Damping dynamics of bubble-driven oscillatory flows

Oscillatory flows in confined geometries are susceptible to instability, presenting challenges in microfluidics, acoustics, and biomedical systems. Trapped air volumes passively damp these flows due to gas compressibility, yet a first-principles model capturing the full spatiotemporal response has been lacking. Here, we derive a unified theoretical framework that characterizes the damping of oscillatory liquid flows by a trapped air volume. The model reveals a dimensionless product (τω) as the governing scaling parameter, linking air compliance and fluidic resistance to amplitude reduction, phase shift, and a transient mean drift of the liquid front. This framework, analogous to a resistance–capacitance circuit in fluidic form, provides a complete analytical solution tested experimentally across a broad range of frequencies, resistances, and air volumes. By unifying amplitude, phase, and transient dynamics under a single scaling law, this work transforms trapped air from an unpredictable artifact into a quantifiable design element, offering fundamental insight into damping mechanisms in two-phase oscillatory flows.