In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of
the L-alpha lamellar and L-3 sponge phases displays a phenomenon of epitaxy
: the layers of the lamellar phase tend to make a constant non-trivial angl
e with the interface. Thin samples of lamellar phase embedded in the sponge
phase are thus submitted to oblique anchoring conditions and defects are c
reated in the lamellar phase in order to satisfy the bulk lamellar ordering
and the boundary conditions. We have studied small droplets of lamellar ph
ase in the sponge phase. They do not exhibit the classic L-alpha defects (f
ocal conic domains) but wall defects, which appear in order to satisfy the
smectic elasticity and the boundary conditions. Moreover we show through ex
periments in controlled geometry that, even in the presence of focal conic
domains, wall defects control the size and periodicity of the textures whic
h are observed at the interface.