Dynamical renormalization group calculation of a two-phase sharp interface model

Area of Science:

• Physics
• Materials Science
• Chemical Engineering

Background:

• Interface dynamics are crucial in phase transitions and material processing.
• Understanding growth regimes (quasistatic vs. rapid) is key to controlling material properties.

Purpose of the Study:

• To analyze the temporal evolution of interfaces separating two phases.
• To investigate the transition in growth exponents between quasistatic and rapid solidification regimes.

Main Methods:

• Renormalization group theory
• Scaling theory
• Exact calculation of a sharp interface model

Main Results:

• Under rapid solidification, characteristic length R(t) scales as t(1/2).
• Total interface surface area S(t) scales as t((d-1)/2).
• Observed transition in exponents complements prior quasistatic regime findings (R(t) ~ t).

Conclusions:

• The transition in growth exponents suggests a complex evolution towards self-similar late-stage growth.
• Findings provide insights into the fundamental mechanisms governing solidification dynamics.