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Integral representation of channel flow with interacting particles
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
2017 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 6, article id 063110Article in journal (Refereed) Published
Abstract [en]

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 flow at the particle surface, which can be determined numerically. We introduce the equation of motion that describes hydrodynamic interactions between arbitrary, possibly different, distant particles, with interactions determined by the product of the mobility matrix and the dipole moment. Further, the problem of three identical interacting spheres initially aligned in the streamwise direction is considered and the experimentally observed "pair exchange" phenomenon is derived analytically and confirmed numerically. For nonaligned particles, we demonstrate the formation of a configuration with one particle separating from a stable pair. Our results suggest that in a dilute initially homogenous particulate suspension flowing in a channel the particles will eventually separate into singlets and pairs.

Place, publisher, year, edition, pages
2017. Vol. 96, no 6, article id 063110
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Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-220595DOI: 10.1103/PhysRevE.96.063110ISI: 000417834600010Scopus ID: 2-s2.0-85038211455OAI: oai:DiVA.org:kth-220595DiVA, id: diva2:1175013
Note

QC 20180117

Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17Bibliographically approved

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Ge, ZhouyangBrandt, Luca

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