Spectral Boundary Element Method for Liquid Bridge Dynamics Between Capillary and Substrate

Micro/Nanolithography is an emerging technique to create micro/nano features on substrate. New capillary based lithography method has been developed to overcome the limitations (e.g. directly contact of the substrate) of existing lithography techniques including dip-pen nanolithography nano-imprint lithography and electron-beam lithography. The understanding of the behavior of the liquid bridge formed between a capillary tube and a substrate is essential for the recently developed capillary based lithography method that is non-invasive to the substrate. A three-dimensional spectral boundary element method has been employed to describe the dynamics of liquid bridge. Starting with a steady-state liquid bridge shape, the transient bridge deformation is computed as the capillary tube is retracting away from the substrate. Several relations between the dynamic contact angle and contact line speed have been employed and discussed. The computational results are compared with experimental findings. The influences of liquid properties and retracting speed on the bridge dynamics are investigated.