Integral representation of channel flow with interacting particles.

@article{Fouxon2017IntegralRO,
  title={Integral representation of channel flow with interacting particles.},
  author={Itzhak Fouxon and Zhouyang Ge and Luca Brandt and Alexander M. Leshansky},
  journal={Physical review. E},
  year={2017},
  volume={96 6-1},
  pages={
          063110
        }
}
We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from the particles at horizontal distances exceeding the channel height and derive a multipole expansion of the flow which is dipolar to the leading approximation. We show that the dipole moment of an arbitrary particle is a weighted integral of the stress and the… 

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