A criterion for the pinning and depinning of an advancing contact line on a cold substrate

• Published in: The European physical journal. ST, Special topics Special topics, 2020-09, Vol.229 (10), p.1867-1880
• Main Authors: Herbaut, Rémy, Dervaux, Julien, Brunet, Philippe, Royon, Laurent, Limat, Laurent
• Format: Article
• Language: English
• Subjects: Atomic; Biological Physics; Capillary pressure; Challenges in Nanoscale Physics of Wetting Phenomena; Classical and Continuum Physics; Condensed Matter; Condensed Matter Physics; Contact angle; Contact pressure; Critical velocity; Exact solutions; Fluid Dynamics; Fluid mechanics; Materials Science; Measurement Science and Instrumentation; Mechanics; Melt temperature; Molecular; Nonlinear Sciences; Optical and Plasma Physics; Pattern Formation and Solitons; Physics; Physics and Astronomy; Pinning; Regular Article; Soft Condensed Matter; Solidification; Substrates; Supercooling; Temperature dependence; Thermal conductivity
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2020-900261-5

The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold substrate at T p < T f , where T f 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 T f − T p , 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 T p