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Shear thickening of a non-colloidal suspension with a viscoelastic matrix

Published online by Cambridge University Press:  18 October 2019

Adolfo Vázquez-Quesada Open the ORCID record for Adolfo Vázquez-Quesada [Opens in a new window] ,
Pep Español ,
Roger I. Tanner  and
Marco Ellero
Adolfo Vázquez-Quesada*
Affiliation:
Department of Theoretical Condensed Matter Physics, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Pep Español*
Affiliation:
Departamento de Física Fundamental, UNED, Apartado 60141, 28080 Madrid, Spain
Roger I. Tanner*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia
Marco Ellero*
Affiliation:
Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48400 Bilbao, Spain IKERBASQUE, Basque Foundation for Science, Calle de María Díaz de Haro 3, 48013 Bilbao, Spain Zienkiewicz Centre for Computational Engineering (ZCCE), Swansea University, Bay Campus, Swansea SA1 8QQ, UK
*
†Email addresses for correspondence: adolfo.vazquez@uam.es, pep@fisfun.uned.es, roger.tanner@sydney.edu.au, mellero@bcamath.org
†Email addresses for correspondence: adolfo.vazquez@uam.es, pep@fisfun.uned.es, roger.tanner@sydney.edu.au, mellero@bcamath.org
†Email addresses for correspondence: adolfo.vazquez@uam.es, pep@fisfun.uned.es, roger.tanner@sydney.edu.au, mellero@bcamath.org
†Email addresses for correspondence: adolfo.vazquez@uam.es, pep@fisfun.uned.es, roger.tanner@sydney.edu.au, mellero@bcamath.org
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Abstract

We study the rheology of a non-colloidal suspension of rigid spherical particles interacting with a viscoelastic matrix. Three-dimensional numerical simulations under shear flow are performed using the smoothed particle hydrodynamics method and compared with experimental data available in the literature using different constant-viscosity elastic Boger fluids. The rheological properties of the Boger matrices are matched in simulation under viscometric flow conditions. Suspension rheology under dilute to semi-concentrated conditions (i.e. up to solid volume fraction $\unicode[STIX]{x1D719}=0.3$) is explored. It is found that at small Deborah numbers $De$ (based on the macroscopic imposed shear rate), relative suspension viscosities $\unicode[STIX]{x1D702}_{r}$ exhibit a plateau at every concentration investigated. By increasing $De$, shear thickening is observed, which is related to the extensional thickening of the underlying viscoelastic matrix. Under dilute conditions ($\unicode[STIX]{x1D719}=0.05$), numerical results for $\unicode[STIX]{x1D702}_{r}$ agree quantitatively with experimental data in both the $De$ and $\unicode[STIX]{x1D719}$ dependences. Even under dilute conditions, simulations of full many-particle systems with no a priori specification of their spatial distribution need to be considered to recover precisely experimental values. By increasing the solid volume fraction towards $\unicode[STIX]{x1D719}=0.3$, despite the fact that the trend is well captured, the agreement remains qualitative with discrepancies arising in the absolute values of $\unicode[STIX]{x1D702}_{r}$ obtained from simulations and experiments but also with large deviations existing among different experiments. With regard to the specific mechanism of elastic thickening, the microstructural analysis shows that elastic thickening correlates well with the average viscoelastic dissipation function $\unicode[STIX]{x1D703}^{elast}$, requiring a scaling as $\langle \unicode[STIX]{x1D703}^{elast}\rangle \sim De^{\unicode[STIX]{x1D6FC}}$ with $\unicode[STIX]{x1D6FC}\geqslant 2$ to take place. Locally, despite the fact that regions of large polymer stretching (and viscoelastic dissipation) can occur everywhere in the domain, flow regions uniquely responsible for the elastic thickening are well correlated to areas with significant extensional component.

JFM classification

Complex Fluids: Suspensions Non-Newtonian Flows: Viscoelasticity Non-Newtonian Flows: Rheology
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 1070 - 1094
Copyright
© 2019 Cambridge University Press 

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