Convection of binary fluid in a two-layer system with variable porosity under finite-frequency vibrations
DOI:
https://doi.org/10.17072/1994-3598-2018-2-58-67Keywords:
бинарная жидкость, неоднородная пористая среда, двухслойная система, модуляция поля тяжести, вибрации, синхронные и субгармонические колебания жидкостиAbstract
We consider a linear stability problem for the mechanical equilibrium in a system of two horizontal layers, one of which is filled with a binary fluid and the other contains a porous medium saturated with the fluid under gravity field. The layers oscillate vertically, with finite frequency and amplitude. The porous medium is inhomogeneous in the direction transverse to the layers. Linear equilibrium distributions of temperature and concentration in the layers are given. Taking into account the Floquet theory, we find the regions of parametric instability of equilibrium with respect to synchronous and subharmonic perturbations for various frequencies and amplitudes of vibrations. The numerical solution of the problem is obtained on the basis of shooting method and Galerkin method. It is shown that synchronous convective oscillations arise in the system heated from below in the limiting case of high-frequency vibrations. These vibrations stabilize the fluid equilibrium state. Convection occurs in a resonant manner and the stability threshold lowers monotonically as the frequency of vibration decreases and its amplitude increases. The change in the type of instability from the short-wave to long-wave ones, which are typical for layered systems, is observed with the variation of porosity gradient and buoyancy ratio. The latter defines a relative contribution of the concentration difference to the fluid density gradient. Short-wave convective rolls locate in the binary fluid layer with a low buoyancy ratio and are features of the medium with the porosity decreasing with depth. Long-wave rolls penetrate pores of the medium, which is saturated with the binary fluid of a high buoyancy ratio and has the porosity increasing with depth. It is determined that the short-wave parametric instability develops at the lower vibration amplitudes than their values in the case of the long-wave instability. The subharmonic fluid oscillations in the pores are possible at the vibration amplitudes, which are an order of magnitude larger than the amplitudes for the appearance of such oscillations in the fluid layer overlying the porous medium.References
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