In the previous chapter we mentioned that fluid viscosity might alter the critical Weber number that divides the parameter space into regimes of absolute and convective instability. The effects of gas and liquid viscosities are investigated separately in this chapter, not just to understand each individual effect but also to demonstrate the coupled effect, which is unexpected. In Chapter 3, stability analysis for an inviscid liquid sheet of uniform thickness was applied locally to investigate the stability of gradually thinning liquid sheets. The thinning was either due to axial expansion or gravitational acceleration. The local application of the inviscid theory for a uniform sheet to the two different cases of nonuniform sheets was made judiciously. Likewise the viscous theories given in this chapter can be applied judiciously to a gradually thinning viscous sheet whatever the cause of the thinning. The thinning may be caused by kinematic requirements, gravitational acceleration, or viscous extrusion. The breakup of a viscous liquid sheet in an inviscid gas is expounded in Section 4.1. The effect of gas viscosity is elucidated in Section 4.2. The effects of liquid and gas viscosities on the onset of sheet breakup are summarized in Section 4.3.

A Viscous Sheet in an Inviscid Gas

The basic flow attributed to G. I. Taylor is given in Section 4.1a, and its stability is analyzed in Section 4.1b. The physical mechanism of the sheet breakup is discussed in Section 4.1c, based on energy considerations.