For the geometry below, derive an expression for the force per length (F/L) for a thin liquid bridge with surface tension adhering an infinitely

For the geometry below, derive an expression for the force per length (F/L) for a thin liquid bridge with surface tension γ adhering an infinitely long, thin cylinder to a flat plate. Assume that the capillary number for this system is small (i.e., the liquid mass negligible compared to surface tension effects). Assume that the contact angle between the liquid and solids is θ = 0° 

 What is the F/L when φ--> 0?