Falling Liquid Films

Preface. -Acknowledgements. -Nomenclature. -Introduction. -Review of Phenomenology. -Modelling: state-of-the-art. -Structure of the book. -1 Flow and heat transfer. -1.1 Governing equations and boundary conditions. -1.2 Dimensionless equations, scalings and parameters. -1.3 The role of the Biot number. -1.4 Salient features. -1.5 References and further reading. -2 Primary instability. -2.1 Linear stability analysis. -2.2 Transverse disturbances. -2.3 Longtitudinal disturbances. -2.4 Mechanism of the hydrodynamic instability. -2.5 Salient features. -2.6 References and further reading. -3 Boundary layer-like approximation. -3.1 Boundary layer equations. -3.2 2D Boundary Layer Equations. -3.3 Strong surface tension limit. -3.4 Shkadov’s scaling. -3.5 Reduction of the governing equations. -3.7 Scalings: three sets of parameters. -3.8 Salient features. -3.9 References and further reading. -3.10 Appendix. -4 Methodologies for flows at low Re. -4.1 Long-wave asymptotic expansion. -4.2 Validity domain of the Benney equation. -4.3 Parametic study for closed and open flows. -4.4 Regularization a la Pade. -4.5 Comparison of the different one-equation models. -4.6 Weakly nonlinear models. -4.7 Salient features. -4.8 References and further reading. -4.9 Appendix. -4.10 Physical parameters. -4.11 Small Biot number, analogy with forced convection. -5 Methodologies for moderate Re. -5.1 Averaged two-equation models. -5.2 Relaxing the self-similar assumption. -5.3 Methods of weighted residuals. -5.4 First-order formulation. -5.5 Comparison of methods of weighted residuals. -5.6 Second-order formulation -5.7 Reduction of the full second order model. -5.8 Salient features. -5.9 References and further reading. -6 Isothermal case: 2D flow. -6.1 Linear stability analysis. -6.2 Travelling waves. -6.3 Spatial evolution of 2D waves. -6.4 Salient features. -6.5 References and further reading. -6.6 Appendix. -7 Isothermal case: 3D flow. -7.1 Phenomenology. -7.2 2D modelling of 3D film flows. -7.3 Floquet Analysis: 3D stability of 2D waves. -7.4 2D simulations of 3D flows. -7.5 Salient features. -7.6 References and further reading. -7.7 Appendix. -8 Interaction of 3D solitary waves. -8.1 A model system for low-dimensional complexity. -8.2 Speed of 3D solitary pulses. -8.4 Approximate analytical solution. -8.5 Coherent structures theory. -8.6 Salient features. -8.7 References and further reading. -9 Heated films. -9.1 Formulation. -9.2 Formulation at first order. -9.3 Reduced models. -9.4 Regularized model. -9.5 Linear stability results. -9.6 Solitary waves. -9.7 Refined models. -9.8 Three-dimensional wave patterns. -9.9 Salient features. -9.10 References and further reading. -9.11 Appendix. -10 Reactive falling films. -10.1 Problem definition and governing equations. -10.2 Long-wave theory. -10.3 Kapita-Shkadov model and weighted residuals. -10.4 Salient features. -10.5 References and further reading. -10.6 Appendix. -11 Outlooks. -11.1 What has been offered/achieved. -11.2 Open questions - Suggestions. -11.3 References and further reading. -Conclusions. -Bibliography. -Index. -Summary.