Saffman-Taylor instability

In order to study the onset of the Saffman-Taylor instability for the PPG-silica suspensions, we estimated the imposed shear rate 2v/b at which the unstable finger for the first time appears. The 2v/b values are obtained as 72, 30, 17, and 11 s for the 2.5, 5.0, 7.5, and 10.0 wt% PPG-silica suspensions, respectively and they are independent of the injection pressure. Moreover, these values are close to the critical shear rates of the corresponding PPG-silica... 

An important problem is to analyze the stability of fluid flows. With the exception of the Taylor-Couette and Saffman Taylor problems, this chapter has focused on stability questions when the base state of the system was one with no motion (or rigid-body motion), so that instability addresses the conditions for spontaneous onset of flow. An equally valid question is whether a particular flow, such as Poiseuille flow in a pipe (or any of the other flows that we have analyzed in previous chapters of this book), is stable, especially to infinitesimal perturbations as linear instability determines whether the particular flow is actually realizable in experiments. This question was first mentioned back in Chapter 3 when we analyzed simple unidirectional flow problems and noted that solutions such as Poiseuille s solution for flow through a tube was a valid solution of the Navier-Stokes equations for all Reynolds numbers, even though common experience tells us that beyond some critical Reynolds number there is a transition to turbulent flow in the tube. 

Figure 11.30 Craze formation and growth by the Saffman-Taylor meniscus instability mechanism (courtesy of E. J. Kramer). An anaiysis of the viscous motions with the WLF equation aiiows an estimation of the temperature of the crazes on formation.

A problem that is somewhat analogous to the instability of an accelerating interface occurs when two superposed viscous fluids are forced by gravity and an imposed pressure gradient through a porous medium. This problem was analyzed in a classic paper by Saffman and Taylor.16 If the steady state is one of uniform motion with velocity V vertically upwards and the interface is horizontal, then it can be shown that the interface is stable to infinitesimal perturbations if... 

The mosl important early work on interfacial instabilities is that of Saffman and Taylor (1958) who considered the stability of an interface between two immiscible fluids moving vertically through a porous medium. Wooding (1959,... 

---