Chapman and Hall/CRC
480 pages | 131 B/W Illus.
Capillary Flows with Forming Interfaces explores numerous theoretical problems that arise in the mathematical description of capillary flows. It focuses on developing a unified approach to a variety of seemingly very different capillary flows of practical importance where classical fluid mechanics leads to nonphysical results.
The book begins with a review of the conceptual framework of fluid mechanics and then proceeds to analyze the roots of singularities, such as the moving contact-line problem and the capillary breakup problem. The author then examines how different singular flows can be described as particular cases of a general physical phenomenon of interface formation. He illustrates the developed mathematical models and experimentally verifies them through a number of example problems relevant to engineering applications.
The conceptual framework provided in this reference enables further progress in developing mathematical models of capillary flows.
The book also allows readers to make informed strategic choices regarding available numerical codes and the in-house development of these codes.
"Overall, this book is well written. Even the discussion of various models is attractive. For mathematicians interested in capillary flows, reading it would be useful, in order to avoid working on meaningless questions."
—Mathematical Reviews, Issue 2009g
Free-surface flows in nature and industry
Scope of the book
FUNDAMENTALS OF FLUID MECHANICS
Elements of thermodynamics
Classical boundary conditions
Physically meaningful solutions and paradoxes of modeling
MOVING CONTACT LINES: AN OVERVIEW
Essence of the problem
Molecular dynamics simulations
Review of theories
The key to the moving contact-line problem
BOUNDARY CONDITIONS ON FORMING INTERFACES
Modeling of interfaces
Liquid-gas and liquid-solid interfaces
Open questions and possible generalizations
MOVING CONTACT LINES: MATHEMATICAL DESCRIPTION
Flow in the immediate vicinity of a moving contact line
Dynamic wetting at small capillary numbers
De-wetting and re-wetting
Comparison with experiments and some estimates
Examples: flows in a quasi-static regime
Dynamic wetting at finite capillary numbers
Summary and outstanding modeling issues
CUSPS, CORNERS AND COALESCENCE OF DROPS
Singularities of free-surface curvature in experiments
Singularity-free solution: cusp or corner?
Coalescence of drops
BREAKUP OF JETS AND RUPTURE OF FILMS
Drop formation: emerging singularity
Experiments on capillary pinch-off
"Missing" physics and its qualitative verification
Axisymmetric capillary pinch-off: singularity-free solution
Pinch-off from a molecular viewpoint
Rupture of films
APPENDIX A: Elements of vector and tensor calculus
APPENDIX B: Equations of fluid mechanics in curvilinear coordinates
APPENDIX C: Complex representation of biharmonic functions
APPENDIX D: Physical properties of some fluids