A criterion for the pinning and depinning of an advancing contact line on a cold substrate
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-900261-5
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
A criterion for the pinning and depinning of an advancing contact line on a cold substrate R´emy Herbaut1,2,a , Julien Dervaux1 , Philippe Brunet1,b , Laurent Royon2 , and Laurent Limat1 1
2
Universit´e de Paris, Laboratoire Mati`ere et Syst`emes Complexes, UMR 7057 CNRS, 75013 Paris, France Universit´e de Paris, Laboratoire Interdisciplinaire des Energies de Demain, UMR 8236 CNRS, 75013 Paris, France Received 2 November 2019 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at Tp < Tf , where Tf is the melting temperature, and infinite thermal conductivity. We propose a model of contact-line dynamics derived from lubrication theory, where equilibrium between capillary pressure and viscous stress is at play. Here it is adapted to a quadruple line geometry, where vapour, liquid, frozen liquid and basal substrate meet. The Stefan thermal problem is solved in an intermediate region between molecular and mesoscopic scales, allowing to predict the shape of the solidified surface. The apparent contact angle versus advancing velocity U takes a minimal value, which is set as the transition from continuous advancing to pinning. We postulate that this transition corresponds to the experimentally observed critical velocity, dependent on undercooling temperature Tf − Tp , below which the liquid is pinned and advances with stick-slip dynamics. The analytical solution of the model shows a qualitatively fair agreement with experimental data, and the best agreement is obtained from the adjustment of a mesoscopic cut-off length as fitting parameter. We discuss of the dependence of this cut-off length on Tp
1 Introduction Contact line dynamics is a still challenging problem motivating many studies. The multi-scale nature of the problem, the existence of several conflicting models, combined with the difficulty to obtain exhaustive and reproducible data has left this problem still open [1–3]. Of special difficulty is the case in which the contact line motion is combined with phase change, like for instance evaporation/condensation of the liquid [4–7], colloids or particles deposition [8–11], or solidification of a liquid moving on a cold substrate [12–17]. In this latter case, as well as in that of colloid a b
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The European Physical Journal Special Topics
deposition [8], it is observed that the continuous advancing or receding of a contact line can be interrupted when one reduces the velocity U down to a threshold Uc for contact line pinning [16], below which stick-slip behaviour can be observed as well [14,17]. Understanding these phenomena is of crucial importance for several applications, including 3D printing [18], or aircraft icing [19]. To a
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