Ilya I. Ryzhkov

Benchmark values for the Soret, thermodiffusion and molecular diffusion coefficients of the ternary mixture tetralin+isobutylbenzene+n-dodecane with 0.8-0.1-0.1 mass fraction

With the aim of providing reliable benchmark values, we have measured the Soret, thermodiffusion and molecular diffusion coefficients for the ternary mixture formed by 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane for a mass fraction of 0.8-0.1-0.1 and at a temperature of 25°C. The experimental techniques used by the six participating laboratories are Optical Digital Interferometry, Taylor Dispersion technique, Open Ended Capillary, Optical Beam Deflection, Thermogravitational technique and Sliding Symmetric Tubes technique in ground conditions and Selectable Optical Diagnostic Instrument (SODI) in microgravity conditions. The measurements obtained in the SODI installation have been analyzed independently by four laboratories. Benchmark values are proposed for the thermodiffusion and Soret coefficients and for the eigenvalues of the diffusion matrix in ground conditions, and for Soret coefficients in microgravity conditions.Graphical abstract

On thermal diffusion and convection in multicomponent mixtures with application to the thermogravitational column

The theoretical framework for describing the multicomponent mixtures with the Soret effect is revised and extended. The separation ratio, a fundamental parameter characterizing the influence of thermal diffusion on convective phenomena, is generalized to the multicomponent case. It is shown how to define this parameter for a particular component of the mixture. To characterize multicomponent system as a whole, the net separation ratio Ψ, which does not depend on the choice of solvent, is introduced. Based on these results, the dimensionless equations for convection in multicomponent mixture are derived. The proposed formulation is applied to analyzing the steady state separation in the thermogravitational column (TGC). The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The distributions of velocity, temperature, and composition in a multicomponent system are found. The relevant parameters here are the solutal Rayleigh numbers, which char...

Experimental and theoretical study of vibration-induced thermal convection in low gravity

Vibrations acting on a fluid with density gradient induced by temperature variations can cause relative flows. High-frequency vibration leads to the appearance of time-averaged (mean) flows (or streaming flows), which can essentially affect heat and mass transfer processes. This phenomenon is most pronounced in the absence of other external forces (in particular, static gravity). In this work, an extensive experimental and computational study of thermal vibrational convection in a reduced-gravity environment of a parabolic flight is performed. The transient evolution of the temperature field in a cubic cell subjected to translational vibration is investigated by optical digital interferometry. The mean flow structures previously reported in numerical studies are confirmed. The transition from four-vortex flow to a pattern with a large diagonal vortex and two small vortices is observed in the transient state. The experiments reveal a significant enhancement of heat transfer by vibrational mean flows with increasing the vibrational strength. Three-dimensional direct numerical simulation with real microgravity profile and two-dimensional numerical modelling based on averaging approach provide a very good agreement with the experimental results. The influence of residual gravity on heat transfer and bifurcation scenario is first investigated numerically and correlated with the experimental data. It is demonstrated that gravity effects on non-uniformly heated fluids can be reproduced in weightlessness by applying vibrations to the system.

Long-wave instability of a multicomponent fluid layer with the Soret effect

The long-wave instability of a vertical multicomponent fluid layer is investigated. The basic state is a plane parallel flow with linear profiles of temperature and composition in the cross section. The compositional stratification is induced by the Soret effect. The problem is reduced to that without cross-diffusion effect by a linear change of composition and separation ratios that characterize the Soret separation. This is the first report where such transformation is derived for the equations of multicomponent convection with thermal diffusion. It simplifies the system reducing the number of control parameters and can be applied to a variety of multidiffusive convection problems (e.g., Rayleigh–Benard configuration). It is shown that the long-wave instability is caused by the interplay between the basic flow and concentration waves with long scale in the vertical direction. In the general case of n-component mixture, several stable regions in the parameter space are identified. A complete parametric s...

Contribution to the benchmark for ternary mixtures: Measurement of diffusion and Soret coefficients in 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane onboard the ISS

The paper is devoted to processing the data of DCMIX 1 space experiment. In this experiment, the Optical digital interferometry was used to measure the diffusion and Soret coefficients in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane at mass fractions of 0.8/0.1/0.1 and at 25°C. The raw interferometric images were processed to obtain the temporal and spatial evolution of refractive indices for two laser beams of different wavelengths. The method for extracting the diffusion and thermal diffusion coefficients originally developed for optical beam deflection was extended to optical digital interferometry allowing for the spatial variation of refractive index along the diffusion path. The method was validated and applied to processing the data for Soret and diffusion steps in 5 experimental runs. The obtained results for the Soret coefficients and one of the eigenvalues of diffusion matrix showed acceptable agreement within each step. The second eigenvalue was not determined with sufficient accuracy.Graphical abstract

Thermocapillary instabilities in liquid bridges revisited

The study of convective thermocapillary instabilities in liquid bridges [J. J. Xu and S. H. Davis, Phys. Fluids 27(5), 1102 (1984)] is revisited. A new branch of neutral mode m = 1 is found. The previously reported results are confirmed in the range of low Prandtl numbers. It is shown that for large Prandtl numbers, the flow becomes unstable at much smaller values of the Marangoni number than it was reported previously. The calculations are performed for adiabatic and heat conductive free surface. In both cases, the critical mode is m = 1. The previously reported change of critical mode from m = 1 to m = 0 with increasing the Prandtl number is not confirmed. The corrected results provide a better agreement with the experimental data.

