Fluid mixing from viscous fingering.

Area of Science:

• Fluid dynamics
• Hydrodynamic instabilities
• Chemical engineering

Background:

• Mixing efficiency at low Reynolds numbers is crucial for many processes.
• Hydrodynamic instabilities, like viscous fingering, can enhance mixing by creating flow heterogeneity.
• Understanding these instabilities is key to optimizing mixing.

Purpose of the Study:

• To describe the dissipative structure of miscible viscous fingering.
• To propose a predictive two-equation model for scalar variance and dissipation rate.
• To identify optimal viscosity contrasts for maximizing interfacial area and minimizing mixing time.

Main Methods:

• Analysis of the dissipative structure of miscible viscous fingering.
• Development of a two-equation model for scalar variance and its dissipation rate.
• Theoretical prediction of optimal viscosity contrasts based on Péclet number.

Main Results:

• The study describes the dissipative structure of miscible viscous fingering.
• A two-equation model for scalar variance and dissipation rate is proposed.
• Optimal viscosity contrasts are predicted to maximize interfacial area and minimize mixing time for a given Péclet number.

Conclusions:

• Miscible viscous fingering is an effective mechanism for enhancing mixing at low Reynolds numbers.
• The proposed two-equation model provides a framework for upscaling dissipation due to fingering.
• This research offers insights into optimizing mixing processes through controlled hydrodynamic instabilities.