Stability of a liquid bridge between nonparallel hydrophilic surfaces

Formation of liquid bridges between two solid surfaces is frequently observed in industry and nature, e.g. in printing applications. When the two solid surfaces are not parallel (with a dihedral angle ψ between them), an interesting phenomenon emerges: if ψψ exceeds a critical angle (denoted as ψcψc) the bridge is no longer stable, and propels itself toward the cusp of the surfaces. In this work we performed, for the first time, a systematic study on the parameters influencing ψcψc by combining experimental, theoretical, and numerical investigations. It was shown that ψcψc is determined by the advancing contact angle (θaθa) and Contact Angle Hysteresis (CAH)(CAH) of the surfaces: it increases as θaθa or CAHCAH increases, and these two parameters have a nonlinear and interdependent influence on ψcψc. Based on our quantitative results, an empirical equation is presented to predict the critical angle, ψc=f(θa,CAH)ψc=f(θa,CAH) in closed analytical form. This equation can be used to calculate ψcψc for bridges formed by moving down a pre-tilted surface towards a sessile drop on a stationary lower surface, or bridges between initially parallel surfaces which the top surface tilts after bridge formation.