## The Kinematics of Mixing: Stretching, Chaos, and TransportIn spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included. |

### Contents

Introduction | 1 |

Computation of stretching and efficiency | 4 |

Flow trajectories and deformation | 18 |

Conservation equations change of frame and vorticity | 42 |

6 | 87 |

Bibliography | 94 |

Chaos in Hamiltonian systems | 130 |

Mixing and chaos in twodimensional timeperiodic flows | 154 |

Mixing and chaos in threedimensional and open flows | 220 |

diffusion and reaction in lamellar structures | 273 |

Cartesian vectors and tensors | 319 |

List of frequently used symbols | 342 |

355 | |

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### Common terms and phrases

analysis average behavior blob breakup calculate called chaotic Chapter complex components computations Consider constant continued corresponding cycle defined definition deformation denoted diffusion direction discussed distribution drop effects efficiency eigenvalues elements elliptic equations example experimental experiments Figure fixed flow fluid mechanics frame function given gives Hamiltonian systems hyperbolic important indicated initial conditions integrable length linear manifolds mapping material means measure mixer mixing motion moving Note obtain orientation Ottino particle periodic points perturbation picture placed Poincaré sections position possible present Problem produce reaction reference region represents respect rotation scales shear shown shows similar simple solution space stable steady streamlines stretching striation structure surface tensor theorem thickness transformation turbulent two-dimensional unstable v₁ vector velocity field viscous volume vortex vorticity wall x₁