Equilibrium shapes of axisymmetric liquid solder menisci around a vertical cylinder on a horizontal substrate

In this paper, equilibrium shapes of axisymmetric liquid solder joint menisci around a vertical cylinder on a horizontal plane substrate were calculated by numerically solving the Laplace equation of capillarity. The boundary conditions are the contact angles formed with the cylinder and with the substrate, subject to the prescribed liquid solder volume constraint. Numerical solutions were obtained by implementing the 4th-order Runge-Kutta technique and the Shooting Method simultaneously. For a given solder volume, the equilibrium shapes of axisymmetric solder menisci, the capillary height on the cylinder and the radius of the wetted circle on the substrate are sensitive to the contact angles. Except the vertical wetted area on the cylinder, the horizontal wetted area on the substrate and the cross-section area of the axisymmetric meniscus were found to be approximately linear functions of the liquid solder volume in a small range. Finally, the effects of cylinder radius on the equilibrium shapes and on the both wetted areas were studied.