화학공학소재연구정보센터
Chemical Engineering Science, Vol.64, No.23, 4919-4928, 2009
Experimental investigation of transition to laminar mixing of a homogeneous viscous liquid in a tilted-rotating tank
A tilted and partially filled rotating tank is investigated experimentally at O(1) Reynolds and small (<< 1) capillary numbers, to study the mixing of a viscous homogeneous fluid. Of particular interest is the transition from a previously studied low Reynolds number flow regime [Ward, T., Metchik, A., 2007. Viscous fluid mixing in a titled tank by periodic shear. Chemical Engineering Science 62, 6274-6284], that exhibited two large vortices, to the laminar flow regime which results in additional vortex generation. In the laminar Reynolds number limit O(1) the two primary vortices generated by the liquid rotation axis can interact with the bottom wall, generating two secondary counter-rotating vortices, via a cascade that is qualitatively similar to the well known Moffatt [1964. Viscous and resistive eddies near a sharp corner. journal of Fluid Mechanics 18, 1-18] vortices in Stokes flow. While the secondary vortices aid in transporting material from the walls to the bulk, they also intensify in magnitude with increasing rotation rate leading to finite sized unmixed regions via the appearance of KAM-like surfaces [Alvarez-Hernandez, M.M., Shinbrot, T., Zalc, J., Muzzio, FJ., 2002. Practical chaotic mixing. Chemical Engineering Science 57, 3749-3753]. This suggests that there may be an optimal tilt angle, for a given speed, with which to achieve the maximum mixed cross sectional area within a minimum amount of elapsed time. Experiments are performed using a 90% glycerol, 10% water mixture at two volume portions with angles ranging between 25 degrees and 65 degrees measured from the horizontal. Laser fluorescence is used to illuminate the vortices via experimental Poincare mapping [Fountain, G.O., Khakhar, D.V., Ottino, J.M., 1998. Visualization of three dimensional chaos. Science 281, 683-686], and the resulting images are analyzed to determine the mixed cross sectional area versus elapsed time. (C) 2009 Elsevier Ltd. All rights reserved.