Stability response of liquid bridges to maximum volume asymmetric perturbations

The stability response of a bounded axisymmetric liquid bridge to maximum volume asymmetric perturbations is investigated using theory and experiments. Based on stability theory, a liquid bridge undergoes maximum volume asymmetric instability when the contact angle reaches 180$^{\circ}$, for all radial Bond numbers $Bo_R=\Delta \rho g R^2/\gamma$, where $\Delta \rho$ is the density difference between the bridge liquid and ambient fluid, $g$ the acceleration due to gravity, $R$ the bridge radius, and $\gamma$ the liquid surface tension. The Young--Laplace equation is solved to estimate the maximum stable volume before rotund drop instability occurs for radial Bond numbers in the range $0.1 < Bo_R < 5$. Experiments are performed using water on surfaces with identical chemical signatures on both top and bottom substrates. A needle connected to the bottom substrate is used to increase the bridge volume in small increments to reduce surface waves. The maximum volume theoretical limit of $V_{max}=(2/3)^{1/3}{Bo}^{-2/3}$ is compared with experiments. Deviations in contact angle and volume are explained by comparing experiments with numerical results.