Water-drop response to sudden accelerations

Abstract

The deformation of initially spherical drops of radius r₀ subjected to an external flow of velocity u is experimentally examined for a large range of Weber and Bond numbers. Observations of the changes in the response are compared with recent analytical predictions. The data show that beyond a critical Weber number the response ceases to be vibratory and becomes monotonic with time. Subsequently, it is found that, although the response is unstable, the deformation imposed by the external aerodynamic pressure distribution remains the dominant factor. Measurements of the drag coefficient yield a mean value ofC_D = 2·5 over a large Reynolds-number range. The time at which Taylor instability occurs is shown to be inversely proportional to Bond number to the one-quarter power. There is little evidence of the instability occurring until a normalized time $t^{*} = (\epsilon^{\frac{1}{2}}\bar{t}u/r_0)$ is approximately unity; here ε is the gas/liquid density ratio (ρ/ρ′) and $\bar{t}$ is the real time.