Liquid bridge equilibrium contours between non-circular supports

The equilibrium shape of a liquid bridge confined between two parallel solid supports of arbitrary shape is analyzed theoretically. The influence of the shape of the solid supports, the volume of the liquid bridge and the axial, lateral, and centrifugal forces acting on it are considered The theoretical study is performed using three different techniques: (i) a numerical process for the minimization of the free energy associated with the fluid configuration, (ii) a second-order analytical expansion around the cylindrical solution to the Young-Laplace equation, and (iii) a finite-difference scheme to numerically integrate the Young-Laplace equation. The two numerical methods are in excellent agreement, indicating the degree of accuracy of the calculations, and there is also good agreement between the analytical expansion and the numerical solutions for moderately large values of the perturbation parameters.