Non-Linear Response of Deforming Drops

Abstract

WHEN a liquid drop is suddenly exposed to an external flow-field, its initial response is either vibration or continuous deformation algebraically with time. Harper, Grube and Chang¹ have approximated the transition between these two states, and have concluded that the drop ceases to vibrate at a critical Weber number We_c of about 7.3. (We is the ratio of the forces due to aerodynamic pressure and surface tension, that is, We=(ρ_gU² ∞ rσ) where ρ_g is the gas density, U∞ the flow velocity, r the drop radius and σ the surface tension.) Above the critical value, the non-uniform surface pressure distribution exerted by the external flow causes the drop to deform continuously and ultimately to burst. This communication describes observations of the non-linear response (at Weber numbers near We_c) after the drop distortion has become large compared with the initial radius.