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Über dieses Buch

This book gives a systematic investigation of convection in systems comprised of liquid layers with deformatable interfaces.

This new edition includes completely updated and new material on flows in ultra thin films and brings up to date progress made in the technology on micro and nano scales. Also, this revised edition will reflect progress in the dynamics of complex fluids.



1. Introduction. Models of Interfacial Convection

In the present chapter, the models used for the description of interfacial convection on different scales are discussed. We start with the consideration of classical large-scale models based on the sharp-interface approach and macroscopic conservation laws. The main physical mechanisms that produce interfacial convection, the dependence of fluid density and surface tension on temperature, and the composition of the fluid are considered. Then we introduce the models for the description of ultrathin-film dynamics, which are based on lubrication approximation and incorporate intermolecular forces. Also, some mesoscopic models are presented. In conclusion, we briefly describe microscopic approaches used for modeling interfacial phenomena.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

2. Types of Convective Instability in Systems with an Interface

In this chapter, we present a brief description of the linear stability approach and discuss the problem of nonlinear pattern selection for stationary and wavy patterns. Then we discuss different types of convective instability characteristic for systems with an interface. As the basic model, we use the two-layer model (see Section 1.2.3).

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

3. Bénard Problem in Multilayer Systems with Undeformable Interfaces

In the previous chapter, we studied convection in systems with a


interface. Now we begin the investigation of the case that the fluid system has


interfaces. We will see that the interaction between different interfaces leads to the appearance of qualitatively new types of instability. In the present chapter, we will consider the case that the deformations of interfaces are negligible. The influence of the interfaces’ deformations will be analyzed in Chapter 4.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

4. Bénard Problem in Multilayer Systems with Deformable Interfaces

The present chapter is devoted to the investigation of phenomena related to deformations of interfaces. As explained in Chapter 1, these phenomena take place at finite values of the Galileo number


; thus, the Grashof number


has to be set equal to zero. In Section 4.1, we recall the formulation of the problem previously presented in Section 1.2.4. Section 4.2 contains the results of the linear stability analysis. In Section 4.3 we derive and simulate the longwave amplitude equations that describe the interaction between the deformations of both interfaces.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

5. Stability of Flows

In the present chapter, the stability of convective flows in multilayer systems is considered. First, we will discuss general mechanisms of instabilities for flows generated by a surface-tension gradient applied along the surface (Section 5.1). Then, we present a linear analysis of thermocapillary flows in two-layer systems subject to an inclined temperature gradient (Section 5.2). Results of the investigation of buoyancy-thermocapillary convection in two-layer and three-layer systems are given in Sections 5.3 and 5.4, respectively. Section 5.5 contains an analysis of deformational instabilities of thermocapillary flows in three-layer systems.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

6. Flows in Ultrathin Two-Layer Films

As explained in Section 1.5, the dynamics of very thin films (with the thickness less than 100 nm) needs a special approach: it is strongly affected by intermolecular forces. The present chapter is devoted to a systematic description of recent results obtained in that field.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros

7. Outlook

The theory of interfacial convection contains many branches which are beyond the scope of the present book. In this chapter, we present an outlook of the most important scientific directions and new tools of the investigation.

Alexander Nepomnyashchy, Ilya Simanovskii, Jean Claude Legros


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