PHYSICAL REVIEW E 100, 013106 (2019) Experimental characterization of the growth dynamics during capillarity-driven droplet generation Bhaskarjyoti Sarma, Vijay Shahapure, Amaresh Dalal, * and Dipankar N. Basu † Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781039, India (Received 14 March 2019; revised manuscript received 30 May 2019; published 15 July 2019) The transient dynamics of a growing droplet in a yarn is explored following the spatiotemporal evolution of the three-phase contact line as well as the liquid-air interface with the help of videographic techniques and subsequent image analyses. The spontaneous capillary flow of liquids in a porous network is used to generate a droplet on the freely hanging end of a yarn whose other end is dipped continuously in a liquid reservoir. The growing droplet initially moves upward due to surface tension until the attainment of a critical volume, beyond which gravity is able to pull it downward until detachment. Based upon the spatiotemporal trajectory of the three-phase contact line of the droplet, the entirety of the associated growth dynamics can be divided in three distinct regimes, namely, “radial growth,” “axial growth,” and “motion” stages. The transition from one to the other is governed by the subtle interplay between the capillary and the gravity forces. Several experimental fluids are considered to elucidate the effect of the fluid properties on the transient contact line and interfacial dynamics of drops. The kinetics of the three-phase contact line and the radius of the droplet is found to follow two distinct exponential scaling laws, developed through the combination of the relevant forces. A mathematical model has also been proposed to predict the critical volume of the growing droplet in relation to its final volume, beyond which gravity controls the transient dynamics. DOI: 10.1103/PhysRevE.100.013106 I. INTRODUCTION The transmission of liquids through the porous network of the naturally abundant, as well as the synthetic objects, is a ubiquitous phenomenon and has been studied extensively both by the researchers and industrialists since ages [1–7]. Specif- ically, the immense potential of spontaneous capillary flows (SCF) in transporting liquids through the porous networks of yarns, without the use of external pumping, have been put into use in numerous industrial and day-to-day applications which primarily encompass textile [8,9], mold preparation indus- tries [10], biomedical devices [11–13], forensic laboratories [14,15], household drying [16,17], coating processes, etc. The wicking ability of the constituent yarns emerges to be one of the most influential parameters for successful operation of these devices and processes, as has been envisaged in several experimental and analytical studies [3,18–22]. Drop formation from a nozzle or orifice is another inter- esting hydrodynamic phenomenon with a wide and varied range of uses, such as inkjet printing [23,24], spray formation [25,26], DNA microarray deposition [27], microencapsulation [28,29], etc. The rich underlying physics associated with the dynamics of growth and breakup of a liquid drop from a nozzle (or orifice) has been explored exhaustively with the help of experimental [30–33] and computational techniques [34–38] over the last few decades. Two contrasting modes of drop formation dynamics, namely, dripping and jetting [33,39], have been identified with the help of high-speed * Corresponding author: amaresh@iitg.ac.in † Corresponding author: dnbasu@iitg.ac.in visualization techniques and subsequent image processing [40,41]. One of the pioneering attempts to capture the bifur- cation process of pendant drops was reported by Hauser et al. [42] and was reproduced a decade later by Peregrine et al. [43]. In recent years, owing to the advancement of high-speed imaging techniques, researchers are able to visibly explore many intricate physics of drop formation and breakup, the crucial dynamics in the vicinity of pinch-off [37,44] in par- ticular, which remained unfathomed only until the last decade. Such advanced experimental tools and methods have immense contributions in uncovering the relevant phenomenon, leading to some wonderful recent efforts, such as the formation of a drop from a wettable nozzle [45], tilted nozzle [46], droplet formation in dense suspension [47], etc., which has high relevancy with the industrial processes. Therefore, it is very much evident that numerous research works have separately explored drop formation in nozzles and wicking in yarns. However, we have not found any effort toward integrating both in the form of drop generation by wicking in the porous network of a yarn. This study makes an honest attempt to bridge this gap by unveiling the dynamics of drop formation from an unwoven yarn under varying flow conditions. A simple experimental arrangement constructed by using a yarn, as shown in Fig. 1, serves the purpose of addressing many new aspects in the regime of drop dripping, that have heretofore been unexplored. The prime focus of this paper is a systematic investigation of the transient dynamics of the three-phase (air-liquid-yarn) contact line of the droplet during its growth in a yarn under the effect of gravity and interfacial forces. By bringing the yarn in contact with the liquid in a reservoir, a flow field can be established owing to the continuous wicking of the liquid in 2470-0045/2019/100(1)/013106(12) 013106-1 ©2019 American Physical Society