Nonlinear bubble resonance: Geometric mechanisms and onset scaling

The oscillatory dynamics of trapped nonwetting fluids in pore constrictions influence multiphase flow and transient fluid mobility in geologic media. Although the small-amplitude linear response is relatively well understood, the mechanism responsible for nonlinear behavior at finite-amplitudes remains unclear. Here we develop a nonlinear pore-scale model for a harmonically excited trapped bubble and validate it against computational fluid dynamics simulations. An asymptotic expansion of the capillary pressure shows that the nonlinearity arises from the spatial variation of pore curvature: higher-order geometric terms produce a softening and asymmetric capillary restoring force. These nonlinear effects manifest as a resonance-frequency downshift and an oscillation-center drift, indicating that the trapped bubble behaves as an asymmetric Duffing-type oscillator. A dimensionless nonlinearity number, N_{nc}, is introduced to quantify the competition between geometric amplification and viscous dissipation in a given pore-fluid system. Our results show that the onset of nonlinear response is determined by a critical N_{nc}, which is near 7.3. This criterion provides a quantitative basis for identifying the onset of nonlinear interfacial mobilization under transient forcing in constricted porous media.