TEMPORAL INSTABILITY OF PLANE GAS SHEETS IN A VISCOUS-LIQUID MEDIUM

This paper reports a linear temporal instability analysis of an incomp ressible plane gas sheet in a quiescent viscous liquid medium of infin ite expanse. Results indicate that there exist two unstable modes of d isturbance waves, sinuous and varicose, and surface tension always red uces, while the relative velocity between the gas and liquid phases an d the gas density always enhance instability development. For both uns table modes, the presence of liquid viscosity increases the instabilit y limit, which is however independent of the absolute value of viscosi ty. It is also shown that the sinuous mode becomes stable when the gas Weber number, defined as the ratio of aerodynamic forces to surface t ension forces, is less than the critical value of one. At slightly lar ger gas Weber numbers, liquid viscosity exhibits dual effects-it may e nhance or suppress the growth of unstable disturbances, depending on s pecific flow conditions. However, for sinuous mode at high Weber numbe rs and varicose mode at any Weber numbers, liquid viscosity always red uces disturbance growth rates and dominant wave numbers. Unlike the ca se for plane liquid sheets, varicose mode controls the instability pro cess for all Weber number ranges and for both inviscid and viscous liq uids, and only at high Weber numbers, do varicose and sinuous modes be come almost equally important. It is further found that the wave propa gation velocity for both unstable modes is much smaller than the gas v elocity at the mode of maximum instability, implying that the disturba nce waves appear almost stationary rather than travelling-wave type, i n contrast with the plane liquid sheet results. (C) 1996 American Inst itute of Physics.