Polygonal Droplets on Microstructured Surfaces

Rishi Raj1, Solomon Adera1, Ryan Enright2, and Evelyn N. Wang1

1Mechanical Engineering, MIT, Cambridge, MA 02139, USA 2Bell Labs Ireland, Alcatel-Lucent Ireland, Dublin, Ireland

Dense Micropillar Array

20 µm

Sparse Micropillar Array

200 µm

Side View Camera

Angle of 0o

TOP VIEW

SIDE VIEW

In this work, we demonstrate interesting polygonal Wenzel droplets on

microstructured surfaces. Dynamic contact angle experiments on functionalized

(𝜃𝑓𝑙𝑎𝑡,𝐴 = 87°, 𝜃𝑓𝑙𝑎𝑡,𝑅 = 70°) cylindrical silicon micropillar arrays (diameter D, pitch L, and

height H) in a square pattern were performed using a Microgoniometer (MCA-3, Kyowa

Interface Science). Water was dispensed using a piezo ink jet at a rate of 0.75 nL/sec.

Liquid addition was stopped approximately at 20-25 seconds after which the droplet was

allowed to evaporate to ambient at 38% relative humidity. Top views droplet images

were captured in addition to the side profile visualization of along the two axes of

symmetry.

Visualization of the contact line dynamics enabled the development of a

thermodynamic model to explain the associated anisotropy in the de-pinning contact

angles along the two axes of symmetry. The ratio of pillar diameter D to pitch which is L

along 0° and √2𝐿 along 45° axes governs the advancing contact angles which dictate

the droplet contact line shape during growth as illustrated in Figure 1 and Figure 2.

The difference between the de-pinning contact angles along these two directions is

larger for high pillar density resulting in a square contact line as shown in Figure 1. An

octagonal droplet is observed with sparse pillar arrays as shown in Figure 2.

Interesting features such as sharp droplet edges due to a square contact line

(Figures 1c and 1d, solid arrows) and magnified view of the contact area (Figures 2a,

2c, 1a, and 1c, dashed arrows) due to liquid droplet lens effect are also illustrated.

The visualization provides key insights into complex droplet shapes during growth

which are critical for condensation heat transfer on superhydrophobic surfaces.

ACKNOWLEDGEMENTS

The authors acknowledge the National Science Foundation, Battelle’s National Security

Global Business, and Industrial Development Agency Ireland for their financial support.

10 µm

Along 0° ∶ cos 𝜃0°,𝐴 = 𝐷

𝐿𝑐𝑜𝑠 𝜃𝑓𝑙𝑎𝑡,𝐴 + 90° + 1 −

𝐷

𝐿cos (𝜃𝑓𝑙𝑎𝑡,𝐴)

Along 45° ∶ cos 𝜃45°,A = 𝐷

2𝐿𝑐𝑜𝑠 𝜃𝑓𝑙𝑎𝑡,𝐴 + 90° + 1 −

𝐷

2𝐿cos (𝜃𝑓𝑙𝑎𝑡,𝐴)

a

b

c

d

a

b c

d

FIGURE 2: Droplet shape evolution during growth and evaporation on sparse micropillar arrays (𝐷, 𝐿, 𝐻 = 4, 10, 5 𝜇m).

FIGURE 1: Droplet shape evolution during growth and evaporation on dense micropillar arrays (𝐷, 𝐿, 𝐻 = 7, 10, 5 𝜇m).

200 µm

a. b. c. d.

0o 45o

X

Y X Y

advancing

phase

advancing

phase

a. b. c. d.

√2𝐿

𝐿

X

Y

𝐷 𝐻

10 µm