“…If the length of the surface in the direction of the flow is much longer than the film thickness or Reynolds number is small, lubrication assumption can be utilized for the liquid flow on the planar surface. For the flow of condensate on the fin top [11,12,13,14,15,35] or the flow of liquid on a heated planar substrate towards the contact line [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34], lubrication assumption has been widely utilized. For a cylindrical surface, on the other hand, Reynolds number is defined as Re = u ϕ δ ν, where u ϕ is the mean angular velocity in ϕ-direction, and the extent of the flow is expressed as the function of the radius of the cylindrical surface (L f low = R o ϕ).…”