Capillary Flows with Forming Interfaces: 1st Edition (Hardback) book cover

Capillary Flows with Forming Interfaces

1st Edition

By Yulii D. Shikhmurzaev

Chapman and Hall/CRC

480 pages | 131 B/W Illus.

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Hardback: 9781584887485
pub: 2007-09-14
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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.

Reviews

"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

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

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
SCI055000
SCIENCE / Physics
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical