Mixing of miscible liquids: Dimensionless scaling for intermediate-to-large density differences in a stirred tank

TL;DR

This study presents a dimensionless scaling law for mixing time in stirred tanks with miscible liquids, based on numerical simulations varying Reynolds and Richardson numbers, resulting in a universal master curve.

Contribution

Derived an exponential scaling law for dimensionless mixing time using Power, Froude, and Richardson numbers, unifying data across different conditions.

Findings

Mixing time correlates positively with Richardson number.

Reynolds number influence was less clear.

All data collapsed onto a single master curve using the scaling law.

Abstract

Mixing of miscible liquids is an essential process in multiple industrial settings, usually with the intent to homogenize the product. This seemingly simple process is in fact a complex hydrodynamic problem that has a direct impact on the product quality. In this study, numerical simulations of a stirred tank were performed with a 50/50 ratio of liquids and systematically varied the Reynolds and Richardson numbers. A positive correlation between the mixing time and the Richardson number was observed, as reported in the literature. The influence of the Reynolds number was not as pronounced and clear. Based on the Power, Froude and Richardson numbers, we were able to derive an exponential scaling for the dimensionless mixing time that collapsed all our data onto one master curve.