Effect of a triple contact line on the thermokinetics of dropwise condensation on an immiscible liquid surface Sanat Kumar Singha, Prasanta Kumar Das * and Biswajit Maiti Within the framework of classical nucleation theory, a thermokinetic model is developed for the line- tension-associated condensation on an immiscible liquid substrate considering both interfacial and peripheral molecular transport. Along with the free energy minimization principle, a modified classical theory, based on detailed balance analysis, has been employed to determine relevant thermokinetic parameters for heterogeneous nucleation of water droplets as a function of the pseudo-contact angle, submergence angle, and equivalent Young's contact angle. A triple contact line is found to have a considerable effect on both thermodynamics with the associated line tension and kinetics with the related peripheral molecular transport. The growth rate of the formed droplet increases for lower values of the pseudo-contact angle and submergence angle. Besides, positive line tension increases for higher values of the pseudo-contact angle and submergence angle and lower values of the equivalent Young's contact angle, while negative line tension exhibits a reverse trend. With decreasing pseudo-contact angle and submergence angle and increasing equivalent Young's contact angle, the free energy barrier decreases appreciably. Subsequently, the rate of nucleation increases which, in turn, suggests the possibility of condensation enhancement under such conditions. Using the heterogeneous nucleation experimental data, the present thermokinetic formulation is capable of estimating the values of microscopic contact angles and line tension of a given lenticular three-phase system. 1. Introduction In recent years, there has been a considerable interest in the scientic community in the formation and self-assembly of ordered patterns of microporous structures, i.e. ‘breath gures’. 1–3 The key mechanism that determines the formation and the subsequent growth of the condensing droplets in the breath gures is dropwise condensation. 4 Dropwise condensa- tion or droplet nucleation 5 on rigid or so elastic 6 substrates is not only an abundant natural phenomenon 7 but also has several natural processes 7 and industrial applications. 8 Although associated with various simplied assumptions, Classical Nucleation Theory (CNT) is adopted most widely to describe the phenomena of heterogeneous nucleation. 9 Thermokinetic models have also been developed for heterogeneous nucleation on diverse geometrical substrates namely planar, 10,11 spher- ical, 12–16 conical 17–19 etc. In this context, it needs to be mentioned that mostly rigid substrates are considered for all the aforesaid geometries. 20 When a droplet forms in between an ambient supersaturated vapour and an extrinsic substrate, a triple contact line where all the three distinct phases intersect each other always exists. 21 The three-phase contact line tension, which can be considered as the one-dimensional equivalent to the interfacial tension, plays a pivotal role when the droplet becomes small. 22 The effect of contact line tension cannot be neglected in the phenomenon of nucleation of nano-sized droplets on rigid planar, 23–28 spherical, 29–32 or conical 33 substrates. Moreover, along with the interfacial molecular transport 11,13,17 through the vicinity of the droplet–vapour interface, the peripheral molecular trans- port 33–35 in the neighbourhood of the triple line from the thin adsorbed layer should be considered during the initial stage of nucleation. So, the presence of triple line is found to have a considerable effect on the thermokinetics of heterogeneous nucleation on rigid substrates. However, less attention was paid towards the thermokinetic mechanism of heterogeneous nucleation on an immiscible liquid substrate considering the effect of triple line. 36–40 In this paper, we have developed a modied CNT-based thermokinetic model for condensation on an immiscible liquid surface, considering the combined effect of the line tension and the peripheral molecular ux. Under steady-state condition, we have studied some thermokinetic traits of heterogeneous nucleation of a lenticular droplet in terms of various associated physico-chemical properties, kinetic char- acteristics, ambient conditions, and geometric parameters. Based on a rigorous analytical treatment, a quantitative Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India. E-mail: pkd@mech.iitkgp.ernet.in Cite this: RSC Adv. , 2016, 6, 41506 Received 3rd March 2016 Accepted 18th April 2016 DOI: 10.1039/c6ra05724a www.rsc.org/advances 41506 | RSC Adv., 2016, 6, 41506–41515 This journal is © The Royal Society of Chemistry 2016 RSC Advances PAPER Published on 20 April 2016. Downloaded by Indian Institute of Technology Kharagpur on 26/04/2016 16:53:03. View Article Online View Journal | View Issue