Frozen states and order-disorder transition in the dynamics of confined membranes

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.