Mixing energy as a scaling variable for liquid drawdown in stirred tanks

Abstract

In this paper, liquid drawdown and dispersion in both a stirred tank (ST) and a confined impeller stirred tank (CIST) are considered at high hold-up (10% and 30% by volume). The process of dispersion is characterized using six variables: the point of initial disruption of the liquid-liquid interface (Nid); the impeller speed where the last pool of liquid is completely dispersed from the surface (Ncd); the time required to reach complete dispersion at Ncd (tcd); the time to reach the equilibrium chord length distribution, also at Ncd (teq); the Sauter mean chord length at tcd (cl32-cd); and cl32 at the equilibrium time, teq (cl32-eq). The chord length distribution (CLD) was measured using a focused beam reflectance measurement (FBRM). The scaling approach most often recommended in the literature is to scale Ncd with Pcd/m but the significant variations in tcd show that there are inherent dynamics in the system making the instantaneous, or equilibrium variable Pcd/m a poor choice for scaling or comparison of performance. An alternate scaling variable, the mixing energy (Jcd/m), is proposed to capture this information. While scaling with Pcd/m is limited to a single geometry, scaling cl32-cd against Jcd/m collapses the cl32-cd data well across four impeller geometries, three tank configurations, and hold-ups of 10% and 30%. The slope of the line changes when one of the impellers is completely submerged in the second phase before mixing starts, but the correlation remains strong. When the second phase is fed at the impeller, the new data falls on the same line.