Lipid membranes are ubiquitous in biological systems. They play a central role as cell walls. The dynamics of cell adhesion involves a complex molecular machinery. However, we wish to understand some of its basic properties by means of simple physical modeling.
We have studied the adhesion dynamics of membranes confined between two porous walls. We have derived a nonlinear and nonlocal evolution equation for the membrane, which is studied by means of asymptotic analysis. We have also solved the full equation numerically. We find that adhesion systematically leads to frozen states with a characteristic wavelength. An order-disorder transition is obtained by increasing the porosity of the walls. Thermal fluctuations restore the coarsening leading to macroscopic adhesion patches.