Model of Two Vertical Cylinders

Due to the capillary interaction between the cylinders, the contact lines on the cylinders are not horizontal. Otherwise, no horizontal force could be generated because the integrals in Eqn. (3.6) would be zero. The capillary force calculation can be performed in the following two regimes divided based on the separation distance between the cylinders small or moderate separation and large separation. 

When two cylinders are spaced at a small or moderate distance iiqay 4C 1), the following mathematical description is valid [14]  

On the cylinder surfaces, the boundary conditions in the bipolar coordinates can be expressed as [13] 

In the bipolar coordinates, Tis constant on the cylinder surface, (o and are related as 

The unit vector tangential to the contact line is described as 

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