Normal stress measurements in sheared non-Brownian suspensions

Abstract

Measurements in a cylindrical Taylor–Couette device of the shear-induced radial normal stress in a suspension of neutrally buoyant non-Brownian (noncolloidal) spheres immersed in a Newtonian viscous liquid are reported. The radial normal stress of the fluid phase was obtained by measurement of the grid pressure Pg, i.e., the liquid pressure measured behind a grid which restrained the particles from crossing. The radial component of the total stress of the suspension was obtained by measurement of the pressure, Pm, behind a membrane exposed to both phases. Pressure measurements, varying linearly with the shear rate, were obtained for shear rates low enough to insure a grid pressure below a particle size dependent capillary stress. Under these experimental conditions, the membrane pressure is shown to equal the second normal stress difference, N2, of the suspension stress whereas the difference between the grid pressure and the total pressure, Pg−Pm, equals the radial normal stress of the particle phase, Σrrp. The collected data show that Σrrp is about 1 order of magnitude higher than the second normal stress difference of the suspension. The Σrrp values obtained in this manner are independent of the particle size, and their ratio to the suspension shear stress increases quadratically with ϕ, in the range 0<ϕ<0.4. This finding, in agreement with the theoretical particle pressure prediction of Brady and Morris [J. Fluid Mech. 348, 103–139 (1997)] for small ϕ, supports the contention that the particle phase normal stress Σrrp is due to asymmetric pair interactions under dilute conditions, and may not require many-body effects. Moreover we show that the values of Σrrp, normalized by the fluid shear stress, ηf|γ̇| with ηf the suspending fluid viscosity and |γ̇| the magnitude of the shear rate, are well-described by a simple analytic expression recently proposed for the particle pressure.