By A. Nepomnyashchy, I. Simanovskii, J.C. Legros
This publication includes a systematic research of the convection in structures with interfaces. For the 1st time, it classifies the entire identified different types of convective instabilities in such structures, and discusses the peculiarities of multilayer structures. The e-book offers an summary of the wide range of regular and oscillatory styles, waves, and different dynamic phenomena attribute for multilayer fluid platforms. quite a few actual results, together with warmth and mass move, thermal and mechanical couplings at the interfaces, interfacial deformability, the impression of surfactants on forms of convective motions are investigated. The textual content might be priceless for researchers and graduate scholars in fluid mechanics, nonlinear dynamics and utilized arithmetic in addition to for physicists and chemical engineers drawn to the research of the interfacial physico-chemical approaches and of their purposes.
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Extra resources for Interfacial Convection in Multilayer Systems (Springer Monographs in Mathematics)
2, are shown in Fig. 6(a). The monotonic instability of the mechanical equilibrium state generates an intensive convective motion in the top layer and a relatively weak motion in the bottom layer caused mainly by the viscous stresses that act at the interface (viscous or mechanical coupling). Note that the corresponding vortices in the top and bottom layers rotate in the opposite directions and the isotherms in both layers are distorted in the opposite way (see Fig. 6(b)). With the growth of G, beyond the boundary with respect to the bottom-layer instability (line 2a in Fig.
Similar arguments can be used for the explanation of the appearance of anticonvection in the case χ 1, β 1. Actually, the conditions for the excitation of the instability described above turned out to be rather restrictive, and in fact only one physical system satisfying these conditions was found (water / mercury). , 2002; Simanovskii, 2004). Assume that a constant heat release rate Q (Q may be positive or negative) is set at the interface z = 0. 35) A1 = − G(1 + κa) G(1 + κa) ✐ ✐ ✐ ✐ ✐ ✐ “main” — 2006/4/25 — 15:46 — page 34 — #42 ✐ 34 ✐ 2 Types of Convective Instability in Systems with an Interface (s = −1 for heating from above).
1/2 − ν 1/2 )2 Large Marangoni number. 52) is satisfied and the wave number k of the disturbance satisfies the inequality tanhk − ν 1/2 tanhka > 0. 53) are the conditions of the “survival” of the oscillatory instability for a fixed k in the limit M → ∞. 52) is violated, but in that case, inside the instability region there should exist a discriminant curve on which the frequency of oscillations becomes equal to zero. 52) is not satisfied. Note that in the case χ = 1, a = 1, there is no monotonic instability at all (see Sec.