Formación de burbujas en líquidos viscosos contenidos en conos y cilindros

Abstract

In this work we consider the problem of growth and detachment of gas bubbles in reservoirs filled with viscous liquids whose walls are very close to the gas injection orifice, in such a manner that the walls affects the bubble shape and its maximum volume of growing. Using the Stokes equations for slow viscous flow, we have studied two cases of interest: a) the case where the walls make a vertical inverted cone, and b) the case of a cylindrical wall concentric to the injection orifice. In both cases the fluid flow equations were solved numerically by using the Boundary Element Method (BEM), and the results are given in terms of the bubble shapes, their maximum volumes and other properties of interest for different values of the Bond and Capillary numbers. We present a qualitative comparison with the experimental bubbles obtained at constant gas flow rates, in the air-gliceryn and air-silicone oil systems. This comparison allows us to conclude that the numerical solutions describe very well this phenomenon. Our results also show that possibility of change of the cone angle or the cylinder radius yields an efficient method to control the shape and size of the produced bubbles.