Abstract
A conceptual and mathematical framework for the singularity-free modeling of non-equilibrium solidification/melting and non-isothermal dynamic wetting is developed where both processes are embedded into a broader class of physical phenomena as particular cases. This allows one to consider problems describing fluid flows with phase transitions and dynamic wetting occurring independently or interactively in a regular conceptually consistent way without ad hoc assumptions. The simplest model formulated on the basis of this approach explains, at this stage qualitatively, the arrest of the moving contact line observed experimentally in the impact and spreading of a molten drop on a cold substrate. The classical Stefan problem and the model of isothermal dynamic wetting as an interface formation process are recovered as limiting cases.
Highlights
A conceptual and mathematical framework for the singularity-free modeling of non-equilibrium solidification/melting and non-isothermal dynamic wetting is developed where both processes are embedded into a broader class of physical phenomena as particular cases
IV, we show how it reduces to the Stefan model and the model for isothermal dynamic wetting as limiting cases
Since Wilson’s pioneering formula[34] proposed in 1900 and still in use today in continuum mechanics under the name of “kinetic undercooling,”[35,36] all theories of solidification in physical chemistry are aimed at expressing the velocity at which the solidification front propagates as a function of the temperature at the front, various activation energies, energy of growth, configurational entropy, enthalpy, and other such concepts
Summary
Dynamic wetting and solidification come together in a number of situations, both in natural phenomena and in various technologies. These schemes of the process have been, first, questioned by de Ruiter et al.[5] who observed that “as shown by both the spreading radius and the contact angle data, the drop dynamics prior to arrest is experimentally indistinguishable from isothermal spreading without solidification” so that “the motion of the contact line is completely unaffected by the cooling prior to the arrest.” This would not have been the case should the flow geometry near the contact line continuously vary due to the solidification front having its edge at the contact line and increasing its slope, as in Refs. VII, we put the developed framework into a broader modeling context from the continuum mechanics and physical chemistry perspective and discuss some of the assumptions made in the derivation of the simplest model and possible ways of its generalization
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