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Modeling Axisymmetric Flows


Author: Stanley Middleman

Publisher: Academic Press

Publish Date: 1st August 1995

ISBN-13: 9780080536637

Pages: 299

Language: English



This concise book is intended to fulfill two purposes: to provide an important supplement to classic texts by carrying fluid dynamics students on into the realm of free boundary flows; and to demonstrate the art of mathematical modeling based on knowledge, intuition, and observation. In the authors words, the overall goal is make the complex simple, without losing the essence–the virtue–of the complexity.Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops is the first book to cover the topics of axisymmetric laminar flows; free-boundary flows; and dynamics of drops, jets, and films. The text also features comparisons of models to experiments, and it includes a large selection of problems at the end of each chapter.

Table of Contents

Preface. Acknowledgements. Laminar Axisymmetric Flows Basic Dynamic and Kinematic Equations. Steady Fully Developed (Poiseuille) Flow. Flow through a Tube with a Variable Radius–The Lubrication Approximation. An IntegralTechnique for Solution of the Lubrication Equations. The Excess Pressure Loss across the Constriction. The Velocity Field through the Constriction. Flow through an Annular Region with a Variable Radius. Axisymmetric Flow through a Leaky Tube. LaminarFlow through a Tube with a Thin Annular Adherent Liquid Film Axisymmetric Flow through a Lubricated Tube. Removal of an Annular Liquid Layer by Shearing–A Quasi-steady Model. The Instability of a Static Annular Film of Liquid. The Deposition of a ThinAnnular Film of Liquid inside a Capillary. A More Careful Discussion of the Geometry and Dynamics of a Free Boundary Problem. Depletion of an Annular Liquid Film. Steady Laminar Axisymmetric Flow from a Tube: Exit Effects The Horizontal Jet. Draw-down of a Vertical Jet. A Note on Dimensionless Groups. The Transitions from Drops to a Coherent Jet and Back to Drops Dripping from a Vertical Tube. Drops on Demand. Stability of a Horizontal Jet. Linear Stability of an Inviscid Jet. Linear Stability of the Viscous Jet. A One-Dimensional Approximation to the Jet Equations. The Nonlinear Analysis of Jet Stability. Impingement of a Coherent Jet Normal to a Rigid Surface Introduction. A Boundary Layer Model (Watson, 1964). The Hydraulic Jump. Displacement of a Thin Viscous Film by an Impinging Turbulent Jet. Two-Fluid Homann Flow. Laminar Flow over a Disk. The Transfer of a Drop from a Capillary to an Impermeable Surface Introduction. Shape of a Static Drop. Breakaway of a Pendent Drop. Stability of an Axisymmetric Bridge. Impact of a Drop with a Solid Surface. The Isolated Drop on an Impermeable Surface Spreading of an Isolated Drop with No Surface Tension. Spreading of a Drop with Surface Tension. Capillary Penetration Dynamics Introduction. Capillary Wicking. Inertial Effects. Radial Penetration through a Narrow Planar Space. Penetration Fed by a Drop of a Finite Volume. Wicking of a Drop into a Porous Surface. Ultrathin Films: Disjoining Pressure Introduction. Effect of the Disjoining Pressure on Equilibrium Films. Dewetting. The Interaction of a Deformable Drop with a Surface The Approach of a Solid Sphere to a Rigid Plane. Slow Approach of a Viscous Drop to a Solid Surface. The Dimpled Drop. Film Evolution Equation for the Dimpled Drop. Inertial Effects in Film Thinning. Drops and Bubbles Crossing Liquid Interfaces. Coalescence of Drops and Bubbles. Afterword. Index.