The Dispersion of Viscous Liquids by Turbulent Flow in a Static Mixer

Authors:

Paul D. Berkman

Richard V. Calabrese

This research report investigates the dispersion of viscous liquids within a Kenics static mixer under turbulent flow conditions to determine how internal viscous forces influence droplet breakage. By analyzing dilute suspensions of various oils in water, the study demonstrates that increased dispersed phase viscosity leads to larger equilibrium mean drop sizes and broader size distributions. The findings culminate in a semi-empirical correlation that extends the classical Weber Number result to account for viscous resistance, providing a more comprehensive model for predicting mixer performance.

Key Learnings

• Viscosity’s Role in Stability: Unlike inviscid liquids, where stability is governed solely by surface tension, viscous liquids are stabilized by both surface and internal viscous forces, which significantly resist droplet breakage in turbulent environments.
• Impact on Drop Size: Both the equilibrium mean drop size (D₃₂) and the maximum stable drop size (Dₘₐₓ) increase almost linearly with the viscosity of the dispersed phase and decrease as the Reynolds number (energy dissipation) increases.
• Broadening Distributions: Increasing the viscosity of the dispersed phase results in a broader drop size distribution, shifting the volume frequency toward larger diameters and creating a less uniform dispersion.
• Evolution of the Predictive Model: The study extends the classical Weber Number correlation by introducing a Viscosity Group (Vi). This new semi-empirical equation successfully accounts for viscous resistance while collapsing back to the standard W e result for low-viscosity liquids.
• Mixing Efficiency and Entrance Effects: While equilibrium is generally reached within the mixer, the method of introducing the dispersed phase (initial drop size) can influence the final size distribution, particularly the large-size "tail" at high viscosities and low Reynolds numbers.
• Kenics Mixer Performance: The 24-element mixer provides sufficient residence time for equilibrium, and the resulting drop size distributions are found to be normally distributed in volume, similar to results observed in turbulent stirred tank contactors.