Dynamics of liquid films coating the inner wall of an oscillating circular tube

This study investigates the dynamics of thin liquid films coating the inner wall of a rigid cylindrical tube subjected to oscillatory motion. Using long wave theory, an evolution equation for the air–liquid interface is derived. Linear stability analyses of both unforced and oscillatory-forced systems reveal strong agreement between the long-wave model and Orr–Sommerfeld predictions for unforced cases. Nonlinear dynamics is explored by introducing sinusoidal initial disturbances, demonstrating that tube oscillations can suppress liquid film instability and prevent plug formation. Three distinct evolutionary stages are identified: (1) surface tension-dominated exponential growth, (2) oscillation-induced growth suppression, and (3) stabilization into periodic solutions. Parametric studies show that large/small initial disturbance amplitudes accelerate/delay film evolution but do not alter final plug formation outcomes. Critical film thickness phase diagrams further indicate that increasing oscillation frequency more effectively stabilizes films than amplifying oscillation amplitude. Additionally, variations in maximum film thickness under different Ohnesorge numbers are quantified. These findings provide theoretical insights for biomedical applications such as bronchial airway closure prevention and liquid membrane systems influenced by periodic wall oscillations.