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The relation of steady evaporating drops fed by an influx and freely evaporating drops

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Abstract

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, Leicestershire, UK

    Desislava Todorova & Uwe Thiele

  2. Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion–Israel Institute of Technology, 32000, Haifa, Israel

    Len M. Pismen

Authors
  1. Desislava Todorova
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  2. Uwe Thiele
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  3. Len M. Pismen
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Correspondence to Desislava Todorova.

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Todorova, D., Thiele, U. & Pismen, L.M. The relation of steady evaporating drops fed by an influx and freely evaporating drops. J Eng Math 73, 17–30 (2012). https://doi.org/10.1007/s10665-011-9485-1

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  • DOI: https://doi.org/10.1007/s10665-011-9485-1

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