Phase separation of binary fluids with dynamic temperature (original) (raw)
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Pattern study of thermal phase separation for binary fluid mixtures
International journal of numerical methods for heat and fluid flow, vol:21, iss:5 (2010), 2011
Purpose -The purpose of this paper is to present numerical results about phase separation of binary fluid mixtures quenched by contact with cold walls. Design/methodology/approach -The thermal phase separation is simulated by using a hybrid lattice Boltzmann method that solves the continuity and the Navier-Stokes equations. The equations for energy and concentration are solved by using a finite-difference scheme. This approach provides a complete description of the thermo-hydrodynamic effects in the mixture. Findings -A rich variety of domain patterns are found depending on the viscosity and on the heat conductivity of the mixture. Ordered lamellar structures are observed at high viscosity while domains rounded in shape dominate the phase separation at low viscosity, where two scales characterize the growth of domains.
Phase separation of incompressible binary fluids with lattice Boltzmann methods
Physica A: Statistical Mechanics and its Applications, 2004
We introduce new versions of lattice Boltzmann methods (LBM) for incompressible binary mixtures where fluctuations of total density are inhibited. As a test for the improved algorithms we consider the problem of phase separation of two-dimensional binary mixtures quenched from a disordered state into the coexistence region. We find that the stability properties of LBM are greatly improved. The control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent.
Phase-separating binary fluids under oscillatory shear
Physical Review E, 2003
We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time TR of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear. 05.70.Ln, 47.20.Hw, 47.11.+j, 83.10.Tv
EPL (Europhysics Letters), 2012
We investigate the effects of heat conduction, viscosity, and Prandtl number on thermal liquid-vapor separation via a lattice Boltzmann model for van der Waals fluids. The set of Minkowski measures on the density field enables to divide exactly the stages of the spinodal decomposition (SD) and domain growth. The duration tSD of the SD stage decreases with increasing the heat conductivity κT but increases with increasing the viscosity η. The two relations can be fitted by tSD = a + b/κT and tSD = c + dη + (eη) 3 , respectively, where a, b, c, d and e are fitting parameters. For fixed Prandtl number Pr, when η is less than a critical value ηc, tSD shows an inverse power-law relationship with η. However, when η > ηc, tSD for Pr > 1 shows qualitatively different behavior. From the evolution of the Péclet number Pe, the separation procedure can also be divided into two stages. During the first stage, the convection effects become more dominant with time over those of the diffusivity, while they are reverse in the second stage.
Phase separation in thermal systems: LB study and morphological characterization
We investigate thermal and isothermal symmetric liquid-vapor separations via a FFT-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 of 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 main reasons for the differences in thermal system. Different from the case with isothermal phase separation, 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 more quickly. The increasing of mean temperature makes lower the interfacial stress in the following way:
Dynamics of phase separation of sheared binary mixtures after a nonisothermal quenching
Physical Review Fluids
When a symmetric regular binary mixture, subjected to a constant shear, is quenched into the unsteady region of its phase diagram under a temperature gradient, it phase separates following very complicated patterns. The phase separation process is simulated using a thermodynamics-based phase-field model where the fundamental balance equations are coupled with the constitutive equations for the diffusive fluxes of chemical species, momentum, and energy by applying the rules of nonequilibrium thermodynamics. The evolution of phase separation shows distinct features, being more complex than a simple superposition of patterns emerging in a shear flow and under a thermal gradient when taken individually. The imposed temperature gradient causes a preferential nucleation at the cooler wall, so that the emerging droplets drift towards the center of the domain while following the imposed flow field, causing a change in droplet movement as they cross the domain centerline and enhancing coalescence. The imposed temperature gradient breaks the symmetry compared to instantaneous quenching, with stable droplets which remain attached to the cooler wall and move coherently with it. The capillary number (N Ca) determines breakup and phase separation evolving as stripes for N Ca 1, while droplets nucleate and grow for N Ca 1. The Lewis number (N Le) affects the pace and propagation of phase separation: for N Le > 10 phase separation takes place rather uniformly, being similar to instantaneous quenching, while for N Le < 0.1 the mixture cools slowly and a phase separation front proceeds from the cooler wall. A similar behavior is induced by a composition-dependent thermal conductivity. The mixture dimensionless heat capacity (N c) has a significant effect on phase separation because, for N c 1, heat dissipation counterbalances the effect of the applied temperature quench, thus retarding or even reversing the process of phase separation. These results and the variety of patterns reproduced by the model highlight the necessity of integrating a consistent thermodynamic description to the hydrodynamics and heat transport in phase-field modeling.
Enhanced heat transport during phase separation of liquid binary mixtures
Physics of Fluids, 2007
We show that heat transfer in regular binary fluids is enhanced by induced convection during phase separation. The motion of binary mixtures is simulated using the diffuse interface model, where convection and diffusion are coupled via a nonequilibrium, reversible Korteweg body force. Assuming that the mixture is regular, i.e., its components are van der Waals fluids, we show that the two parameters that describe the mixture, namely the Margules constant and the interfacial thickness, depend on temperature as T −1 and T −1/2 , respectively. Two quantities are used to measure heat transfer, namely the heat flux at the walls and the characteristic cooling time. Comparing these quantities with those of very viscous mixtures, where diffusion prevails over convection, we saw that the ratio between heat fluxes, which defines the Nusselt number, N Nu , equals that between cooling times and remains almost constant in time. The Nusselt number depends on the following: the Peclet number, N Pe , expressing the ratio between convective and diffusive mass fluxes; the Lewis number, N Le , expressing the ratio between thermal and mass diffusivities; the specific heat of the mixture, as it determines how the heat generated by mixing can be stored within the system; and the quenching depth, defined as the distance of the temperature at the wall from its critical value. In particular, the following results were obtained: ͑a͒ The Nusselt number grows monotonically with the Peclet number until it reaches an asymptotic value at N Nu Ϸ 2 when N Pe Ϸ 10 6 ; ͑b͒ the Nusselt number increases with N Le when N Le Ͻ 1, remains constant at 1 Ͻ N Le Ͻ 10, and then decreases when N Le Ͼ 1; ͑c͒ the Nusselt number is hardly influenced by the specific heat; ͑d͒ the Nusselt number decreases as the quenching rate increases. All these results can be explained by physical considerations. Predictably, considering that convection is within the creeping flow regime, the Nusselt number is always of o͑10͒.
Hydrodynamics of Binary Fluid Phase Segregation
Physical review letters, 2002
Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations ...