Pressure waves propagating through bubble-containing liquids in tubes experience considerable attenuation. Researchers at the University of Tsukuba have derived an equation describing this phenomenon, demonstrating that beyond liquid viscosity and compressibility, variations in tube cross-sectional area contribute to wave attenuation.

Their analysis reveals that the rate of change in tube cross-sectional area represents a critical parameter governing pressure wave attenuation in such systems.

Pressure waves propagating through bubble-containing liquids in tubes, known as “bubbly flow,” behave distinctly from those in single-phase liquids, necessitating precise understanding and control of their propagation processes.