Normal stress differences in non-Brownian fiber suspensions

International audienceIn this paper, we present an experimental study of the normal stress differences that arise in non-Brownian rigid fiber suspensions subject to a shear flow. While early measurements of the normal stress in fiber suspensions in Newtonian fluids measured only N 1 − N 2 , the recent work of Snook et al. J. Fluid Mech. 758 486 (2014) and the present paper provide the first measurements of N 1 and N 2 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, Σ 22 , 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 a r = L/d, and a wide range of concentrations have been tested. N 1 is found to be positive while N 2 is negative and the magnitude of both normal stress differences increases when nL 2 d increases, n being the number fraction of fibers. The magnitude of N 2 is found to be much smaller than N 1 only for high aspect ratios and low fiber concentrations