The statistical physics and dynamics of double supported bilayers are studied theoretically.
The main goal in designing double supported lipid bilayers is to obtain model systems
of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate
being screened by the lower bilayer. The fluctuation-induced repulsion between membranes
and between the lower membrane and the wall are explicitly taken into account using
a Gaussian variational approach. It is shown that the variational parameters, the
"effective" adsorption strength and the average distance to the substrate, depend
strongly on temperature and membrane elastic moduli, the bending rigidity and the
microscopic surface tension, which is a signature of the crucial role played by membrane
fluctuations. The range of stability of these supported membranes is studied, showing
a complex dependence on bare adsorption strengths. In particular, the experimental
conditions to have an upper membrane slightly perturbed by the lower one and still
bound to the surface are found. Included in the theoretical calculation of the damping
rates associated with membrane normal modes are hydrodynamic friction by the wall
and hydrodynamic interactions between both membranes.