An experimental and numerical study of capillary rise with evaporation John Polansky * , Tarik Kaya Carleton University, Department of Mechanical and Aerospace Engineering, Ottawa, ON, Canada article info Article history: Received 11 June 2014 Received in revised form 27 November 2014 Accepted 7 December 2014 Available online Keywords: Meniscus Capillary rise Heat pipes Imbibition LucaseWashburn equation abstract An experimental and numerical study of spontaneous imbibition into capillary tubes subject to phase change is presented. A mathematical model is developed to predict the motion of a meniscus while undergoing phase change. The model addresses slip at the wall, viscous effects of the vapour in the capillary tube and transient evaporation. A set of experiments were performed for three fluids (acetone, n-pentane and iso-octane), three capillary tube diameters (0.5, 1.0, and 2.0 mm) and five heating con- ditions (0, 0.7, 2.7, 6.0 and 10.6 W). The experimental results demonstrated that the meniscus rise was altered by varying degrees of evaporation. A comparison of the experimental data and the mathematical model yielded a good correlation for the 1 mm capillaries, and deviated for both the 0.5 mm and 2 mm cases. It was found that an asymptotic transient mass function was unable to improve the fit to experiment. © 2015 Elsevier Masson SAS. All rights reserved. 1. Introduction Capillary action is found to occur naturally in hydrology, anat- omy and plant physiology; with industrial applications spanning textiles, biosensors, oil recovery, civil engineering and space based technologies. The static and dynamic aspects of capillary forces are of particular importance in space, as surface tension forces domi- nate small scale fluid flows given the reduced gravitational effects on the flow. Thus, the engineering applications of capillaries in space are common to liquid fuelled rocket motors and heat pipe based thermal control systems. In general, the utilisation of capil- lary structures for enhancing heat transfer presents a unique challenge. Historically the statics of a meniscus have been well studied, while the dynamics of its rise have been a more recent point of investigation. The early works of Lucas [1], Washburn [2], Bell and Cameron [3] and Bosanquet [4] founded much of the theoretical framework for capillary dynamics. Such works continue to be the basis from which more comprehensive mathematical models are being devised. Subsequent works have sought to address the problem of capillary rise dynamics using theory, numerical solutions and experimentation. Some studies have included effects such as: dynamic contact angle [5e13], surfactants [14,15], gas/vapour displacement [14,16], slip [2,17,18], phase change [5,19,20], vena- contracta/jet [13,21e24] and tube inclination [25]. Others have sought to capture the various regimes of capillary rise thereby leading to criteria predicting oscillatory behaviour [24,26,27]. Fries and Dreyer [28] investigated the timing of competing forces during capillary rise, followed by their systematic analysis of non- dimensional governing equations describing imbibition [29]. While the majority of studies have focused on cylindrical capillaries and Newtonian fluids; Levine et al. [18] expanded the study to that of channel based imbibition, while Kornev and Neimark [30] extended to viscoelastic fluids. Complementing the theoretical and numerical studies of capil- lary rise dynamics, some experimentation has shed light on the true physics and dynamics. Siebold et al. [6] experimentally confirmed that the meniscus changes curvature during the dy- namic portion of the rise. This changing interface shape was also confirmed by Lorenceau et al. [21], where the interface was observed to produce a liquid finger during the initial stages of capillary rise. Other factors postulated and experimentally captured include the viscous pressure drop associated with the displacement of the gas/vapour occupying the capillary. The effects of vapour displacement pressure drop were confirmed experimentally by Zhmud et at. [14], and shown to have considerable impact on the dynamics of capillary rise. Furthermore, slip at the solideliquid * Corresponding author. E-mail address: john.polansky@carleton.ca (J. Polansky). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts http://dx.doi.org/10.1016/j.ijthermalsci.2014.12.020 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved. International Journal of Thermal Sciences 91 (2015) 25e33