Hydrodynamical description of first-order phase transitions: Analytical treatment and numerical modeling

TL;DR

This paper presents analytical and numerical solutions for hydrodynamical models of first-order phase transitions, focusing on seed dynamics, viscosity effects, and implications for nuclear systems and heavy-ion collisions.

Contribution

It provides a combined analytical and numerical framework for modeling seed growth and dissolution near first-order phase transitions, including viscosity and surface tension effects.

Findings

Seeds become spherical over time due to hydrodynamical evolution.

Viscosity and surface tension significantly influence seed dynamics.

Fluctuations are suppressed near the critical point due to viscosity and critical slowing down.

Abstract

Solutions of hydrodynamical equations are presented for an equation of state allowing for a first-order phase transition. The numerical analysis is supplemented by analytical treatment provided the system is close to the critical point. The processes of growth and dissolution of seeds of various sizes and shapes in meta-stable phases (like super-cooled vapor and super-heated liquid) are studied, as well as the dynamics of unstable modes in the spinodal region. We show that initially nonspherical seeds acquire spherical shape with passage of time. Applications to the description of the first-order phase transitions in nuclear systems, such as the nuclear gas-liquid transition occurring in low energy heavy-ion collisions and the hadron-quark transition in the high energy heavy-ion collisions are discussed. In both cases we point out the important role played by effects of viscosity and surface tension. It is shown that fluctuations dissolve and grow as if the fluid were effectively very viscous. Even in the spinodal region seeds may grow slowly due to viscosity and critical slowing down. This prevents the enhancement of fluctuations in the near-critical region, which is frequently considered as a signal of the critical point in heavy-ion collisions.