On the separation of multicomponent mixtures in a cylindrical thermogravitational column

This work studies the stationary separation of a multicomponent mixture in a thermogravitational column (TGC). The existing theory for a flat-plate column is extended to the case of a cylindrical column. The equations of motion and heat/mass transfer are written in cylindrical coordinates to take into account the impact of the cylinders curvature and the ratio of their radii on the separation process. To characterize the impact of each component on convective motion induced by thermal diffusion, the dimensionless separation ratios are used. A multicomponent system as a whole is described by the net separation ratio. The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The profiles of velocity, temperature, composition, and density in the column with a multicomponent mixture are found and their dependence on the separation ratios and the ratio of cylinders radii is analyzed. The vertical separation is described by the solutal Rayleigh numbe...

Stationary and transient Soret separation in a binary mixture with a consolute critical point

Abstract.The stationary and transient Soret separation in a binary mixture with a consolute critical point is studied theoretically. The mixture is placed between two parallel plates kept at different temperatures. A polymer blend is used as a model system. Analytical solutions are constructed to describe the stationary separation in a binary mixture with variable Soret coefficient. The latter strongly depends on temperature and concentration and enhances near a consolute critical point due to reduced diffusion. As a result, a large concentration gradient is observed locally, while much smaller concentration variations are found in the rest of the layer. It is shown that complete separation can be obtained by applying a small temperature difference first, waiting for the establishment of stationary state, and then increasing this difference again. In this case, the critical temperature lies between hot and cold wall temperatures, while the mixture still remains in the one-phase region. When the initial (mean) temperature or concentration are shifted away from the near-critical values, the separation decreases. The analysis of transient behavior shows that the Soret separation occurs much faster than diffusion to the homogeneous state when the initial concentration is close to the critical one. It happens due to the decrease (increase) of the local relaxation time during the Soret (Diffusion) steps. The transient times of these steps become comparable for small temperature differences or off-critical initial concentrations. An unusual (non-exponential) separation dynamics is observed when the separation starts in the off-critical domain, and then enhances greatly when the system enters into the near-critical region. It is also found that the transient time decreases with increasing the applied temperature difference.Graphical abstract

The influence of nanoparticle migration on forced convective heat transfer of nanofluid under heating and cooling regimes

In this paper, laminar convective heat transfer of water-alumina nanofluid in a circular tube with uniform heat flux at the tube wall is investigated. The investigation is performed numerically on the basis of two-component model, which takes into account nanoparticle transport by diffusion and thermophoresis. Two thermal regimes at the tube wall, heating and cooling, are considered and the influence of nanoparticle migration on the heat transfer is analyzed comparatively. The intensity of thermophoresis is characterized by a new empirical model for thermophoretic mobility. It is shown that the nanoparticle volume fraction decreases (increases) in the boundary layer near the wall under heating (cooling) due to thermophoresis. The corresponding variations of nanofluid properties and flow characteristics are presented and discussed. The intensity of heat transfer for the model with thermophoresis in comparison to the model without thermophoresis is studied by plotting the dependence of the heat transfer coefficient on the Peclet number. The effectiveness of water-alumina nanofluid is analyzed by plotting the average heat transfer coefficient against the required pumping power. The analysis of the results reveals that the water-alumina nanofluid shows better performance in the heating regime than in the cooling regime due to thermophoretic effect.Graphical abstract

Finite Ion Size Effects on Electrolyte Transport in Nanofiltration Membranes

Received XX.10.2016, received in revised form XX.11.2016, accepted XX.12.2016 The pressure–driven electrolyte transport through nanofiltration membrane pores with specified wall potential is investigated theoretically. The finite ion size effect is taken into account by introducing an additional term to electrochemical potential. The two–dimensional Navier–Stokes, Poisson, and modified Nernst–Planck equations are solved numerically in a high aspect ratio nanopore connecting two reservoirs with a larger diameter. The calculations are performed for potassium chloride aqueous solution. In the case of point–like ions, the non–physical rise of counter–ion concentration is observed near the pore wall at large applied voltages. When finite ion size is taken in account, the concentration of counter–ions decreases significantly and saturates to the maximum value. It leads to lower osmotic pressure jump and larger magnitude of potential in the pore. The stronger co–ion depletion observed for finite size ions results in the increase of salt rejection, membrane potential, and required pressure drop. Taking into account the steric effect allows to calculate the characteristics of nanofiltration process in much wider range of applied voltages.