Anatoliy Vorobev

Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number

Turbulent fluctuations in magnetohydrodynamic flows are known to become anisotropic under the action of a sufficiently strong magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds number using direct numerical simulations and large eddy simulations of a forced flow in a periodic box. A series of simulations is performed with different strengths of the magnetic field, varying Reynolds number, and two types of forcing, one of which is isotropic and the other limited to two-dimensional flow modes. We find that both the velocity anisotropy (difference in the relative amplitude of the velocity components) and the anisotropy of the velocity gradients are predominantly determined by the value of the magnetic interaction parameter. The effects of the Reynolds number and the type of forcing are much weaker. We also find that the anisotropy varies only slightly with the length scale.

Shapes and dynamics of miscible liquid/liquid interfaces in horizontal capillary tubes.

We report optical observations of the dissolution behaviour of glycerol/water, soybean oil/hexane, and isobutyric acid (IBA)/water binary mixtures within horizontal capillary tubes. Tubes with diameters as small as 0.2mm were initially filled with one component of the binary mixture (solute) and then immersed into a solvent-filled thermostatic bath. Both ends of the tubes were open, and no pressure difference was applied between the ends. In the case of glycerol/water and soybean oil/hexane mixtures, we managed to isolate the dissolution (the interfacial mass transfer) from the hydrodynamic motion. Two phase boundaries moving from the ends into the middle section of the tube with the speeds v∼D(1/3)t(-2/3)d(2) (D,t and d are the coefficient of diffusion, time and the diameter of the tube, respectively) were observed. The boundaries slowly smeared but their smearing occurred considerably slower than their motion. The motion of the phase boundaries cannot be explained by the dependency of the diffusion coefficient on concentration, and should be explained by the effect of barodiffusion. The shapes of the solute/solvent boundaries are defined by the balance between gravity and surface tension effects. The contact line moved together with the bulk interface: no visible solute remained on the walls after the interface passage. Changes in temperature and in the ratio between gravity and capillary forces altered the apparent contact angles. The IBA/water system had different behaviour. Below the critical (consolute) point, no dissolution was observed: IBA and water behaved like two immiscible liquids, with the IBA phase being displaced from the tube by capillary pressure (the spontaneous imbibition process). Above the critical point, two IBA/water interfaces could be identified, however the interfaces did not penetrate much into the tube.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

Modelling of the in-flight synthesis of TaC nanoparticles from liquid precursor in thermal plasma jet

A simple and efficient numerical model describing the processes of nucleation, growth and transport of multi-component nanoparticles is developed. The approach is conceptually similar to the classical method of moments but can be applied to co-condensation of several substances. The processes of homogeneous nucleation, heterogeneous growth, and coagulations due to Brownian collisions are considered in combination with the convective and diffusive transport of particles and reacting gases within multi-dimensional geometries. The model is applied to the analysis of multi-component co-condensation of TaC nanoparticles within a dc plasma reactor.

Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field

Instability and transition to turbulence in a temporally evolving free shear layer of an electrically conducting fluid affected by an imposed parallel magnetic field is investigated numerically. The case of low magnetic Reynolds number is considered. It has long been known that the neutral disturbances of the linear problem are three-dimensional at sufficiently strong magnetic fields. We analyse the details of this instability solving the generalized Orr–Sommerfeld equation to determine the wavenumbers, growth rates and spatial shapes of the eigenmodes. The three-dimensional perturbations are identified as oblique waves and their properties are described. In particular, we find that at high hydrodynamic Reynolds number, the effect of the strength of the magnetic field on the fastest growing perturbations is limited to an increase of their oblique angle. The dimensions and spatial shape of the waves remain unchanged. The transition to turbulence triggered by the growing oblique waves is investigated in direct numerical simulations. It is shown that initial perturbations in the form of superposition of two symmetric waves are particularly effective in inducing three-dimensionality and turbulence in the flow.

Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating

A theoretical model describing the response of a single-phase near-critical fluid to small-amplitude, high-frequency translational vibrations is developed on the basis of the multiple-scale and averaging methods. Additionally to the usual terms of thermal convection, the equations and boundary conditions contain new terms responsible for the generation of pulsating and average flows due to vibrational forcing and fluid compressibility. The effect of compressibility is taken into account both in the boundary layers and in the bulk. A number of classical problems of convection and thermoacoustics are considered on the basis of the new model.

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 droplets elongation along the tubes 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.

Linear stability of a horizontal phase boundary subjected to shear motion

We investigate the stability of slowly smearing phase boundary that appears at the contact of two miscible liquids. A hydrodynamic flow is imposed along the boundary. The aim is to find out whether the slow diffusive smearing of a boundary can be overrun by faster mixing. The phase-field approach is used to model the evolution of the binary mixture. The linear stability in respect to 2D perturbations is studied. If the heavier liquid lies above the lighter liquid, the interface is unconditionally unstable due to the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The imposed flow accelerates the growth of the long-wave modes and suppresses the growth of the short-wave perturbations. Viscosity, diffusivity and capillarity reduce the growth of perturbations. If the heavier liquid underlies the lighter one, the interface can be stable. The stability boundaries are defined by the strength of gravity (density contrast) and the intensity of the imposed flow. Thinner interfaces are usually characterised by larger zones of instability. The thermodynamic instability, identified for the thicker interfaces with the thicknesses greater than the thickness of a thermodynamically equilibrium phase boundary, makes such interfaces unconditionally unstable. The zones of instability are enlarged by diffusive and capillary terms. Viscosity plays its stabilising role.Graphical abstract

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 Ficks 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 (Stevar and Vorobev, 2012). 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 barodiffusion. 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.

Phase diagram of a binary mixture in a closed cavity

Normally, the phase diagram is reported as a property of the binary mixture. We show that the phase diagram (that is, the zones of thermodynamic stability of the states of the binary mixture) is also affected by the size of the container. We investigate the thermodynamic stability of the binary mixture in a closed cavity, and identify the zone in parameters where the binary mixture is heterogeneous in equilibrium (the zone of spinodal decomposition), the zone where the mixture is always homogeneous in equilibrium, and the zone where the transition between these two states is possible (the metastable nucleation zone). In addition, we investigate the properties of the smallest single droplet that may be in equilibrium in the closed cavity (for the given average concentration, all smaller droplets would always dissolve). We show that the size of such droplets depends on the cavitys size, as ∼L^{1/2}.