STABILITY OF FLOW OF FLUIDS IN TUBE & CHANNEL

Abstract

We have analyzed the linear stability of a liquid film flowing down outside of a cylindrical tube under the action of gravity. The shear imposed liquid film is in contact with a passive gas and the fluid-fluid interface is covered with a monolayer of indissoluble surfactant. The stability of liquid film outside of tube have been analyzed extensively in literature because of its applicability in numerous technological applications (like fiber coating and pulmonary flows). The cylindrical gas-liquid interface is unstable to capillary instability for this configuration. One of the primary objective is to see the effect of shear stress on the stability of fluid in the direction of gravity and against the direction of gravity. We have examined this feature both by numerical analysis and zero Reynolds number and long wave length asymptotic analysis. Our results demonstrate that it is possible to control the capillary instability by imposing shear with surfactant. However, when surfactants are present in any fluid-fluid interface, the interface is prone to another type of instability known as Marangoni instability mode. Previous study on planar film flows and multi-layer planar channel flows have shown that the Marangoni mode gets unstable only when interfacial shear stress is present in the system. Film flows, both planar and cylindrical, inherently have stress free interfaces. However, the same has not been analyzed yet for cylindrical film flows. Thus, the work presented in the thesis establishes that the stability of the capillary film flows outside of tube is determined by both by Marangoni and capillary mode