Universal representations of evaporation modes in sessile droplets

Abstract

In this work, we provide a simple method to represent the contact line dynamics of an evaporating sessile droplet. As a droplet evaporates, two distinct contact line dynamics are observed. They are collectively known as modes of evaporation, namely Constant Contact Radius (CCR) and Constant Contact Angle (CCA). Another intermediate mode-Stick-Slide (SS) or mixed mode is also commonly observed. In this article, we are able to provide a graphical representation to these modes (named as MOE plot), which is visually more comprehensive especially for comparative studies. In addition, the method facilitates quantitative estimation for mode of evaporation (named as MOE fraction or MOEf), which doesn't exist in literature. Thus, various substrates can now be compared based on mode of evaporation (or contact line dynamics), which are governed by fluid property and surface characteristics.

Fig 1. Droplet contact line dynamics.

(a) Normalized CR, CA vs. time. (b) Equivalent polar plot (MOE plot) of (a) with nomenclature.

Fig 2. Theoretical sketch for MOE plots in three different modes.

(a) CCR (b) CCA (c) SS.

Fig 3. MOE plots.

(a) For different substrates (hydrophobic and hydrophilic) with three distinct modes of evaporation. (b) For PDMS only. Non-dimensional time coordinates (t/t_e) are also marked, where t_e is evaporation duration. Standard deviation error across repeated trials is within 4%.

Fig 4. Mode of evaporation factor (MOE_f).

(a) Determination of MOE_f using area measurements from MOE plot. Here, $\text{ar}(\widehat{\text{xy}})$, stands for area of the sector x0y. As $\widehat{\text{cd}}$ is a non-circular arc, it is segmented into small sectors at the data points between c and d. Circular arc assumption is applied to each sector and area of sector c0d is obtained as sum of all. See S1 Supporting Information for details about area calculation ar(SS) (b) MOE_f for the substrates in Fig 3. (c) MOE_f plot for droplets with different initial volumes.

Fig 5. Physical significance of MOE_f.

(a) Variations in evaporation duration for different MOE_f values (experiments from three different substrates with different initial volumes) (b) Theoretical plot for variations in droplet evaporation time for strictly CCR and CCA modes in all possible initial contact angles (reprinted by permission from [24]). (c) MOE plot and corresponding MOE_f with evaporation time for data obtained from Shin, Dong Hwan, et al. [25]).