  We investigate a new diffuse-interface model that describes creeping
two-phase flows (i.e., flows exhibiting a low Reynolds number), especially
flows that permeate a porous medium. The system of equations consists of a
Brinkman equation for the volume averaged velocity field as well as a
convective Cahn--Hilliard equation with dynamic boundary conditions for the
phase-field, which describes the location of the two fluids within the domain.
The dynamic boundary conditions are incorporated to model the interaction of
the fluids with the wall of the container more precisely. In particular, they
allow for a dynamic evolution of the contact angle between the interface
separating the fluids and the boundary, and also for a convection-induced
motion of the corresponding contact line. For our model, we first prove the
existence of global-in-time weak solutions in the case where regular potentials
are used in the Cahn--Hilliard subsystem. In this case, we can further show the
uniqueness of the weak solution under suitable additional assumptions.
Moreover, we further prove the existence of weak solutions in the case of
singular potentials. Therefore, we regularize such singular potentials by a
Yosida approximation, such that the results for regular potentials can be
applied, and eventually pass to the limit in this approximation scheme.
