Dmitrii V. Lyubimov

Stability of plane-parallel vibrational flow in a two-layer system

Abstract The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved for both (a) inviscid and (b) viscous fluids. A transformation is found which reduces the linear stability problem under the inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.

Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed.

Vibration controlled convection — preparation and perspective of the Maxus 4 experiment

Abstract A comparatively new possibility to influence convection in crystal growth melts is the application of controlled interface vibration, especially in systems with free melt surfaces like the float-zone process. The present paper concerns the development and testing of a vibrational device which will be integrated into a microgravity crystal growth facility for the growth of silicon crystals. In the case of silicon grown by the float-zone technique, time-dependent thermocapillary convection is present even under mirogravity and leads to unfavourable variations of the crystal composition profile. The developed setup can operate in the range of approximately 0.1 to 50kHz producing maximum amplitudes of 0.25μm (non resonance case) and 3.5μm (resonance case) respectively. The power consumption is below 5W, the maximum operation temperature of the device is restricted to 200°C, limited by an epoxy-based connection between vibrator and sample. The first microgravity application will be during the European Maxus 4 campaign in April 2001.

The Effect of Solute Immobilization on a Stability of a Diffusion Front in Porous Media Under Gravity Field

In the present paper, we consider the effect of solute immobilization on a stability of planar diffusion front in gravity field. The case when heavy admixture diffuses from upper boundary into a bulk of semi-infinite domain of porous medium is investigated. In this situation, the base state formed by the diffusion corresponds to the layer of heavier liquid located above the lighter one. This unsteady base state is potentially unstable to the Rayleigh–Taylor fingering instability of front. The instability conditions are examined using the quasi-static method within the fMIM diffusion model. It is found that the immobilization results in the increase in the critical time for instability significantly, whereas the effect of immobilization on the critical wave number is weak. The stability maps in the parameter space are obtained.

Noise effect on convection generation in a modulated gravity field

The noise effect on the stability of equilibrium in systems with slowly varying parameters is investigated. With reference to some model examples and for the case of convection in a closed region in the presence of gravity modulation it is shown that taking the noise into account is of key importance at low modulation frequencies, since it can even change the sign of the effect: modulation leads to equilibrium stabilization in the absence of the noise and to destabilization in its presence.

Discretization of an admixture flux within the framework of the fractal model of anomalous diffusion

Within the framework of the fractal mobile-immobile medium model describing non-Fickian effects occurring in admixture seepage due to particle adhesion to the solid matrix, an expression for the admixture flux is derived. Flow discretization intended for finite-difference calculations is proposed and used as a basis for a conservation-law scheme for solving the model equations with account for admixture sources. Several one-dimensional test problems of admixture propagation in an imposed seepage flow are solved using the approach developed.