Modeling Axisymmetric Flows

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.