Effects of nonlinear interfacial kinetics and interfacial thermal resistance in planar solidification

Abstract

Large temperature discontinuities were recently measured at a solid-liquid interface during heat transport processes. These observations suggest that when heat flows between two phases, the interface is not well characterized by assuming thermal equilibrium. This can be of importance in rapid solidification processes. In this paper we consider a planar front model that solidifies from its undercooled melt. We use a generalized interfacial boundary condition that includes nonlinear kinetic effects and allows for a temperature discontinuity. The effects of the new boundary condition on the solidification rates and the temperature profile are reported as a function of time. Our analysis shows that the undercooling regime where constant phase-front velocities are observed at steady states (traveling-wave solutions) are unaffected by the new boundary conditions. These solutions arise when the Stephan number is larger than 1. On the other hand, the solidification rates and the steady-state velocities are greatly affected by the assumed conditions at the interface. Incorporation of an interface thermal resistance, or Kapitza resistance, generates temperature discontinuities at the interface, leads to reduced solidification rates and the Mullins-Sekerka instability arises at longer wavelengths deformation of the planar front.

Boundary conditions and heat resistance at the moving solid–liquid interface

“…This expression generalizes the expression for the temperature jump found in Ref. [6] and reduces to it when L 3 = 0:…”

“…In the absence of the energy dissipation at the interface and for states close to equilibrium we have derived the expression for the temperature jump at the interface generalizing the previous result of Ref. [6]. The obtained expression, Eq.…”

“…Taking into account this experimental results, Palmieri et al [6] have supposed that the temperature discontinuity can also be essential at the moving phase interface, especially during fast solidification. These authors have considered influence of Kapitza resistance on the planar front dynamics during of solidification from undercooled state.…”

“…Therefore, in Eq. (6), µ is the chemical potential, ̺ is the mass density, h is the enthalpy and T ± are the boundary temperatures of phases. The heat flux in the normal direction to the interface is denoted as J ± qn = n • J ± q , where n is the unit vector to the interface and v s n = n • υ s is the normal component of the interface velocity.…”

“…In the linear approximation with respect to an equilibrium boundary conditions at the interface were obtained in Ref. [6] and present the set of Onsager relations. In these relations, the dissipative currents are the solidification rate and the energy flux through the interface and driving forces are interphase temperature jump and departure of the interfacial temperature from the equilibrium temperature T M of solidification.…”