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Cross-stream migration of non-spherical particles in a second-order fluid – theories of particle dynamics in arbitrary quadratic flows

Published online by Cambridge University Press:  15 May 2020

Cheng-Wei Tai Open the ORCID record for Cheng-Wei Tai [Opens in a new window] ,
Shiyan Wang Open the ORCID record for Shiyan Wang [Opens in a new window]  and
Vivek Narsimhan Open the ORCID record for Vivek Narsimhan [Opens in a new window]
Cheng-Wei Tai
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Shiyan Wang
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
Vivek Narsimhan*
Affiliation:
Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN47907, USA
*
†Email address for correspondence: vnarsim@purdue.edu
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Abstract

Particle migration in viscoelastic suspensions is vital in many applications in the biomedical community and the chemical/oil industries. Previous studies have provided insight into the motion of spherical particles in simple viscoelastic flows, yet the combined effect of more complex flow profiles and particle shapes is under-explored. Here, we develop approximate analytical expressions for the polymeric force and torque on an arbitrarily shaped particle in a second-order fluid, subject to a general quadratic flow field. This model is exact for the case when the first and second normal stress coefficients satisfy $\unicode[STIX]{x1D713}_{1}=-2\unicode[STIX]{x1D713}_{2}$. Under this assumption, we examine how particle shape alters cross-stream particle migration (i.e. lift) and particle orientation in both shear- and pressure-driven flows. In shear-driven flows, we observe that spheroidal particles adjust their orientation to align their longer axis along the vorticity direction, although significant deviations from slender-body theories occur for finite aspect ratios. In a slit-like pressure-driven flow, we identify scaling theories to quantify how the particle lift depends on shape for a wide variety of shapes. We find that prolate particles slowly transition to a log-rolling state as they approach the flow centre, with the lift initially being larger than that of an equal-volume sphere, but then becoming smaller as log-rolling emerges. The net effect is a smaller average migration speed for particles with larger aspect ratio. Lastly, we discuss future directions for experimental studies on particle dynamics as well as directions to extend the current work towards more complicated systems.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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