Capillary Flows with Forming Interfaces

Published:
September 14, 2007 by Chapman and Hall/CRC - 480 Pages
Author(s):
Yulii D. Shikhmurzaev, University of Birmingham, UK

Purchasing Options

Hardback
$94.95
Add to cart
ISBN 9781584887485
Cat# C7486
 

Features

  • Discusses capillary flows where the conventional mathematical modeling leads to nonphysical singularities
  • Examines the advantages and disadvantages of various theoretical approaches to modeling singular flows
  • Develops a unified approach to the mathematical description of singular capillary flows and provides simple, ready-to-use, experimentally verified models along with solutions that illustrate thee models' application to problems of practical importance
  • Includes topics rarely covered in standard texts, such as assumptions behind boundary conditions, the Lagrangian representation of the equations of motion, and the use of the Airy stress function for Stokes flows
  • Presents logical connections between different phenomena with summaries that outline the main points, ensuring a full, practical understanding of the material
  • Reviews the necessary mathematics in several appendices

    • Summary

    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.

    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

    Editorial 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

    Related Titles