension, we used two kinds of surfactants of Span 20 (Hydrophilic lipophilic balance,
HLB=8.6) and Tween 20 (HLB=16.7). A surfactant was added in the 1 mM NaCl solution, and the
surface tension was measured after 15 min (equilibrium).1 The value of liquid surface tension with
the Span 20 concentration of 2  10-5, 4  10-5, 6  10-5, and 6  10-4 M corresponds to 47, 42, 38, and
30 mN/m, respectively. The value of liquid surface tension with the Tween 20 concentration of 4 
10-5, 1  10-4, and 1  10-3 M corresponds to 37, 35, and 35 mN/m, respectively. As the surface
tension decreased with the surfactant concentration, it was more difficult to make the droplet jump.
[1] O. Raccurt, J. Berthier, P. Clementz, M. Borella, and M. Plissonnier, J. Micromech. Microeng.
17, 2217 (2007).
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