Valentina Shevtsova

Measurement of the Soret and diffusion coefficients for benchmark binary mixtures by means of digital interferometry

We report on the development of the optical digital interferometry (ODI) technique for measuring diffusion and Soret coefficients. The unique feature of this method is that it traces the transient path of the system in the entire two-dimensional cross section of a cell. In this way, it is applicable not only for measurements of Soret coefficients, but also for studying diffusive transport mechanism and convection. Presently, this method is not widely used and, in our view, not because of fundamental limitations but rather due to a lack of properly developed postexperimental procedures of the raw data analysis. Thus, in this paper our attention is focused on the successive analysis of different steps: the fringe analysis, the choice of reference images, the thermal design of the cell, and multiparameter fitting procedure. Using the ODI technique, we have measured the diffusion and the Soret coefficients for three binary mixtures composed of dodecane (C(12)H(26)), isobutylbenzene, and 1,2,3,4-tetrahydronaphtalene at a mean temperature of 25(∘)C and 50 wt. % in each component. These measurements were compared with their benchmark values and show an agreement within less than 3%.

A comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water-isopropanol mixtures

We report on the measurement of diffusion (D), thermodiffusion (D(T)), and Soret (S(T)) coefficients in water-isopropanol mixtures by three different instrumental techniques: thermogravitational column in combination with sliding symmetric tubes, optical beam deflection, and optical digital interferometry. All the coefficients have been measured over the full concentration range. Results from different instruments are in excellent agreement over a broad overlapping composition (water mass fraction) range 0.2 < c < 0.7, providing new reliable benchmark data. Comparison with microgravity measurements (SODI/IVIDIL (Selected Optical Diagnostic Instrument/Influence of VIbration on DIffusion in Liquids)) onboard the International Space Station and with literature data (where available) generally gives a good agreement. Contrary to theoretical predictions and previous experimental expectations we have not observed a second sign change of S(T) at low water concentrations.

OSCILLATORY CONVECTIVE MOTION IN DEFORMED LIQUID BRIDGES

The transition from two-dimensional thermoconvective steady flow to a time-dependent flow is considered for a liquid with a high Prandtl number (Pr=105) in a liquid bridge with a curved free surface. Both thermocapillary and buoyancy mechanisms of convection are taken into account. The computer program developed for this simulation transforms the original nonrectangular physical domain into a rectangular computational domain. To solve the problem in body-fitted curvilinear coordinates, the time-dependent Navier–Stokes equations were approximated by central differences on a stretched mesh. For liquid bridges with a flat interface, the instability corresponding to an azimuthal wave number of m=0 is not found for the investigated range of Marangoni numbers. The instability corresponding to an m=0 is found for relatively low Marangoni numbers only in liquid bridges with a nonflat, free surface, and nonzero Rayleigh number. The steady state becomes unstable to axially running waves. It is shown that the onset ...

Three-dimensional simulations of hydrodynamic instability in liquid bridges: Influence of temperature-dependent viscosity

The development of thermocapillary convection inside a cylindrical liquid bridge is investigated by using a direct numerical simulation of the three-dimensional (3D), time-dependent problem for a wide range of Prandtl numbers, Pr=1,3,4,5 and Pr=35. Above the critical value of temperature difference between the supporting disks, two counterpropagating hydrothermal waves bifurcate from the two-dimensional (2D) steady state. The existence of standing and traveling waves is discussed. The dependence of viscosity upon temperature is taken into account. The critical Reynolds number and critical frequency at which the system undergoes a transition from a 2D steady state to a 3D oscillatory flow decreases if the viscosity diminishes with temperature. The stability boundary is determined for Pr=3–5 with a viscosity contrast (νmax/νmin) up to a factor 10. Near the threshold of instability the flow organization is similar for the constant and variable viscosity cases despite the large difference in critical Reynolds...

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...

Influence of vibrations on thermodiffusion in binary mixture: A benchmark of numerical solutions

Double-diffusive and vibrational convection with the Soret effect is considered in a cubic rigid cell filled with water (90%) and isopropanol (10%), subjected to a temperature difference between opposite lateral walls. Numerical simulations are carried out for g-jitter induced flow. The direction of g-jitter is the same as the residual gravity vector, which is perpendicular to the applied temperature gradient. Along with various combinations of static and oscillatory components, vibrations with two different frequencies are examined: (a) when the period of oscillations is smaller than any characteristic time (viscous, thermal, and diffusion), f=0.2Hz; (b) when the period of oscillations is comparable with viscous time, f=0.01Hz. Component separation due to the Soret effect under these driving actions is analyzed. The concept of time-averaged models is applied for the explanation of the high-frequency results. The interplay between the mean and fluctuating motions is discussed. Three research groups perfor...

Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane

We present a comprehensive analysis of experimental results obtained for Fickian diffusion in the benchmark ternary liquid mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane (nC12) with equal mass fractions. Isothermal diffusion coefficients have been measured by two independent experimental methods: by Taylor dispersion technique, and by a counter flow cell fitted with an optical interferometry device. The experimental diffusion matrices have been critically analyzed regarding the Onsager reciprocal relations, for which we introduce a matrix asymmetry index s(2) that is independent of the frame of reference and the component order.

Diffusion, thermal diffusion, and Soret coefficients and optical contrast factors of the binary mixtures of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene.

We have measured the Soret (S(T)), diffusion (D), and thermal diffusion (D(T)) coefficients of the three binary benchmark mixtures of dodecane (C12), isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene at T = 25°C for at least five different concentrations each, covering the entire binary composition range. The two different optical techniques employed, optical beam deflection and optical digital interferometry, are in good to excellent agreement. Additionally, we have carefully measured the optical contrast factors (∂n/∂c)(p, T) and (∂n/∂T)(p, c). If the temperature and composition dependence of the mixture density is taken into account, both the Lorentz-Lorenz (LL) and the Looyenga (LO) equations give reasonable predictions of (∂n/∂c)(p, T). In case of (∂n/∂T)(p, c), only the LO equation yields good predictions in case of constant molecular polarizabilities α(i) of the pure compounds. If the apparent temperature dependence of α(i) is explicitly taken into account, excellent predictions are obtained both from the LL and the LO equations.

Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

The paper presents a three-dimensional numerical study of the bifurcations and onset of chaotic regime for the thermoconvective oscillatory flow in cylindrical liquid bridge. Three-dimensional Navier–Stokes equations in Boussinesq approximation are solved numerically by finite volume method. Silicone oil 1cSt, with rather large Prandtl number, Pr=18.8, is chosen as test liquid. The simulations are done at normal gravity conditions and unit aspect ratio. The dependence of viscosity of the fluid upon temperature allows us to be close to the real phenomenon. Both spatial and temporal changes occurring in the system are analyzed. The results are compared to the experimental data. A following sequence of well-defined dynamic regimes was detected when temperature difference between the supporting disks is increasing: steady, periodic, quasiperiodic, periodic, and chaotic. The observed succession of bifurcations on the way to chaos is similar to the one coming from experiments. Except for these dynamic bifurcati...