1 Characterization of Mixing in a Simple Paddle Mixer Using Experimentally Derived Velocity Fields Douglas Bohl1, Naratip Santitissadeekorn2, Akshey Mehta1, and Erik Bollt2 1Department of Mechanical and Aeronautical Engineering 2Department of Mathematics Clarkson University Potsdam, NY Abstract The flow field in a cylindrical container driven by a flat bladed impeller was investigated using Particle Image Velocimetry (PIV). Three Reynolds numbers (0.02, 8, 108) were investigated for different impeller locations within the cylinder. The results showed that vortices were formed at the tips of the blades and rotated with the blades. As the blades were placed closer to the wall the vortices interacted with the induced boundary layer on the wall to enhance both regions of vorticity. Finite Time Lyapunov Exponents (FTLE) were used to determine the Lagrangian Coherent Structure (LCS) fields for the flow. These structures highlighted the regions where mixing occurred as well as barriers to fluid transport. Mixing was estimated using zero mass particles convected by numeric integration of the experimentally derived velocity fields. The mixing data confirmed the location of high mixing regions and barriers shown by the LCS analysis. The results indicated that mixing was enhanced within the region described by the blade motion as the blade was positioned closed to the cylinder wall. The mixing average within the entire tank was found to be largely independent of the blade location and flow Reynolds number. I. Introduction I.1 Background Mixing is a fundamental process in many natural and industrial flow fields. In flows such as the current one under investigation (i.e. highly viscous, low speed flows),2 small-scale motions are not available and mixing is a result of large-scale motion in the flow. Batch mixers, similar to food mixers, are a primary method for the processing of many materials. However, there are inherent drawbacks to a batch mixing process (e.g. inconsistent mixture quality, residual voids and fissures, limited pot life, etc.). The study of these devices is complicated by several factors which include rheological properties of the fluids, complex geometries, and device scaling issues. Recent interest in developing more efficient, controllable mixing processes has focused attention on developing a better understanding on the physics of these devices. The development of computational tools is attractive in that computational tools allow for relatively rapid and simple changes to both geometry and operating conditions to determine optimal mixing protocols. Many researchers have investigated batch mixing configurations numerically (e.g. [1-4]). Stretching and mixing has been a primary interest [1, 2, 4] while fluid properties and power consumption[3] have also been a focus. Computational models have also been utilized to study other mixer configurations (e.g. continuous mixers [5-7], static mixers [8, 9]). Experimental work on planetary mixers has historically centered on scalar measurements such as power consumption, mixing patterns or final mixture characterization. Zhou et al. [10] investigated the power consumption in a double planetary mixer with Newtonian and non-Newtonian fluids. It was found that the power curve for non-Newtonian fluids was found to collapse to the curve for Newtonian fluids when the Metzner-Otto Reynolds number was used for scaling. Clifford et al. [11] studied the effects of Reynolds number on the mixing in a simplified pin planetary mixer. Mixing patterns were derived using flow visualization and compared to computed fields.3 The mixing patterns were found to have a Reynolds number dependence. At low Reynolds number, simulating Stokes flow, the mixing occurred in local regions of the tank limited by the motion of the pin. As the Reynolds number was increased the mixing was observed over progressively larger regions in the tank. Youcefi et al. [12] experimentally and computationally investigated the effect of fluid elasticity on the flow induced by a rotating flat plate impeller. In this work torque measurements were also made and used to determine the power number as a function of the fluid type and Reynolds number. It was found that the power number data collapsed onto a single curve for all Newtonian and non-Newtonian pseudoplastic fluids when the effective Reynolds number was used for the pseudoplastic fluids. Recently researchers have started to apply optical measurement techniques to better understand the flow fields in many different mixing devices. Bohl [13] utilized Particle Image Velocimetry (PIV) velocity data to investigate the flow in a simplified batch mixer. Jaffer et al. [14] applied PIV to kneading elements in a twin-screw extruder. Bakalis and Karwe [15] used Laser Doppler Velocimetry (LDV) to measure the velocity profiles in the nip and translation regions of a twin-screw extruder. Yoon et al. [16] investigated the flow in a Rushton turbine using PIV. Utomo et al. [17] combined LDV and computational simulations to quantify the flow patterns and energy dissipation in a batch rotor-stator mixer. These studies have shown the utility in applying non-intrusive diagnostic technique to better understand the flow fields in these devices. I.2 Dynamical Systems Approach – Lagrangian Coherent Structures The study of Lagrangian Coherent Structures (LCS) was introduced by Haller as a mathematical formalism based on Finite Time Lyapunov Exponents (FTLE) [18-22]. The4 LCS's are descriptive of finite-time attracting and repelling material surfaces and serve as finite time analogues of hyperbolic invariant manifolds, which have been classically used to study transport in autonomous dynamical systems. Given a vector field describing a nonautonomous dynamical system, the FTLE is a scalar field whose ridges represent pseudo-barriers across which transport is greatly hindered, a statement made formal by Shadden at al. [23]. Thus the FTLE field can be used to segment space into regions of related dynamical activity. This means that two particles starting in the same FLTE region will tend to flow together in time as the dynamical