Dynamics of traveling waves near the onset of convection in binary fluid mixtures

doi:10.1016/0167-2789(89)90140-1

Physica D: Nonlinear Phenomena

Volume 37, Issues 1–3, July 1989, Pages 319-333

https://doi.org/10.1016/0167-2789(89)90140-1 Get rights and content

Abstract

We report a study of oscillatory convection in ethanol/water mixtures in a rectangular container which is heated from below. For negative values of the separation ratio, Ψ, convection begins with a linear instability to a state of counterpropagating traveling waves. For sufficiently weak Ψ, the effects of propagation, nonlinear competition between waves traveling in opposite directions, and feedback due to endwall reflections lead to complex dynamical behavior just above the onset of convection. This regime is characterized by weak nonlinearity and small convective amplitudes. The observed states consist basically of a slow alternation between left- and right-going waves. However, the detailed character of these states is extremely sensitive to the geometry of the convection cell and the Rayleigh number. Many of these observations can be understood in terms of recent calculations using coupled Ginzburg-Landau equations which take into account the convective nature of the instability at low Rayleigh numbers.

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Beneficial effects of using a binary mixture on the performance of a heat pipe in microgravity have also been demonstrated [18]. There is a vast literature on convection in binary fluids driven by a vertical [19–22] temperature gradient, but almost all of it is devoted to nonvolatile liquids, where solutocapillary stresses arise due to the Soret effect [23] rather than differential phase change. We should also mention studies of the role of solutocapillary stresses in nucleate boiling [24], droplet evaporation [25], and thin film evaporation [26].
A horizontal temperature gradient can cause a flow in a layer of liquid with a free surface via several different mechanisms. The most universal one is due to thermocapillary stresses that arise due to the temperature dependence of surface tension. For binary liquids, the flow can also be driven by solutocapillary stresses that arise due to the dependence of surface tension on the composition of the liquid. For some binary liquids, such as water-alcohol mixtures, solutocapillary stresses are primarily due to phase change (e.g., differential evaporation or condensation of the two components), and these two mechanisms can counteract each other. A recent experimental study (Li and Yoda, 2016) has demonstrated that the flow direction can be reversed by changing the amount of air present inside the experimental apparatus. To understand how the presence of air affects the interfacial stresses, we have developed and implemented numerically a comprehensive two-sided transport model, which accounts for transport of heat, mass, and momentum in both phases and phase change across the interface and is able to reproduce the experimental results. The detailed analysis of these results shows that air tends to suppress phase change and hence solutocapillary stresses. Removing the air enhances phase change, instead suppressing the variation in the interfacial temperature and hence thermocapillary stresses.
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Dynamics of traveling waves near the onset of convection in binary fluid mixtures

Abstract

Phys. Rev. A

Phys. Rev. A

Phys. Rev. A

Physica D

Phys. Rev. A

Phys. Rev. A

Phys. Rev. A

Phys. Rev. A

J. Fluid Mech.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Nucl. Phys. B (Proc. Suppl.)

Nucl. Phys. B (Proc. Suppl.)

Phys. Rev. A