In the absence of coalescence, coarsening of emulsions land foams) is contr
olled by molecular diffusion of the dispersed-phase species from one emulsi
on droplet (or foam bubble) to another. Previous studies of dilute emulsion
s have shown how the osmotic pressure of a trapped species within droplets
can overcome the Laplace pressure differences that drive coarsening, and "o
smotically stabilize" the emulsion. Webster and Cates (Langmuir 1998, 14, 2
068-2079) gave rigorous criteria for osmotic stabilization of mono- and pol
ydisperse emulsions, in the dilute regime. We consider here whether analogo
us criteria exist for the osmotic stabilization of mono- and polydisperse c
oncentrated emulsions and foams. We argue that in such systems the pressure
differences driving coarsening are small compared to the mean Laplace pres
sure. This is confirmed for a monodisperse 2D model, for which an exact cal
culation gives the pressure in bubble i as P-i = P + Pi + P-i(G), with P th
e atmospheric pressure, IT the osmotic pressure, and P-i(G) a "geometric pr
essure" that reduces to the Laplace pressure only for a spherical bubble, a
nd depends much less strongly on bubble deformation than the Laplace pressu
re itself. In fact, for Princen's 2D emulsion model, P-i(G) is only 5% larg
er in the dry limit than the dilute limit. We conclude that osmotic stabili
zation of dense systems typically requires a pressure of trapped molecules
in each droplet that is comparable to the Laplace pressures the same drople
ts would have if they were spherical, as opposed to the much larger Laplace
pressures actually present in the system. We study the coarsening of foams
and dense emulsions when there is an insufficient amount of the trapped sp
ecies present. Various rate-limiting mechanisms are considered, and their d
omain of applicability and associated droplet growth rates discussed. In a
concentrated foam or emulsion, a finite yield threshold for droplet rearran
gement among stable droplets may be enough to prevent coarsening of the rem
ainder.