Effects of temperature on spinodal decomposition and domain growth of liquid-vapor systems with smoothed particle hydrodynamics

Abstract

We present a numerical method for simulations of spinodal decomposition of liquid-vapor systems. The results are in excellent agreement with theoretical predictions for all expected time regimes from the initial growth of "homophase fluctuations" up to the inertial hydrodynamics regime. The numerical approach follows a modern formulation of the smoothed particle hydrodynamics method with a van der Waals equation of state and thermal conduction. The dynamics and thermal evolution of instantaneously temperature-quenched systems are investigated. Therefore, we introduce a simple scaling thermostat that allows thermal fluctuations at a constant predicted mean temperature. We find that the initial stage spinodal decomposition is strongly affected by the temperature field. The separated phases react on density changes with a change in temperature. Although, the thermal conduction acts very slowly, thermal deviations are eventually compensated. The domain growth in the late stage of demixing is found to be rather unaffected by thermal fluctuations. We observe a transition from the Lifshitz-Slyozov growth rate with 1/3 exponent to the inertial hydrodynamics regime with a rate of 2/3, only excepted from simulations near the critical point where the liquid droplets are observed to nucleate directly in a spherical shape. The transition between the growth regimes is found to occur earlier for higher initial temperatures. We explain this time dependency with the phase interfaces that become more diffuse and overlap with approaching the critical point. A prolonging behavior of the demixing process is observed and also expected to depend on temperature. It is further found that the observations can excellently explain the growth behavior for pure nonisothermal simulations that are performed without thermostat.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics

“…Thus, it allows us to directly follow the path of the separated phases through the phase diagram. Furthermore, the characteristic lengths of the domains are easily calculated without difficult calculations via structure factor and Fourier transforms [6]. Our simulation method expands the fund of methods for realistic treatment of spinodal decomposition and provides deeper insights to the physics involved in phase separation processes.…”

“…A crossover between regimes has been found [23]. Moreover, there is also evidence for a connection between the actual local temperature and the time of initialization of the hydrodynamic regime, such that the regimes can even overlay each other [6]. Since many investigations and comparisons exist concerning this late stage and has become a well studied phenomenon, only few exist for the early stage.…”

“…and the heat term, which is the spatial derivative of heat flux and, therefore, a second derivative of the temperature [6,31,32]. It is given by (9) where…”

“…However, there is strong evidence for nonisothermal behavior [5,6]. Contrarily, very weak coupling allows for a pure thermal treatment of the system, consequentially followed by the latent heating of the system [5].…”

“…The set is closed by the vdW equation of state (EOS) [13,14]. This vdW approach naturally provides surface tension and can intrinsically form diffuse interfaces [6].…”