Annular jets are encountered in many industrial processes. Their stability has been studied in the contexts of ink-jet printing (Hertz and Hermanrud, 1983; Sanz and Meseguer, 1985), encapsulation (Lee and Wang, 1989; Kendall, 1986), gas absorption (Baird and Davidson, 1962), and atomization (Crapper, Dombrowski, and Pyott, 1975; Lee and Chen, 1991; Shen and Li, 1996; Villermaux, 1998). Shen and Li analyzed the spatial-temporal instability of an annular liquid jet surrounded by an inviscid gas. Hu and Joseph (1989) investigated the temporal instability of a three-layered liquid core-annular flow. The instability of annular layeres has been used to model the formation of liquid bridges in microairways in lungs (Newhouse and Pozrikidis, 1992). The related problems of liquid bridge instability are reviewed by Alexander (1998). Annular jet instability is also of considerable theoretical interest because it includes many other flow instabilities as special cases (Meyer and Weihs, 1987). Moreover, it serves to establish knowledge of the fluid physics of flows with two distinctive curved fluid-fluid interfaces subjected to different shear forces, capillary forces, and inertial forces under variable gravitational conditions.

An Annular Jet

Consider the flow of a fluid in an annulus enclosing another fluid, which is surrounded by yet another fluid inside a circular pipe of radius Rω as shown in Figure 10.1. The axis of the pipe aligns with the direction of the acceleration due to gravity g. All three fluids are incompressible.