  Recent experiments have measured the critical Casimir force acting on a
colloid immersed in a binary liquid mixture near its continuous demixing phase
transition and exposed to a chemically structured substrate. Motivated by these
experiments, we study the critical behavior of a system, which belongs to the
Ising universality class, for the film geometry with one planar wall chemically
striped, such that there is a laterally alternating adsorption preference for
the two species of the binary liquid mixture, which is implemented by surface
fields. For the opposite wall we employ alternatively a homogeneous adsorption
preference or homogeneous Dirichlet boundary conditions, which within a lattice
model are realized by open boundary conditions. By means of mean-field theory,
Monte Carlo simulations, and finite-size scaling analysis we determine the
critical Casimir force acting on the two parallel walls and its corresponding
universal scaling function. We show that in the limit of stripe widths small
compared with the film thickness, on the striped surface the system effectively
realizes Dirichlet boundary conditions, which generically do not hold for
actual fluids. Moreover, the critical Casimir force is found to be attractive
or repulsive, depending on the width of the stripes of the chemically patterned
surface and on the boundary condition applied to the opposing surface.
