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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.

This self-contained book explores various theoretical problems that arise in the mathematical description of capillary flows, such as the spreading of liquids on solids and the formation of drops, where conventional modeling leads to nonphysical singularities. It examines the advantages and disadvantages of theoretical approaches to modeling singular flows and identifies a common physical mechanism behind seemingly different singular capillary phenomena. This unifying approach forms the basis for simple, ready-to-use, experimentally verified models along with many solutions that illustrate the models' application to problems of practical importance.

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PREFACE

INTRODUCTION 
Free-surface flows in nature and industry
Scope of the book

FUNDAMENTALS OF FLUID MECHANICS 
Main concepts 
Governing equations 
Elements of thermodynamics 
Classical boundary conditions 
Physically meaningful solutions and paradoxes of modeling

MOVING CONTACT LINES: AN OVERVIEW 
Essence of the problem 
Experimental observations 
Molecular dynamics simulations 
Review of theories
The key to the moving contact-line problem

BOUNDARY CONDITIONS ON FORMING INTERFACES 
Modeling of interfaces
Conservation laws
Liquid-gas and liquid-solid interfaces
Liquid-liquid interfaces 
Summary
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 
Liquid-liquid displacement 
Summary and outstanding modeling issues

CUSPS, CORNERS AND COALESCENCE OF DROPS 
Singularities of free-surface curvature in experiments 
Conventional modeling
"Missing" physics 
Singularity-free solution: cusp or corner? 
Coalescence of drops

BREAKUP OF JETS AND RUPTURE OF FILMS 
Background 
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
Summary

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 

REFERENCES 

INDICES

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