Normal stress differences in non-Brownian fiber suspensions

In this paper, we present an experimental study of the normal stress differences that arise in nonBrownian rigid fiber suspensions subject to a shear flow. While early measurements of the normal stress in fiber suspensions in Newtonian fluids measured only N1 −N2, the recent work of Snook et al. J. Fluid Mech. 758 486 (2014) and the present paper provide the first measurements of N1 and N2 separately. Snook et al perform such measurements with a gap that is very wide compared with the fiber length, whereas the present paper explores the effects of confinement when the gap is 4-10 times the fiber length. The first and the second normal stress differences are measured using a single experiment which consists of determining the radial profile of the second normal stress, along the velocity gradient direction, Σ22, in a torsional flow between two parallel discs. Suspensions are made of monodisperse fibers immersed in a neutrally buoyant Newtonian fluid. Two fiber lengths and three aspect ratios ar = L/d, and a wide range of concentrations have been tested. N1 is found to be positive while N2 is negative and the magnitude of both normal stress differences increases when nL2d increases, n being the number fraction of fibers. The magnitude of N2 is found to be much smaller than N1 only for high aspect ratios and low fiber concentrations. Otherwise, N1 and N2 are of the same order of magnitude. This is in contradiction with what is often assumed (i.e. |N2| << N1) but consistent with the recent numerical work of Snook et al. that includes contact interactions. The effect of confinement on N1 and N2 is studied and it is shown that the more confined the suspension, the greater the magnitude of the normal stress differences. At last, the surface properties of the fibers are changed and the impact on the normal stress differences is discussed.