Nonlinear bubble resonance: Geometric mechanisms and onset scaling

Area of Science:

• Geophysics
• Fluid Dynamics
• Porous Media Physics

Background:

• Oscillatory dynamics of trapped nonwetting fluids in pore constrictions are crucial for multiphase flow and fluid mobility in geologic media.
• While linear responses are understood, the mechanisms behind nonlinear behavior at finite amplitudes remain unclear.

Purpose of the Study:

• Develop a nonlinear pore-scale model for harmonically excited trapped bubbles.
• Validate the model against computational fluid dynamics (CFD) simulations.
• Investigate the origins and manifestations of nonlinear dynamics in trapped bubbles.

Main Methods:

• Developed a nonlinear pore-scale model for trapped bubbles.
• Employed asymptotic expansion of capillary pressure to analyze nonlinear forces.
• Validated model predictions using CFD simulations.
• Introduced a dimensionless nonlinearity number (Nnc) to quantify system behavior.

Main Results:

• Nonlinearity arises from spatial variations in pore curvature, creating an asymmetric capillary restoring force.
• Nonlinear effects include resonance-frequency downshift and oscillation-center drift.
• The trapped bubble acts as an asymmetric Duffing-type oscillator.
• A critical Nnc value near 7.3 determines the onset of nonlinear response.

Conclusions:

• The developed model accurately captures nonlinear dynamics of trapped bubbles.
• The critical Nnc provides a quantitative criterion for predicting nonlinear interfacial mobilization in constricted porous media.
• Understanding these nonlinearities is key for predicting transient fluid mobility in geologic formations.