Extracting droplet height using the pattern distortion technique: from single droplets to arbitrary arrays*

Recent theoretical and numerical models describe the reduced evaporation rates of multiple droplets on surfaces [1,2]. However, the experimental work required to validate these models has fallen behind due to difficulties in determining the transient volumes of droplets arranged in arbitrary 2D patterns [3]. We present a simpler method [4] for determining individual droplet volumes for any arrangement of droplets.  In this technique each droplet acts like a lens which magnifies a pattern placed beneath it. We use an optical transfer matrix method to trace the paraxial rays from the pattern, through the substrate and droplet, to the camera, providing a relationship between the measured magnification and the height of each droplet. The technique is validated against a traditional side-camera method finding excellent agreement. Finally, we take experimental data [5] from various 2D droplet arrays and compare quantitatively to the different theoretical models [1,2].  

  

[1] Wray, A., Duffy, B., & Wilson, S. (2020). Competitive evaporation of multiple sessile droplets. Journal of Fluid Mechanics, 884, A45. doi:10.1017/jfm.2019.919 

[2] Masoud, H., Howell, P., & Stone, H. (2021). Evaporation of multiple droplets. Journal of Fluid Mechanics, 927, R4. doi:10.1017/jfm.2021.785 

[3] Edwards, A. M., Cater, J., Kilbride, J. J., Le Minter, P., Brown, C. V., Fairhurst, D. J., & Ouali, F. F. (2021). Interferometric measurement of co-operative evaporation in 2D droplet arrays. Applied Physics Letters, 119(15), 151601. 

[4] Kilbride, J. J., Ouali, F. F., & Fairhurst, D. J. (2022). In preparation. 

[5] Iqtidar, A., Kilbride, J. J., Ouali, F. F., Fairhurst, D. J., Stone, H., & Masoud, H. (2022) Drying dynamics of sessile-droplet arrays. In preparation.