Abstract :
Asymptotic methods are employed to determine the leading-order equations that
govern the fluid dynamics of slender, and thin and slender, inviscid, irrotational,
planar liquid sheets subject to pressure differences and gravity. Two flow regimes
have been identified depending on the Weber number, and analytical solutions to
the steady state equations are provided. Linear stability studies indicate that the
sinuous mode corresponds to Weber numbers on the order of unity, while the
varicose mode is associated with small Weber numbers. For small Weber numbers,
the nonlinear stability of liquid sheets is determined analytically in terms of elliptic
integrals of the first and second kinds. It is also shown that the sinuous mode
of thin and slender liquid sheets is identical to the same mode for slender sheets.
