What Is the Saffman-Taylor Viscous Fingering Calculator?
In 1958, P.G. Saffman and Sir Geoffrey Taylor identified that when a fluid of low viscosity pushes a fluid of higher viscosity, the planar interface is unstable.
A small advance of the low-viscosity fluid encounters less flow resistance, causing it to accelerate ahead and form fingers.
How Does the Saffman-Taylor Viscous Fingering Calculator Work?
Viscosity contrast drives the instability, while interfacial surface tension suppresses short-wavelength perturbations.
The balance between Darcy viscous forces and Laplace capillary pressure defines a unique fastest-growing wavelength λmax.
Saffman-Taylor Viscous Fingering Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Saffman-Taylor linear stability analysis for fastest-growing viscous finger wavelength.
How to Use the Saffman-Taylor Viscous Fingering Calculator
- Enter fluid viscosities, interface velocity, interfacial tension, and cell gap width.
- Check dominant finger wavelength and growth rate.
Step-by-Step Example Calculation
Waterflooding Secondary Oil Recovery
Input Values:
Understanding Your Result
Higher velocity or higher viscosity contrast produces thinner, more numerous fingers, accelerating breakthrough.
Factors That Affect the Result
- Adding polymers to the displacing water increases its viscosity (μ1), stabilizing the interface against fingering.
When Should You Use This Calculator?
- Enhanced oil recovery (EOR) modeling, groundwater contaminant transport, and microfluidics.
Assumptions & Limitations
- Linear stability analysis in a 2D Hele-Shaw cell with Darcy flow.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical Saffman-Taylor theoretical benchmark.