Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nano
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HE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nanofiber mat coating Noemi Ghillani1,a , Michael Heinz2 , and Tatiana Gambaryan-Roisman2,b 1
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Politecnico di Milano, School of Industrial and Information Engineering, Milan, Italy Institute for Technical Thermodynamics, Technische Universit¨ at Darmstadt, Alarich Weiss Strasse 10, 64287 Darmstadt, Germany Received 29 January 2020 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. Wetting of surfaces with porous coating is relevant for a wide variety of technical applications, such as printing technologies and heat transfer enhancement. Imbibition and evaporation of liquids on surfaces covered with porous layers are responsible for significant improvement of cooling efficiency during drop impact cooling and flow boiling on such surfaces. Up to now, no reliable model exists which is able to predict the kinetics of imbibition coupled with evaporation on surfaces with porous coatings. In this work, we consider one of possible mechanisms of imbibition on a substrate covered by a nanofiber mat. This is the capillary pressure-driven flow in a corner formed between a flat substrate and a fiber attached to it. The shape and the area of the crosssection occupied by the liquid as well as the capillary pressure change along the flow direction. A theoretical/numerical model of simultaneous imbibition and evaporation is developed, in which viscosity, surface tension and evaporation are taken into account. At the beginning of the process the imbibition length is proportional to the square root of time, in agreement with the Lucas-Washburn law. As the influence of evaporation becomes significant, the imbibition rate decreases. The model predictions are compared with experimental data for imbibition of water-ethanol mixtures into nanofiber mat coatings.
1 Introduction Liquid wetting of porous materials, spreading and imbibition into porous layers, as well as the concomitant heat and mass transfer phenomena play an important role in a wide variety of technical applications. Understanding complex wetting and transport phenomena is important for industrial applications such as ink-jet printing and 3D-printing, for building technologies in the control of moisture penetration into a
Present address: Osisoft GmbH, Frankfurt, Germany
b
e-mail: [email protected]
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The European Physical Journal Special Topics
building components and filters in air conditioning systems and HVAC [1]. Moreover, the knowledge of wetting behaviour and mechanisms plays a fundamental role in the development of design rules of functional materials, e.g. superhydrophobic surfaces [2], and of porous coatings used for cooling of electronic devices and heat transfer enhancement in spray cooling [3]. When a liquid drop encounters a porous layer, the transport of liquid over and within this layer is governed by the physical and chemical properties of liqui
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