Capillary Flows with Forming Interfaces

Capillary Flows with Forming Interfaces

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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 more

Product details

  • Electronic book text | 480 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 500 equations; 8 Tables, black and white; 131 Illustrations, black and white
  • 1584887494
  • 9781584887492

Table of contents

PREFACEINTRODUCTION Free-surface flows in nature and industryScope of the bookFUNDAMENTALS OF FLUID MECHANICS Main concepts Governing equations Elements of thermodynamics Classical boundary conditions Physically meaningful solutions and paradoxes of modelingMOVING CONTACT LINES: AN OVERVIEW Essence of the problem Experimental observations Molecular dynamics simulations Review of theoriesThe key to the moving contact-line problemBOUNDARY CONDITIONS ON FORMING INTERFACES Modeling of interfacesConservation lawsLiquid-gas and liquid-solid interfacesLiquid-liquid interfaces SummaryOpen questions and possible generalizationsMOVING CONTACT LINES: MATHEMATICAL DESCRIPTION Flow in the immediate vicinity of a moving contact lineDynamic wetting at small capillary numbersDe-wetting and re-wettingComparison 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 issuesCUSPS, CORNERS AND COALESCENCE OF DROPS Singularities of free-surface curvature in experiments Conventional modeling"Missing" physics Singularity-free solution: cusp or corner? Coalescence of dropsBREAKUP OF JETS AND RUPTURE OF FILMS Background Drop formation: emerging singularityExperiments on capillary pinch-off"Missing" physics and its qualitative verification Axisymmetric capillary pinch-off: singularity-free solutionPinch-off from a molecular viewpoint Rupture of filmsSummaryAPPENDIX 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 INDICESshow more