  We study a model of two polymers confined to a slit with sticky walls. More
precisely, we find and analyse the exact solution of two directed friendly
walks in such a geometry on the square lattice. We compare the infinite slit
limit, in which the length of the polymer (thermodynamic limit) is taken to
infinity before the width of the slit is considered to become large, to the
opposite situation where the order of the limits are swapped, known as the
half-plane limit when one polymer is modelled. In contrast with the single
polymer system we find that the half-plane and infinite slit limits coincide.
We understand this result in part due to the tethering of polymers on both
walls of the slit.
  We also analyse the entropic force exerted by the polymers on the walls of
the slit. Again the results differ significantly from single polymer models. In
a single polymer system both attractive and repulsive regimes were seen,
whereas in our two walk model only repulsive forces are observed. We do,
however, see that the range of the repulsive force is dependent on the
parameter values. This variation can be explained by the adsorption of the
walks on opposite walls of the slit.
