Capillary surfaces. Shape -- stability -- dynamics, in particular under weightlessness. With a foreword by Ulf Merbold.
This book is a rich source of interesting problems in capillarity. A large number of described experiments and numerical results provide the reader with an impression what is going on in the recent research on capillarity. I consider the book as an important contribution in the field of fluid mechanics, and I am sure it will encourage researchers to work in this field. In particular, even for stationary problems, the justification of formal calculations is a challenge for mathematicians. The book is organized as follows: 1. Introduction. This chapter contains a short report about experiments on space missions, and some problems where capillary effects play a dominant role are described. 2. Interface tension and contact angle. It is pointed out that the theory of surface tension is still in a phenomenological state. Moreover, the static and dynamic contact angle, the problem of merging of drops and bubbles and the adhesion forces in liquid films are discussed. 3. Capillary shape and stability. In this chapter the capillary equation (Laplace, Young, Gauss) is derived, and some analytic solutions are considered. 4. Stability criteria. Stability is here by definition if all eigenvalues of an associated quadratic form are positive. Moreover, a minimum-volume condition as a sufficient condition for stability is discussed. 5. Axisymmetric liquid columns at rest und under rotation. The shape and stability of some axisymmetric capillary surfaces are investigated. 6. Liquid zones. This chapter is devoted to the interesting problems of liquid bridges between parallel plates and of double float zones. 7. Canthotaxis, wetting barriers, pinning lines. A series of problems like straight wetting barriers and liquid surfaces in wedges is considered, and numerical results are discussed. 8. Cylindrical containers. The question of the existence of zero gravity solutions is considered for cylindrical containers with a general cross-section. 9: Liquid surfaces in polyhedral containers. This chapter contains some interesting discussion about capillary surfaces in edges and corners of a container. 10. Playing with stability. So-called exotic containers are studied where unexpected behaviour of capillary surfaces occur. For example, it can happen that a continuum of solutions exits. Then the question arises which one is a stable solution. 11. Liquid penetration into tubes and wedges. In particular, the problem of dynamics of liquids in edges and corners is discussed. 12. Oscillations of liquid columns. Experimental results and numerical calculations are described. 13. Microgravity experiments in sounding rockets, spacelabs and EURECA. Finally, in this chapter a series of interesting experiments is listed.
scientific article; zbMATH DE number 2001589