Non-uniformly receding contact line breaks axisymmetric flow patterns
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-900281-3
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Non-uniformly receding contact line breaks axisymmetric flow patterns? Hyoungsoo Kim1,a , Naser Belmiloud2 , and Paul W. Mertens3 1 2 3
Department of Mechanical Engineering, KAIST, Daejeon 34141, South Korea SCREEN SPE Germany GmbH, Fraunhofer Strasse 7, 85737 Ismaning, Germany IMEC, vzw Kapeldreef 75, Heverlee 3001, Belgium Received 26 December 2019 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. We investigate the internal flow pattern of an evaporating droplet using tomographic particle image velocimetry (PIV) when the contact line non-uniformly recedes. We observe a three-dimensional azimuthal vortex pair while the contact line non-uniformly recedes and the symmetry-breaking flow field is maintained during the evaporation. Based on the experimental results, we show that the vorticity magnitude of the internal flow is related to the relative contact line motion. Furthermore, to explain how the azimuthal vortex pair flow is created, we develop a theoretical model by taking into account the relation between the contact line motion and evaporating flux. Finally, we show that the theoretical model has a good agreement with experimental results.
1 Introduction Drying of a liquid droplet on a solid substrate is ubiquitous in ordinary life [1–3] and industry [4–6]. Over the last decade, this phenomenon has been extensively studied because it plays an important role in multidisciplinary applications, including coating and printing methods [5–9], DNA/RNA microarrays [10,11], and health diagnostics [12,13]. Since the first study by Deegan et al. [1], most of the theoretical models assumed that the evaporation flux profile is axisymmetric [1,14–18], which is described as J(r) = j0 [1 − (r/R)2 ]−1/2+π/θ (see Fig. 1a), where j0 is the evaporating flux, R is the droplet radius, and θ is the contact angle [1,14–17,19]. Then, the resulting flow field is always axisymmetric (see Fig. 1b) if the boundary conditions are uniform along the contact line. In contrast, the axisymmetric results no longer hold if there are non-uniform boundary conditions such as non-uniform surface tension [20], non-uniform evaporation rate, non-uniform temperature distribution in the azimuthal direction [21], which are still ongoing projects. In-plane thermal fluctuations were experimentally observed in a volatile liquid droplet on a heated surface [21], a surfactant-added water droplet [22], and even a sessile water droplet [23]. In the previous literature, it showed that there were ? Supplementary material in the form of two avi files available from the Journal web page at https://doi.org/10.1140/epjst/e2020-900281-3 a
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The European Physical Journal Special Topics
Fig. 1. Typical droplet evaporation problem: (a) Schematic of an evaporation rate profile (purple arrows) on the liquid-air interface of a drop on a solid substrate [1]. The length of the purple arrows
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