  We show that some pieces of cylinders bounded by two parallel straight-lines
bifurcate in a family of periodic non-rotational surfaces with constant mean
curvature and with the same boundary conditions. These cylinders are initial
interfaces in a problem of microscale range modeling the morphologies that
adopt a liquid deposited in a chemically structured substrate with striped
geometry or a liquid contained in a right wedge with Dirichlet and capillary
boundary condition on the edges of the wedge. Experiments show that starting
from these cylinders and once reached a certain stage, the shape of the liquid
changes drastically in an abrupt manner. Studying the stability of such
cylinders, the paper provides a mathematical proof of the existence of these
new interfaces obtained in experiments. The analysis is based on the theory of
bifurcation by simple eigenvalues of Crandall-Rabinowitz.
