Plateau-Rayleigh instability

Since the average diameter of the droplets formed via the Rayleigh-Plateau instability of a liquid cylinder is proportional (and similar) to the diameter of the unstable cylinder, r oc Ca also gives an estimate of the radii of the droplets formed by shearing. 

The latter can be further classified in mostly 2D devices (planar or nonplanar) and 3D coaxial injectors whose working principle is related to the Rayleigh-Plateau instability described in following sections. 

FIGURE 20.7 The physical mechanism of Rayleigh-Plateau instability the undeformed jet (a) start to deform due to external pressure oscillations (b) surface deformations are amplified by Laplace pressure effects (c) until a jet breakup occurs (d). The new drops eventually recover their spherical shape (e). 

Whether or not a drop can pinch off during this time depends upon the timescale for the growth of Rayleigh-Plateau instability on a liquid column, which is given by... 

Figure 1.4 Flow instabilities relevant to multifluid systems in microchannel networks. The different miscible or immiscible phases are indicated as 1, 2, 3 and 4. (a) Breakup in a flow-focusing geometry [62, 181] due to a Rayleigh-Plateau instability. Bubble and droplet chains and multiple emulsions were prepared [71]. (b) Pressure-induced breakup [64, 72, 182]. (c) Taylor cone formation...

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