Introduction -- Types of convective instabilities in systems with an interface -- Benard problem in multilayer systems with undeformable interfaces -- Benard problem in multilayer systems with deformable interfaces -- Stability of flows -- Outlook.

The interfacial convection is a widespread phenomenon which has numerous applications. This book describes the basic models of interfacial convection used on different spatial scales. It presents a variety of physical mechanisms and types of instability characteristic for liquid systems with interfaces. The book summarizes results obtained in the field of interfacial convection during a number of decades, including recent developments in exploration of microfluidic convective flows. The book will appeal to researchers and graduate students working in the field of fluid dynamics. It will help readers to master the mathematical approaches which are used for studying convective flows and understand the underlying physical phenomena. This new edition has been updated throughout and contains the significant progress achieved in studying phenomena in ultra-thin films, in systems with phase transitions, multicomponent systems, and nanosuspensions. Reviews of first edition: “In summary, the bulk of this book is excellent…If the authors could expand the content of chapters six and seven to give the same level of coverage as the first five chapters, this would be an even more valuable resource for mathematicians, physicists and engineers working on the stability of thermocapillary flows.” (Journal of Fluid Mechanics, 2007) “This monograph pulls together the large amount of very recent theoretical and experimental works related to interfacial convection in multilayer systems and is a valuable contribution.” (Mathematical Reviews, 2007)