Dynamics of fluid bridges between a rising capillary tube and a 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., the direct contact with 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 and modified to describe the dynamics of the liquid bridge. Starting with a steady-state liquid bridge shape, the transient bridge deformation is computed as the capillary tube is being lifted away from the substrate. The motion of the three-phase contact line on the substrate is taken into consideration. The computational results are validated with the experimental findings. The influences of the lifting speed of the capillary, liquid properties, and contact line slip conditions on the bridge dynamics are investigated. We conclude by computations that with a higher lifting speed of the capillary tube, the contact line radius on the substrate and the bridge neck radius reduce in a faster manner; a smaller residual droplet tends to form on the substrate if the viscosity ratio (the bridge liquid versus the surrounding medium) is larger or the substrate is more slippery to the fluids.