Adhesion between membranes is studied using a phenomenological model, where
the inter membrane distance is coupled to the concentration of sticker mol
ecules on the membranes. The model applies to both adhesion of two flexible
membranes and to adhesion of one flexible membrane onto a second membrane
supported on a solid substrate. We mainly consider the case where the stick
er molecules form bridges and adhere directly to both membranes. The calcul
ated mean-field phase diagrams show an upward shift of the transition tempe
rature indicating that the lateral phase separation in the membrane is enha
nced due to the coupling effect. Hence the possibility of adhesion-induced
lateral phase separation is predicted. For a particular choice of the param
eters, the model exhibits a tricritical behavior. We also discuss the non-m
onotonous shape of the inter-membrane distance occurring when the lateral p
hase separation takes place. The inter-membrane distance relaxes to the bul
k values with two symmetric overshoots. Adhesion mediated by other types of
stickers is also considered.