Viscous fingering in a yield stress fluid

Area of Science:

• Fluid dynamics
• Rheology

Background:

• The Saffman-Taylor instability, or viscous fingering, is a classic phenomenon in fluid dynamics.
• Yield stress fluids, like gels and foams, exhibit unique flow behaviors not captured by standard Newtonian fluid models.

Purpose of the Study:

• To investigate the Saffman-Taylor instability in yield stress fluids.
• To compare experimental results with theoretical predictions for these complex fluids.

Main Methods:

• Theoretical analysis of the dispersion equation for yield stress fluids.
• Experimental studies using gels and foams under conditions exhibiting viscous fingering.

Main Results:

• Theoretical models show similarities to Newtonian fluids, with capillary number incorporating yield stress.
• Experiments with gels demonstrated highly branched fingers, agreeing well with theory.
• A transition from yield stress-dominated to viscous behavior was observed in gels.
• Foam experiments yielded significantly different results, attributed to wall slip phenomena.

Conclusions:

• The Saffman-Taylor instability in yield stress fluids can be theoretically described, with modifications to the capillary number.
• Experimental validation with gels supports the theoretical framework, revealing distinct flow regimes.
• Wall slip is a critical factor affecting viscous fingering in foams, necessitating further investigation.