/ (𝒑 ⋅ ∇ℎ) / is the coupling free energy coupling 𝒑 to the drop surface and accounting for contributions where particles, depending on 𝑐 M* and 𝑐 N* either align themselves parallelly or terminate perpendicularly to the film surface at the drop-vapor and drop-solid boundaries, respectively. For our slender 2D system, we cannot reorient 𝒑 in the depth direction , and hence ℱ ,$-*' is constant for 2D drops. Finally, in eq.( ), 𝐹 . and 𝐹 / ensures two necessary system constraints: 𝐹 . = ℙ D𝑉 -∫ d𝑥(𝐻 -ℎ)