Parameters Governing the Rayleigh Instability

In this section, the parameters influencing the mean diameter dR resulting from the Rayleigh instability are examined. Hereafter, the second fragmentation regime is not considered because a narrow size distribution is already obtained after the first one. The parameters that influence dR are the applied stress a, the viscosity ratio p, the rheological behavior, and the way the shear is applied. 

The straight line deflnes the transition between two regimes in the upper half plane, fast fragmentation occurs ( 1 s) under shear, whereas fragmentation does not take 

To explore the influence of p, the viscosity of the internal phase was varied over four decades, everything else being constant [149]. As can be seen in the log-log plot of Fig.. 9, dp (identically Cflcr) scales with the viscosity ratio as p - the low value of the exponent indicates that dp is only weakly dependent on p. In Fig. 1.20, the evolution of the polydispersity P as a function of p is plotted. As 

In the previous experiments, the shear was applied as a step in less than 1 s. The shear can also be applied following a controlled ramp [150]. Four different protocols are schematically represented in Fig. 1.23. The shear is increased from 

0 to 500 in less than 1 s (a), 10 s (b), and 100 s (c and d). The maximum shear of 500 s is maintained for a duration t and is suddenly interrupted for protocols a, b, and c. For protocol d, the shear is progressively decreased from 500 s to zero in 100 s. To allow comparison, the resulting diameter is plotted (Fig. 1.24) versus total strain y defined as  

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