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The effect of line tension on the axisymmetric nanoscale capillary bridgebetween two identical substrates with convex, concave and flat geometry at theliquid-vapor equilibrium is theoretically studied. The modified Young'sequation for the contact angle, which takes into account the effect of linetension is derived on a general axisymmetric curved surface using thevariational method. Even without the effect of line tension, the parameterspace where the bridge can exist is limited simply by the geometry ofsubstrates. The modified Young's equation further restricts the space where thebridge can exist when the line tension is positive because the equilibriumcontact angle always remain finite and the wetting state near the zero contactangle cannot be realized. It is shown that the interplay of the geometry andthe positive line tension restricts the formation of capillary bridge.

Effect of line tension on axisymmetric nanoscale capillary bridges at the liquid-vapor equilibrium