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Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

Published online by Cambridge University Press:  01 June 2020

Mohammad Sarabian Open the ORCID record for Mohammad Sarabian [Opens in a new window] ,
Marco E. Rosti Open the ORCID record for Marco E. Rosti [Opens in a new window] ,
Luca Brandt Open the ORCID record for Luca Brandt [Opens in a new window]  and
Sarah Hormozi Open the ORCID record for Sarah Hormozi [Opens in a new window]
Mohammad Sarabian
Affiliation:
Department of Mechanical Engineering, Ohio University, 251 Stocker Center, Athens, OH 45701, USA
Marco E. Rosti
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden Complex Fluids and Flows Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onnason, Okinawa904-0495, Japan
Luca Brandt
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, SE 100 44 Stockholm, Sweden
Sarah Hormozi*
Affiliation:
Department of Mechanical Engineering, Ohio University, 251 Stocker Center, Athens, OH 45701, USA
*
† Email address for correspondence: hormozi@ohio.edu
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Abstract

We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito (J. Non-Newtonian Fluid Mech., vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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