Capillary Flows with Forming Interfaces
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Capillary Flows with Forming Interfaces

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Description

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.
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Product details

  • Hardback | 480 pages
  • 156 x 236 x 24mm | 821g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 500 equations; 8 Tables, black and white; 131 Illustrations, black and white
  • 1584887486
  • 9781584887485

Table of contents

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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About Yulii Damir Shikhmurzaev

University of Birmingham, UK
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