DROPLET BREAKUP IN A MODEL OF THE HELE-SHAW CELL

The Hele-Shaw cell involves two immiscible fluids separated by an inte rface. Possible topology changes in the interface are investigated. In particular, we ask whether a thin neck between two masses of the flui d can develop, get thinner, and finally break. To study this, we emplo y the lubrication approximation, which implies for a symmetrical neck that the neck thickness h obeys h(t) + (hh(xxx))x = 0. The question is whether, starting with smooth positive initial data for h, one can ac hieve h = 0, and hence a possible broken neck within a finite time. On e possibility is that, instead of breaking, the neck gets continually thinner and finally goes to zero thickness only at infinite time. Here , we investigate one set of initial data and argue that in this case t he system does indeed realize this infinite-time breakage scenario.