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Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers

Donald L. Koch* and Eric F. Lee

Ibrahim Mustafa

  • School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA

  • Department of Chemical Engineering Technology, Yanbu Industrial College, Yanbu, Kingdom of Saudi Arabia

  • *dlk15@cornell.edu
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Phys. Rev. Fluids 1, 013301 – Published 2 May, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.013301

Abstract

The influence of particle-polymer interactions on the ensemble average stress is derived as a function of the Deborah number for a dilute suspension of spheres in an Oldroyd-B fluid in the limit of small polymer concentrations. The slow rate of decay of the particle-induced polymer stress with separation from a particle presents a challenge to the derivation of the average stress, which can be overcome by removing the linearized polymer stress disturbance before computing the bulk average stress from the particle-induced disturbance. The linearized stress can be shown to have zero ensemble average. The polymer influence on the particle's stresslet is computed with the aid of a generalized reciprocal theorem based on a regular perturbation from Newtonian flow for small polymer concentration. The analysis shows that the particle-polymer contributions to the shear stress and first normal stress difference shear thicken as has been observed in the experiments of Scirocco et al. [Shear thickening in filled Boger fluids, J. Rheol. 49, 551 (2005)]. The particle-polymer contribution to the second normal stress difference is positive at small Deborah numbers but changes sign at a Deborah number of about 2.3.

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References (36)

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Phys. Rev. Fluids 1, 013301– Published 2 May, 2016
  • Received 17 January 2016
Article part of CHORUS

©2016 American Physical Society

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