The rheology of dilute suspensions of slender rods in weak flows

• Published in: Journal of fluid mechanics 1987-07, Vol.180 (1), p.475-494
• Main Authors: Berry, Douglas H., Russel, William B.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Non-newtonian fluid flows; Physics
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112087001915

This paper describes the consequences of pair interactions in dilute suspensions of rigid rods of length 2l and radius a subjected to weak, steady shear flows. The combination of hydrodynamic and Brownian forces increases alignment with the flow, thereby enhancing the shear thinning and strain thickening expected from dilute theories. The theory is asymptotic in Pe [Lt ] 1 and ε = (ln 2l/a)−1 [Lt ] 1 but requires an ad hoc approximation to simplify the form of the hydrodynamic interactions and the rod-rod excluded volume. The theoretical predictions of the Huggins coefficient in simple shear flow are compared with data in the literature for Xanthan gum, a semi-rigid biopolymer. Comparison with semi-dilute theories emphasizes the fundamentally different nature of the interactions in the two regimes and indicates that the transition between the two lies in the range 1.5 [les ][η]0 n [les ] 6.