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Slow viscous flow of two porous spherical particles translatingalong the axis of a cylinder

Published online by Cambridge University Press:  28 December 2018

Xin Yao ,
Chyi Huey Ng ,
Jia Rui Amanda Teo ,
Marcos Open the ORCID record for Marcos [Opens in a new window]  and
Teck Neng Wong Open the ORCID record for Teck Neng Wong [Opens in a new window]
Xin Yao
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
Chyi Huey Ng
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
Jia Rui Amanda Teo
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
Marcos
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
Teck Neng Wong
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
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Abstract

We describe the motion of two freely moving porous spherical particleslocated along the axis of a cylindrical tube with background Poiseuille flowat low Reynolds number. The stream function and a framework based oncylindrical harmonics are adopted to solve the flow field around theparticles and the flow within the tube, respectively. The two solutions areemployed in an iterated framework using the method of reflections. We firstconsider the case of two identical particles, followed by two particles withdifferent dimensions. In both cases, the drag force coefficients of theparticles are solved as functions of the separation distance between theparticles and the permeability of the particles. The detailed flow field inthe vicinity of the two particles is investigated by plotting thestreamlines and velocity contours. We find that the particle–particleinteraction is dependent on the separation distance, particle sizes andpermeability of the particles. Our analysis reveals that when thepermeability of the particles is large, the streamlines are more paralleland the particle–particle interaction has less effect on the particlemotion. We further show that a smaller permeability and bigger particle sizegenerally tend to squeeze the streamlines and velocity contour towards thewall.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media Multiphase and Particle-laden Flows: Particle/fluid flow

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 643 - 678
Copyright
© 2018 Cambridge University Press 

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