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Near-wall dynamics of a neutrally buoyant spherical particle in an axisymmetric stagnation point flow

Published online by Cambridge University Press:  06 April 2020

Qing Li ,
Micheline Abbas Open the ORCID record for Micheline Abbas [Opens in a new window] ,
Jeffrey F. Morris Open the ORCID record for Jeffrey F. Morris [Opens in a new window] ,
Eric Climent  and
Jacques Magnaudet Open the ORCID record for Jacques Magnaudet [Opens in a new window]
Qing Li
Affiliation:
Laboratoire de Génie Chimique, CNRS-Toulouse INP-UPS Université de Toulouse, 4 Allée Emile Monso, 31432Toulouse, France Institut de Mécanique des Fluides de Toulouse, CNRS-Toulouse INP-UPS Université de Toulouse, Allée Camille Soula, 31400Toulouse, France FR FERMAT, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Micheline Abbas*
Affiliation:
Laboratoire de Génie Chimique, CNRS-Toulouse INP-UPS Université de Toulouse, 4 Allée Emile Monso, 31432Toulouse, France FR FERMAT, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Jeffrey F. Morris
Affiliation:
Benjamin Levich Institute and Department of Chemical Engineering, The City College of New York, New York, NY10031, USA
Eric Climent
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS-Toulouse INP-UPS Université de Toulouse, Allée Camille Soula, 31400Toulouse, France FR FERMAT, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
Jacques Magnaudet
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS-Toulouse INP-UPS Université de Toulouse, Allée Camille Soula, 31400Toulouse, France FR FERMAT, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
*
†Email address for correspondence: micheline.abbas@ensiacet.fr
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Abstract

The motion of a neutrally buoyant spherical particle along the axis of an axisymmetric stagnation point flow at a rigid and smooth flat wall (Hiemenz–Homann flow) is investigated in the presence of low-to-moderate inertia effects. The particle dynamics is elucidated using numerical simulation. At distances large compared to the characteristic thickness of the boundary layer $\unicode[STIX]{x1D6FF}=(\unicode[STIX]{x1D708}/B)^{1/2}$, with $\unicode[STIX]{x1D708}$ the kinematic viscosity and $B$ the strain rate of the carrying flow, the particle decelerates as it approaches the wall, due to the ambient pressure increase toward the stagnation point. In this part of the path, its velocity is nearly identical to that of the local undisturbed fluid at the position of its centre. Relative motion between the particle and fluid increases as the wall–particle gap reduces, due to wall-induced hydrodynamic interaction forces. Two distinct evolutions of the net force on the particle are observed, depending on the relative particle size, $a/\unicode[STIX]{x1D6FF}\sim Re^{1/2}$, where $a$ is the particle radius and $Re=2Ba^{2}/\unicode[STIX]{x1D708}$ is the Reynolds number. For $a/\unicode[STIX]{x1D6FF}\lesssim 2$, the force decays monotonically to zero, while it undergoes a sharp rise before returning to zero for larger particles. In the latter case, the particle retains a sufficient velocity even for very small gap widths such that, under usual roughness levels, a rebounding collision would occur. The stress profiles at the particle surface are investigated to separate the various contributions to the hydrodynamic force. Theoretical predictions for near-wall viscous and inertial forces available in the creeping-flow and low-but-finite Reynolds-number limits, respectively, are used to pinpoint the origin of the dominant inertia effect that controls the particle dynamics when the particle gets very close to the wall.

JFM classification

Complex Fluids: Suspensions Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A32
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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