Linear stability of layered two-phase flows through parallel soft-gel-coated walls

Area of Science:

• Fluid Dynamics
• Rheology
• Soft Matter Physics

Background:

• Layered two-phase Poiseuille flows are common in microfluidics and biological systems.
• The interaction between fluid flow and deformable boundaries (soft gels) is complex and not fully understood.
• Understanding instabilities in such systems is crucial for controlling flow behavior and preventing system failure.

Purpose of the Study:

• To analyze the linear stability of two-phase Poiseuille flows confined by soft-gel-coated parallel walls.
• To elucidate the role of elastohydrodynamic coupling between Newtonian fluids and viscoelastic gel layers.
• To identify and characterize different flow instability modes and their dependence on gel properties.

Main Methods:

• Employed long-wave asymptotic analysis to derive analytical expressions for disturbance growth rates.
• Utilized a Chebyshev collocation method for numerical solution of linearized flow equations.
• Conducted an energy budget analysis to understand the physical mechanisms driving instabilities.

Main Results:

• Identified three primary instability modes: liquid-liquid long-wave, liquid-liquid short-wave, and gel-liquid short-wave.
• Demonstrated that gel layers can stabilize or destabilize the liquid-liquid long-wave mode depending on viscosity and position.
• Revealed new gel-liquid interface instabilities, controllable by adjusting gel layer thickness.

Conclusions:

• Elastohydrodynamic coupling significantly influences flow stability in soft-gel-coated channels.
• Gel properties and geometry play a critical role in determining the dominant instability modes.
• The findings offer insights for designing and controlling microfluidic devices and soft material interfaces.