Effect of Basset's hereditary force on bubble dynamics in liquid oxide-based diffusion-bubbling membranes

Innovative liquid oxide-based diffusion-bubbling membranes are a key perspective for efficient oxygen separation from air. The oxygen bubble motion in these membranes is usually described within the framework of a quasi-stationary model allowing negligible characteristic time and characteristic distance of the bubble dynamic relaxation. Here, we show that Basset's hereditary force, associated with the existence of an unsteady boundary layer around the bubble, affects the oxygen bubble dynamics and increases the characteristic time and distance of the bubble dynamic relaxation by two and three orders of magnitude, respectively. An important application of this result is thin-film diffusion-bubbling membranes whose thickness is comparable with the characteristic distance of the bubble dynamic relaxation.