The Cahn-Hilliard equation is the most common model to describe phase separation processes in a mixture of two materials. Moreover, it is further used to describe different phenomena where the distribution and/or motion of two (or more) immiscible materials is considered. Standard Cahn-Hilliard models are usually endowed with homogeneous Neumann boundary conditions for both the phase-field variable and the chemical potential. However, these boundary conditions yield certain limitations: > 1) The diffuse interface separating the materials is enforced to intersect the boundary at a perfect angle of ninety degrees, which is unrealistic in many applications. > 2) No transfer of material between bulk and boundary is allowed and thus, absorption process cannot be described. > For these reasons dynamic boundary conditions for the Cahn-Hilliard equation have been introduced. We take a closer look at dynamic boundary conditions that also exhibit a Cahn-Hilliard type structure. > To describe the evolution of two-phase flows, Navier-Stokes-Cahn-Hilliard models have become a popular choice. As the standard models are subject to a no-slip boundary condition for the velocity field as well as homogeneous Neumann conditions for the Cahn--Hilliard subsystem, they exhibit the aforementioned limitations and are also not well-suited for describing general moving contact line phenomena. However, these issues can also be overcome by the introduction of suitable dynamic boundary conditions.
