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.
Sessile droplets exposed to an incipient condition lead to an inevitable loss of mass, which is critical in many practical applications. By considering an arbitrarily configured two-dimensional array of droplets, here we provide a simple generalized theoretical limit to their lifetime in an evaporating state. Notwithstanding the geometrical and physical complexity of the effective confinement generated due to their cooperative interactions, we show that the consequent evaporation characteristics may be remarkably insensitive to the topographical details of the overall droplet organization, for a wide range of droplet-substrate combinations. With subsequent deployment of particle-laden droplets, however, our results lead to the discovery of a unique pathway towards tailoring the internal flows within the collective system by harnessing an exclusive topologically-driven symmetry breaking phenomenon, yielding a new strategy of patterning particulate matters around the droplet array. Evaporation of sessile droplets (Stauber et. al. 2014; Sáenz et. al. 2015; Schofield et. al. 2018; Ghasemi & Ward, 2010; Xu & Choi, 2012; Chen et al., 2012)is ubiquitous to our day-to-day experiences, including the formation of coffee-rings, ink-stains, as well as many commercial processes including spray painting, ink-jet printing, crop spraying, coating of seeds or tablets, spray cooling and spray drying. In most of these practical scenarios, the droplet arrangement can be best represented by topologically varying two-dimensional structures (2D arrays), resulting in obvious complexities in describing their dynamical characteristics by appealing to a universal physical paradigm.The proximity of neighboring droplets in a multi-dimensional droplet array creates localized regions of vapor accumulation by saturating the interstitial voids. Consequently, an 'effective' vapor mediated confinement is established around the individual droplets. The distribution and extent of vapor accumulation leads to further modifications in the flow dynamics in and around the droplet, culminating in alterations in the global rate of evaporation, thereby influencing the evaporation dynamics of the droplet array in an intriguing manner (Dugas et. al. 2005). Laghezza et. al. (2016), through experiments and numerical simulations, showed that a system of interacting droplets results in increase in the dissolution lifetime of the central droplet. However, their formulation could not predict the droplet dissolution lifetime increment as a function of the droplet array configuration. Toledano et al. (2005)
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