  The adhesion dynamics of a membrane confined between two permeable walls is
studied using a two-dimensional hydrodynamic model. The membrane morphology
decomposes into adhesion patches on the upper and the lower walls and obeys a
nonlinear evolution equation that resembles that of phase separation dynamics,
which is known to lead to coarsening, i.e. to the endless growth of the
adhesion patches. However, due to the membrane bending rigidity the system
evolves towards a frozen state without coarsening. This frozen state exhibits
an order-disorder transition when increasing the permeability of the walls.
