Stability of the steady motion of a liquid plug in a capillary tube

DIEGO MARTIN CAMPANA; SEBASTIÁN UBAL; MARIA DELIA GIAVEDONI; FERNANDO A. SAITA

Mendoza, Provincia de Mendoza, Argentina

Congreso; IX Reunión sobre Recientes Avances en Física de Fluidos y sus Aplicaciones (FLUIDOS-2006); 2006

Facultad de Ingeniería de la Universidad Nacional de Cuyo

The motion of a liquid plug inside a capillary tube is a problem associated with both biological phenomena and technological applications. A simplified model of these problems is the propagation of a volume of liquid inside a capillary tube or a two-dimensional channel whose walls are coated with a thin film of the same fluid. The liquid plug of length Lp propagating on a pre-existing or precursor film of thickness hinfD, leaves behind the deposited or trailing film whose thickness hinfT depends on the relative strength of inertia, viscous and capillary forces. Although not necessarily, the pre-wetting film could be deposited by the gas phase that travels ahead, assuming it is a long bubble. If the displacement is steady (Lp remains constant) hinfD and hinfT will be equal. The objective of the present work is to establish whether a steady state displacement of a liquid plug inside a capillary tube is stable or not. By stable we mean that if a steady state solution is perturbed, the system will recover the initial state after a short transient. If after the perturbation, the distance between the two menisci either continuously increases or decreases until the collapse occurred, the steady state solution will be unstable.