THE FORMATION OF DROPS THROUGH VISCOUS INSTABILITY

The stability of an immiscible layer of fluid bounded by two other flu ids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability anal yses for both one-dimensional and radial flows are presented, with par ticular emphasis upon the behaviour when one of the interfaces is high ly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops. However, in the case of radial flow, both surface tension and the continuous thinning of the interme diate layer as it moves outward may stabilize the system. We investiga te both of these stabilization mechanisms and quantify their effects i n the relevant parameter space. When the outer interface is strongly u nstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state e volves to larger radii, the linear stability theory predicts a cascade to higher wavenumbers. If the growth of the instability is sufficient that nonlinear effects become important, the annulus will break up in to a number of drops corresponding to the dominant linear mode at the time of rupture. In the laboratory, a Hele-Shaw cell was used to study these processes. New experiments show a cascade to higher-order modes and confirm quantitatively the prediction of drop formation. We also show experimentally that the radially spreading system is stabilized b y surface tension at small radii and by the continual thinning of the annulus at large radii.