Universal evaporation dynamics of ordered arrays of sessile droplets

Abstract

Manipulation of an array of surface droplets organised in an ordered structure turns out to be of immense consequence in a wide variety of applications ranging from photonics, near field imaging and inkjet printing on the one hand to bio-molecular analysis and DNA sequencing on the other. While evaporation of a single isolated sessile droplet has been well studied, the collective evaporative dynamics of an ordered array of droplets on a solid substrate remains elusive. Physically, the closed region between the centre and side droplets in the ordered array reduces the mobility of the diffusing vapour, resulting in its accumulation along with enhanced local concentration and a consequent increment in the lifetime of the centre droplet. Here, we present a theoretical model to account for evaporation lifetime scaling in closely placed ordered linear droplet arrays. In addition, the present theory predicts the limiting cases of droplet interaction; namely, critical droplet separation for which interfacial interaction ceases to exist and minimum possible droplet separation (droplets on the verge of coalescence) for which the droplet system achieves maximum lifetime scaling. Further experimental evidence demonstrates the applicability of the present scaling theory to extended dimensions of the droplet array, generalising our physical conjecture. It is also worth noting that the theoretical time scale is applicable across a wide variety of drop–substrate combinations and initial droplet volumes. We also highlight that the scaling law proposed here can be extended seamlessly to other forms of confinement such as an evaporating droplet inside a mini-channel, as encountered in countless applications ranging from biomedical engineering to surface patterning.

Evaporation of multiple droplets

“…Cazabat & Guena 2010;Erbil 2012;Stauber et al 2014;Brutin & Starov 2018;Giorgiutti-Dauphiné & Pauchard 2018). While the majority of research has focused on the drying of single sessile droplets, there is broad interest in understanding the evaporation of multiple drops through experiments, simulations and theory; representative studies include Schäfle et al (1999), Sokuler et al (2010), Carrier et al (2016), Shaikeea, Jyoti & Basu (2016), Laghezza et al (2016), Castanet et al (2016), Bao et al (2018), Hatte et al (2019), Chong et al (2020) and Wray, Duffy & Wilson (2020). Among the most recent of these investigations is the theoretical analysis of Wray et al (2020).…”

Convection-dominated dissolution for single and multiple immersed sessile droplets

“…It is also relevant to the extraction process used in drug delivery (Chou et al 2015). Droplet dissolution is in many ways similar to droplet evaporation, which has been studied extensively over the past decades (Picknett & Bexon 1977;Deegan et al 1997;Popov 2005;Shahidzadeh-Bonn et al 2006;Cazabat & Guena 2010;Gelderblom et al 2011;Erbil 2012;Stauber et al 2015;Hatte et al 2019;Pandey et al 2019), and it is also analogous to bubble dissolution or growth (Epstein & Plesset 1950;Enríquez et al 2014). The basis of all these physical processes is the same, namely the mass gain or loss of the bubble or droplet being proportional to the concentration gradient at the interface, with the concentration field outside the drop or bubble being determined by the advection-diffusion process.…”

The shielding effect extends the lifetimes of two-dimensional sessile droplets

“…In practice, droplets rarely occur in isolation, and so it is important to understand how droplets evaporate in the presence of other evaporating droplets. Previous studies of the evaporation of multiple sessile droplets have employed a variety of experimental, numerical and analytical approaches [27][28][29][30][31][32][33][34][35][36][37][38]. The critical difference between the evaporation of single and of multiple droplets is the occurrence of the shielding effect, namely that the presence of other evaporating droplets increases the local vapour concentration, and so each droplet evaporates more slowly than it would in isolation.…”