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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Related Experiment Video

Updated: Jul 9, 2025

Fabricating High-viscosity Droplets using Microfluidic Capillary Device with Phase-inversion Co-flow Structure
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Rotor-Stator Emulsification in the Turbulent Inertial Regime: Experiments toward a Robust Correlation for the Droplet

Roberta Campardelli1, Giulia De Negri Atanasio1, Claudia Carotenuto2

  • 1Department of Civil, Chemical and Environmental Engineering, University of Genoa, Genoa 16145, Italy.

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Summary

This study introduces a new model to predict oil droplet size in emulsions, crucial for understanding emulsion stability. The developed model accurately quantifies forces influencing droplet size during rotor-stator emulsification.

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Area of Science:

  • Colloid and Surface Chemistry
  • Fluid Dynamics
  • Chemical Engineering

Background:

  • Sauter mean diameter (d32) is key for characterizing stable emulsions.
  • Existing models for d32 lack specificity for rotor-stator systems.
  • Emulsion characterization remains an active research area.

Purpose of the Study:

  • To develop a new predictive model for normalized Sauter mean diameter (d32) in oil-in-water (O-W) emulsions.
  • To investigate the influence of viscous, inertial, and interfacial tension forces on emulsification.
  • To provide a more accurate model for rotor-stator emulsification processes.

Main Methods:

  • Application of a new Π-theorem-based approach.
  • Multiple regression analysis of experimental data.
  • Testing with paraffin, soybean oil, and isopropyl myristate O-W emulsions.

Main Results:

  • A novel empirical correlation for normalized d32 was developed.
  • The model quantifies the impact of key forces and O/W ratio.
  • The new model demonstrated superior accuracy compared to existing literature models.

Conclusions:

  • The proposed model offers enhanced prediction accuracy for rotor-stator emulsification.
  • It provides a quantitative understanding of forces governing droplet size.
  • This work contributes to the ongoing investigation of emulsion characterization.