Instability of fluid cylinders and jets, a highly nonlinear hydrodynamic phenomenon, has fascinated researchers for nearly 150 years. A subset of the phenomenon is the core-annular flow, in which a non-wetting core fluid and a surrounding wall-wetting annulus flow through a solid channel. The model, for example, represents the flow of oil in petroleum reservoirs. The flow may be forced to break up when passing through a channel’s constriction. Although it has long been observed that the breakup occurs near the neck of the constriction, the exact conditions for the occurrence of the forced breakup and its dynamic theory have not been understood. Here, we test a simple geometric conjecture that the fluid will always break in the constrictions of all channels with sufficiently long wavelengths, regardless of the fluid properties. We also test a theory of the phenomenon. Four constricted glass tubes were fabricated above and below the critical wavelength required for the fluid disintegration. In a direct laboratory experiment, the breakup occurred according to the conjecture: the fluids were continuous in the shorter tubes but disintegrated in the longer tubes. The evolution of the interface to its pinch-off was recorded using high-speed digital photography. The experimentally observed core-annulus interface profiles agreed well with the theory, although the total durations of the process agreed less satisfactorily. Nonetheless, as the theory predicts, the ratio between the experimental and theoretical times of the breakup process tends to one with decreasing capillary number. The breakup condition and the dynamic theory of fluid disintegration in constricted channels can serve as quantitative models of this important natural and technical phenomenon.
- Geological and Atmospheric Sciences
Available at: http://works.bepress.com/r_dennis_vigil/1/