Phase separation in thermal systems: A lattice Boltzmann study and morphological characterization

Abstract

We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the local flow velocity depends not only on viscosity but also on temperature.

Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

“…Suppose R is the radius of the sphere, r and r ′ are radial distances of r and r ′ , and the spherical center is the coordinate origin. The Neumann's image principle [16] expresses the polarization potential as a line integral (See also [10,41] for recent work),…”

“…Usually two to three discrete points will provide a high accuracy to approximate the line integral [10,41]. In this section, our analysis focuses on the dependence on L, the levels of reflections.…”

“…The polarization due to interfaces remains a technical difficulty for particle-based computer simulations, and its algorithm development has attracted up-to-date attention [9][10][11][12]. Direct numerical solutions of the Poisson's equation with finite element methods [13] are intensive for Monte Carlo (MC) and molecular dynamics (MD) simulations (for a survey of electrostatic algorithm in sim- * Electronic address: xuzl@sjtu.edu.cn ulations, see [14]), and analytical solutions are only available for simple geometries such as one spherical interface or cylindrical interface where harmonics series expansions or methods of image charges [15][16][17][18][19] can be employed.…”

Lattice Boltzmann modeling and simulation of compressible flows

“…Compared with the hydrodynamic descriptions, both the SRT-LB and MRT-LB present new measurements for the deviations of systems from their thermodynamic equilibria. The LB model is being extended to study the compressibility effects, effects of shocking and detonation, thermal effects on the hydrodynamic instabilities [51] and multiphase flows [58][59][60], etc., which are all-important issues in science and engineering.…”

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

“…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].…”