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

The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold sub-strate at Tp < T f , of infinite thermal conductivity, where T f is the melting temperature. We propose a model derived from lubrication theory of contact-line dynamics, where an equilibrium between capillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple line where the vapour, liquid, solidified 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 liquid surface. The apparent contact angle versus advancing velocity U exhibits 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 − 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. We discuss on the way to get better quantitative agreement, which in particular can be obtained when the mesoscopic cutoff length is made temperature-dependent.The influence of solidification on the spreading of liquids is addressed in the situation of an advanc-ing liquid wedge on a cold substrate atTp< Tf, whereTfis the melting temperature. We proposea model derived from lubrication theory of contact-line dynamics, where an equilibrium betweencapillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple linewhere the vapour, liquid, solidified liquid and basal substrate meet. The Stefan thermal problemis solved in an intermediate region between molecular and mesoscopic scales, allowing to predictthe shape of the solidified liquid surface. The apparent contact angle versus advancing velocityUexhibits a minimal value, which is set as the transition from continuous advancing to pinning. Wepostulate that this transition corresponds to the experimentally observed critical velocity, depen-dent on undercooling temperatureTf−Tp, below which the liquid is pinned and advances withstick-slip dynamics.The analytical solution of the model shows a qualitatively fair agreement withexperimental data. We discuss on the way to get better quantitative agreement, which in particularcan be obtained when the mesoscopic cut-off length is made temperature-dependent