Abstract Summary (Max 250 words)
The mixing characteristics within a stirred tank are influenced not only by the geometry of the mixing system but also by the impeller Reynolds number (Re). In particular, it is well known that poorly mixed regions can form depending on the value of Re. Mixing time serves as an indicator of the time required for the entire tank, including these poorly mixed zones, to reach homogeneity. Correlation equations based on this definition have been widely reported. However, in processes where rapid mixing of added substances is required — especially when uniformity in the well-mixed region is critical — there is a need for correlation equations that specifically represent mixing time in these well-mixed regions. Despite this practical need, such correlations have not yet been reported. In this study, the concentration gradient (∇C), defined as the spatial gradient (∇) of concentration (C), was introduced as a key parameter to characterize mixing. Based on this, mixing time was redefined as the time required for ∇C to become uniform throughout the stirred tank. Using this definition, a correlation equation was derived from the convection-diffusion equation. The validity of the proposed correlation was evaluated using reported data across laminar, transitional, and turbulent flow regimes. The results indicate that the derived equation effectively predicts mixing time under a range of flow conditions.
