Non-Newtonian Fluids Mixing Behavior Behind a Grid

Numerous biological, biomedical or chemical engineering processes involve non-Newtonian fluids as shear-thinning or shear-thickening fluids. As early as 1969, Lumley [1] investigated the influence of the non-Newtonian characteristics on the Kolmogorov cascade. In 1986, De Gennes [2] revisited such point of view by considering more precisely elasticity and shear thinning properties. As of today, the correlation between elasticity and other flow properties is still unclear, recent numerical simulations attempted to clarify the issue with the use of FENE-P or other linear viscoelastic models. The goal of this experimental work is to further clarify these assumptions by using new optical tools (PIV, PLIF) to study non-Newtonian decaying isotropic homogeneous turbulence (IHT), using the approach and analysis of the 1971 work of Comte-Bellot and Corrsin [3] for Newtonian fluids, and more recently (2010, 2011) by Lenoir et al. [4]. The experimental set-up consists of a small, 1m long liquid channel, with a cross-section of 6.6 × 6.6 cm2, as in Simoëns and Ayrault [5]. In order to obtain best possible quasi-isotropic flow for sufficient large Reynolds numbers (see Comte-Bellot and Corrsin [6]), the grid was installed transversally upstream the flow, at the outlet of a contraction chamber; the grid squared mesh was 8mm wide. A PIV Lavision System with two synchronized pulsed YAG Lasers was used to obtain Instantaneous velocity maps on selected vertical plane crossing longitudinally the channel at its center. The flow was seeded with 10μm diameter fluorescent particles for PIV measurements. IHT experiments were done on a 1% carboxymethyl cellulose (CMC) aqueous solution (such dilute CMC solution is non-Newtonian as shown in the 2008 work of Benchabane and Bekkour [7]) and then compared to measurements in water at the same flow rate. To prevent molecular modification of the CMC fluid structure out of its natural shear stress, the flow was driven by gravity, not by a pump. For this study, the water flow Reynolds number was 1600; the flow regime was too low to reach a turbulent state. Frequent rheometer checks were performed during the CMC experiments to verify the preservation of the integral shear thinning properties of the fluids. For the CMC flow, the Reynolds number was determined locally, based on the local viscosity after a Carreau-Yasuda model of order 2, in which γ̇ is the rate of shear strain, η is the viscosity at iteration n, η0 is the viscosity at zero shear rate; λ is a constant with units of time, where 1/λ is the critical shear rate at which viscosity begins to decrease (see Nguyen et al. (2010, 2012) [8], [9]).