Off-critical Composition of Thin Liquid Films of Binary Mixture

This study concentrates on the non-linear solutions of bounded films of binary mixtures with free-modulated surfaces, situated on an energetically neutral solid substrate and subject to periodic boundary conditions on the lateral walls. The Cahn-Hilliard model in its static limit is employed to investigate the problem, and the free surface is considered sharp with its own surface tension. The internal interfaces between the two polymers are allowed to diffuse. The problem is explored through its bifurcations varying several parameters, specifically the surface tension γ, film lateral domain size, and the mean film thickness of homogeneous and laterally (and horizontally) stratified compositions of two layers. The mixture is considered in the off-critical composition with 𝑐 = 0.4. The results reveal a rich family of solutions, providing valuable insights into the structural properties of thin films of binary mixtures،