Something as apparently simple as the shape of the water droplets on the wall after a shower may hide intriguing mathematical questions. In this book, the author provides a comprehensive exposition of the problems concerning the shape and dynamics of liquid droplets on surfaces as well as some of the applications that these issues entail.

The work is organized into nine chapters. They begin with the fundamentals of the Physics of liquid-air liquid-solid interfaces (surface and line tensions, free energy...). Then the problem of droplets on atomically flat, chemically homogeneous, isotropic, insoluble, nonreactive and non-deformed solid surfaces is tackled. This idealistic situation is useful for the contents of the following chapters, where more realistic surfaces are introduced: rough, heterogeneous or non-flat surfaces. This explain the title of the book. At the end of each chapter, the reader will appreciate the so-called bullets: a collection of short paragraphs giving the key points of that chapter.

The main mathematical machinery used by the author is Variational Calculus. Since the shape of droplets minimizes the free energy, some of the classical tools are applied, mainly for the determination of the liquid-solid contact angle. From this, hydrophilic, hydrophobic and other situations are analyzed.

Although the book does not contain sophisticated Mathematics, and taking into account that the book is intended to MSc or PhD students in Physics, Chemical Engineering or Material Sciences, a mathematician may still enjoy and take advantage of this work, specially if he/she is interested in modelization of interface phenomena.

Reviewer:

Marco Castrillon Lopez