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

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

Mar del Plata, Argentina

Workshop; Pan-American Advanced Studies Institute (PASI) on Interfacial Fluid Dynamics: From Theory to Applications; 2007

<!-- @page { size: 21cm 29.7cm; margin: 2cm } P { margin-bottom: 0.21cm } --> The motion of a liquid plug inside a capillary tube is a problem associated with both biological phenomena and technological applications. Frequently plug forms as consequence of capillary instability process (Rayleigh instability) developed over annular liquid films coating the interior surface of a small tube; one example is the instability produced in the liquid lining the pulmonary airways, which can form a plug if the initial thickness of film is enough. Then the pressure difference in the gas phases to both sides of the plug, displace it along the tube over a constant precursor film while it leave a variable trailing film that depends of Ca, Re and length of the plug. If the precursor film is thicker (thinner) than the trailing film, the plug length increase (decrease) as it propagates; in case that both films have the same thickness, a steady motion is accomplish. We say that this configuration will be stable if the plug length returns to it initial one when it is perturbed; otherwise, if after the perturbation the distance between the two menisci either continuously increases or decreases until the plug collapse, the steady state solution will be unstable. In this work we propose an analysis's methodology to determine the stability of the steady displacement, based in the trends of curves representing the thickness of the films as function of the plug length, for fixed Ca and Re. This curves are obtained solving numerically the continuity and Navier-Stokes equations by the finite element method and applying a robust technique -the spine method- to determine the interfacial shape simultaneously with the velocity and pressure. Transient analysis was also conduced to verify the hypothesis about the stability.