Phase-field modelling of a miscible system in spinning droplet tensiometer

The spinning drop tensiometry is used for measurements of surface tension coefficients, especially, when interfaces are characterised by low and ultra-low interfacial stresses. A droplet of lighter liquid is introduced into a rotating capillary that was initially saturated with another heavier liquid. The tube is subject to axial rotation that results in droplet’s elongation along the tube’s axis. The equilibrium shape of the droplet is used to determine the surface tension coefficient. In this work, the evolution of a slowly miscible droplet introduced into a spinning capillary is investigated. This technique is frequently employed for studies of the dynamics of miscible systems, even despite the fact that a strict equilibrium is never achieved in a mixture of fully miscible liquids. The numerical modelling of a miscible droplet is fulfilled on the basis of the phase-field (Cahn-Hilliard) approach. The numerical results are compared against the experimental data pursuing two objectives: (i) to verify the use of the phase-field approach as a consistent physics-based approach capable of accurate tracking of the short- and long-term evolution of miscible systems, and (ii) to estimate the values of the phenomenological parameters introduced within the phase-field approach, so making this approach a practical tool for modelling of thermohydrodynamic changes in miscible systems within various configurations

Drop motion during mass transfer accompanied by interphase convection

The article deals with the experimental study of the mass transfer of acetic acid from the dispersed phase (butyl acetate) to the continuous phase (water). The experiments were carried out on a laboratory column with single floating drops. The presence of the Marangoni effect during the movement of drops and its influence on the trajectories of movement of drops and the kinetics of mass transfer during extraction are shown. The influence of the Marangoni effect is most clearly observed when the driving force of the process is 0.1...0.2 mol/l

Linear stability analysis of a horizontal phase boundary separating two miscible liquids

The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable.We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths

Instabilities in extreme magnetoconvection

Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and Lorentz forces are very strong. It is argued that the instabilities occurring in such flows are often of unique and counter-intuitive nature due to the action of the magnetic field, which suppresses conventional turbulence and gives preference to two-dimensional instability modes not appearing in more conventional convection systems. Tools of numerical analysis suitable for such flows are discussed

Smagorinsky constant in LES modeling of anisotropic MHD turbulence

Turbulent fluctuations in magnetohydrodynamic (MHD) flows can become strongly anisotropic or even quasi-2D under the action of an applied magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds numbers. It has been found in earlier DNS and LES of homogeneous turbulence that the degree of anisotropy is predominantly determined by the value of the magnetic interaction parameter and only slightly depends on the Reynolds number, type of large-scale dynamics, and the length scale. Furthermore, it has been demonstrated that the dynamic Smagorinsky model is capable of self-adjustment to the effects of anisotropy. In this paper, we capitalize on these results and propose a simple and effective generalization of the traditional non-dynamic Smagorinsky model to the case of anisotropic MHD turbulence

Dissolution behaviour of a binary mixture in a capillary tube

We develop a pore-level physical model for the process of miscible displacement through porous media. Using the network model, the current task is reduced to the study of the dissolution dynamics of a binary mixture within a single capillary tube. Tubes of rather small diameters are considered when the typical diffusion and convective time scales are comparable. The test tube filled with the solute is immersed into the solvent-filled thermostatic bath; no pressure difference between the ends of the tubes is applied. Using a high-resolution video-camera, we study the solvent penetration into the test tube. We examine the evolution of the isobutyric acid/water mixture far from and close to the critical (consolute) point (which is 26C for this mixture). The mixture fills the circular glass tubes of diameters 0.4mm-0.8mm and of various lengths. The shape of the interface and its position are tracked and analysed. Based on our observations the following conclusions can be drawn. In all experiments, we observe a front-type propagation of the solvent phase into the tube with a clearly visible interface. The gravity force significantly affects the shape of the interface and the dissolution dynamics in all undertaken experiments. If the mixture temperature is below the critical point, then the uneven one-sided penetration of the solvent into the tube was consistently observed. The solute/solvent interface experiences oscillations of its shape (being either concave or convex at different time moments). If the mixture temperature is above the critical point, then the solvent penetrates evenly from both ends. In both under- and supercritical conditions, the contact line moves with the same speed as the interface, but the apparent contact angle is time- and coordinate-dependent. The rate of the interface propagation varies at different stages of the dissolution process and does not follow the predictions of the diffusion theory

On the phase-field modelling of a miscible liquid/liquid boundary

Mixing of miscible liquids is essential for numerous processes in industry and nature. Mixing, i.e. interpenetration of molecules through the liquid/liquid boundary, occurs via interfacial diffusion. Mixing can also involve externally or internally driven hydrodynamic flows, and can lead to deformation or disintegration of the liquid/liquid boundary. At the moment, the mixing dynamics remains poorly understood. The classical Fick's law, generally accepted for description of the diffusion process, does not explain the experimental observations, in particular, the recent experiments with dissolution of a liquid solute by a liquid solvent within a horizontal capillary \cite{Stevar2012}. We present the results of the numerical study aimed at development of an advanced model for the dissolution dynamics of liquid/liquid binary mixtures. The model is based on the phase-field (Cahn-Hilliard) approach that is used as a physics-based model for the thermo- and hydrodynamic evolution of binary mixtures. Within this approach, the diffusion flux is defined through the gradient of chemical potential, and, in particular, includes the effect of barodiffisuon. The dynamic interfacial stresses at the miscible interface are also taken into account. The simulations showed that such an approach can accurately reproduce the shape of the solute/solvent boundary, and some aspects of the diffusion dynamics. Nevertheless, all experimentally-observed features of the diffusion motion of the solute/solvent boundary, were not reproduced

Dissolution dynamics of miscible liquid/liquid interfaces

The recent achievements gained in understanding of the dissolution dynamics of miscible interfaces are reviewed. Our consideration is restricted to isothermal systems with the mass transfer purely driven by inhomogeneities in the field of concentration. Both experimental and theoretical works are examined. The attention is given to the effects of dynamic surface tension, interfacial diffusion, dynamics of the contact line, and to solutal convective flows. We conclude that, despite ubiquitousness and importance of physical processes involving miscible interfaces, the physics that defines the thermo- and hydrodynamic evolution of such interfaces is still not properly understood, especially in respect to dissolution rate at a miscible liquid/liquid phase boundary and to wetting properties at liquid/solid boundary. A consistent theoretical description for the slowly miscible binary systems is given within the phase-field (Cahn–Hilliard) approach. Nevertheless, there are just a few modelling works that take into account all the effects pertinent to miscible liquid/liquid interfaces