  The exact solution of directed self-avoiding walks confined to a slit of
finite width and interacting with the walls of the slit via an attractive
potential has been calculated recently. The walks can be considered to model
the polymer-induced steric stabilisation and sensitised floculation of
colloidal dispersions. The large width asymptotics led to a phase diagram
different to that of a polymer attached to, and attracted to, a single wall.
The question that arises is: can one interpolate between the single wall and
two wall cases? In this paper we calculate the exact scaling functions for the
partition function by considering the two variable asymptotics of the partition
function for simultaneous large length and large width. Consequently, we find
the scaling functions for the force induced by the polymer on the walls. We
find that these scaling functions are given by elliptic theta-functions. In
some parts of the phase diagram there is more a complex crossover between the
single wall and two wall cases and we elucidate how this happens.
