## Capillary Flows with Forming InterfacesCapillary 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. |

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### Contents

1 | |

Fundamentals of fluid mechanics | 9 |

Moving contact lines An overview | 97 |

Boundary conditions on forming interfaces | 177 |

Moving contact lines Mathematical description | 221 |

Cusps corners and coalescence of drops | 287 |

Breakup of jets and rupture of films | 341 |

Elements of vector and tensor calculus | 397 |

Equations of fluid mechanics in curvilinear coordinates | 407 |

Complex representation of biharmonic functions | 411 |

Physical properties of some fluids | 413 |

415 | |

445 | |

453 | |

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### Common terms and phrases

assumptions asymptotic becomes boundary conditions breakup bulk phases capillary number capillary pressure coalescence coefficients components consider constant contact-line speed continuum approximation continuum mechanics corresponding curves cusp dependence described distributions drop dynamic contact angle dynamic wetting effect equilibrium experimental experiments film finite flow field flow geometry fluid mechanics fluid particles flux forces acting formulation framework free surface given gradient hence hydrodynamic interface formation interfacial layer intermolecular forces kinematics Lagrangian coordinates leading order length scale liquid liquid-gas liquid-solid interface macroscopic Marangoni effect mass mathematical molecular molecules momentum motion moving contact line moving contact-line problem Navier-Stokes equations no-slip condition normal obtained physical properties qualitative Shikhmurzaev singularity slip models solid boundary solid substrate solid surface solution standard model stream function stress tensor surface density surface parameters surface phase surface tension theory thermodynamic thickness thread variables vector velocity viscosity zero

### Popular passages

Page 416 - Bascom, WD, Cottington, RL, and Singleterry, CR (1964), Dynamic surface Phenomena in the spontaneous spreading of oils on solids, in Contact Angle, Wettability and Adhesion, RF Gould, ed., ACS Advances in Chemistry Series No.

Page ix - How wonderful we have met with a paradox, now we have some hope of making progress - Niels Bohr.

Page 420 - Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245-267.

Page 418 - An Experimental Study of Air Entrainment at a Solid/Liquid/Gas Interface", Chem. Eng. Sci. 31, 901-911 (1976). Burley, R. and RPS Jolly, AIChE J. 29, 172-173 (1983). Burley R. and RPS Jolly. "Entrainment of Air Into Liquids by a High Speed Continuous Solid Surface", Chem. Eng. Sci. 39, 1357-1372 (1984).

Page 417 - SHIKHMURZAEV, YD 1999 Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle. Phys. Fluids 11, 1995-2007.

Page 418 - The distribution of velocities in a slightly non-uniform gas, Proc.