Dynamics of binary mixtures in inhomogeneous temperatures

Abstract

A dynamical description for fluid binary mixtures with variable temperature and concentration gradient contributions to entropy and internal energy is given. By using mass, momentum and energy balance equations together with the standard expression for entropy production, a generalized GibbsDuhem relation is obtained which takes into account thermal and concentration gradient contributions. Then an expression for the pressure tensor is derived. As examples of applications, interface behavior and phase separation have been numerically studied in two dimensions neglecting the contributions of the velocity field. In the simplest case with a constant thermal gradient, the growth exponent for the averaged size of domains is found to have the usual value z = 1/3 and the domains appear elongated in the direction of the thermal gradient. When the system is quenched by contact with external walls, the evolution of temperature profiles in the system is shown and the domain morphology is characterized by interfaces perpendicular to the thermal gradient.

Spreading with evaporation and condensation in one-component fluids

“…[32]). In particular, some authors numer-ically studied liquid-liquid phase separation in heat flow [31,36,40,44], but these authors treated symmetric binary mixtures without latent heat. Recently, one of the present authors developed a phase field model for compressible fluids with inhomogeneous temperature, which is called the dynamic van der Waals model [41,42].…”

Flow of Deformable Droplets: Discontinuous Shear Thinning and Velocity Oscillations

“…We consider flow in a channel with no-slip boundary conditions at the top and bottom walls. The flow is driven by a fixed, externally imposed pressure difference, leading to Poiseuille flow in an isotropic fluid, and neutral wetting boundary conditions for each of the droplets [25] (see SI). Parameters used are listed in the SI, together with Reynolds and capillary numbers, and values of ∆p in what follows are given in simulation units.…”

Phase separation of binary fluids with dynamic temperature

“…is the dissipative stress tensor with ζ, η being the bulk and shear viscosities, respectively, d the space dimension, and e = e + K 2 |∇ϕ| 2 the total internal energy density also including gradient contributions. We have recently established the expressions for the pressure tensor Π αβ and chemical potential µ [23] following the approach of Ref. [21].…”

“…). It is therefore more convenient for our purposes to introduce the Schmidt and Prandtl numbers Sc and P r defined as Sc = ν/D and P r = ν/k,where D = |a|Γ with a = (k B T c /n)(T /T c − 1)being the coefficient of the linear term in the chemical potential µ[5,23]. Here T can be chosen as the value of the temperature at the walls.Table Icontains a list of the runs we did, reported in terms of Sc and P r. It is also useful to evaluate the Mach number Ma = |v| max /c s where |v| max is the maximum value of the fluid velocity during evolution.…”