M.Sc Student | Sarig Itai |
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Subject | Interaction between Droplets in a Hele-Shaw cell |

Department | Department of Mechanical Engineering |

Supervisors | Professor Yuli Starosvetsky |

Professor Amir Gat | |

Full Thesis text |

Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow micro-channels. Modeling the dynamics of such systems requires calculation of the forces of interaction between multiple droplets moving relatively to each-other and the surrounding fluid. These forces are commonly approximated by superposition of dipole solutions, which requires an assumption of sufficiently large distance between the droplets. Due to the lack of models of interaction forces between closely spaced droplets, dipole based models are used even for cases which violates the assumption of long distances between the droplets. In addition, some systems involve droplet within a droplet configurations, which were not previously modelled in a Hele-Shaw geometry, to the best of our knowledge. In this work we obtain exact solutions for interaction forces between two relatively moving droplets, and a droplet within a droplet, located within a moving immersing fluid in a Hele-Shaw cell, without limitation on the distance between the droplets. The analysis is performed in the framework of the Hele-Shaw limit, assuming shallow configurations 𝑔/𝑙 ∗ → 0, where 𝑔 is the channel height and 𝑙 ∗ is the characteristic length scale, thus volume forces such as inertia and body forces (gravity) are commonly negligible and the flow is governed by surface related effects such as capillarity and viscosity. Calculation of the forces is achieved by solution of the pressure field in a bi-polar coordinates system and calculation of the force in a Cartesian coordinates system. Our results are validated with numerical computations, experimental data and compared with the existing dipole-based models. We utilize the results to calculate the dynamics of a droplet within a droplet, and of two closely spaced droplets, located within an immersing fluid with a constant speed and oscillating speed. The obtained results may be used to study the dynamics of dense droplet lattices, common to many microfluidic systems.