The formation of liquid bridges between planar and conical substrates is analyzed macroscopically taking into account the line tension. Depending on the value of the line tension coefficient τ and geometric parameters of the system one observes two different scenarios of liquid bridge formation upon changing the fluid state along the bulk liquid-vapor coexistence. For τ > τ~* (τ~* <0) there is a first-order transition to a state with infinitely thick liquid bridge. For τ< τ~* the scenario consists of two steps: First there is a first-order transition to a state with liquid bridge of finite thickness, which upon further increase of temperature is followed by continuous growth of the thickness of the bridge to infinity. In addition to constructing the relevant phase diagram we examine the dependence of the width of the bridge on thermodynamic and geometric parameters of the system.
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