Stability and critical volume of a suspended pendant drop in air via experiments and eigenvalue analysis

In this paper, we study the stability of pendant drops suspended from a syringe needle tip using theory and experiments. We apply an eigenvalue analysis to the Young-Laplace equation for pendant drops to predict the instability type and critical drop volume that detaches and falls from a syringe needle tip due to gravity. We performed pendant drop experiments using different liquids and syringe needle sizes for a wide range of Bond numbers, 0.2 < B-0* < 1.2. Experimental results that included pinched-off drop volumes were compared with values computed at their stability limit from the eigenvalue analysis. The stability analysis was capable of predicting axisymmetric instabilities, and the agreement between volumes at pinch-off found through numerical and experimental analysis depended on the Bond number.