  Using the quasi-exact density-matrix renormalization-group method we
calculate the solvation forces in two-dimensional Ising films of thickness L
subject to identical algebraically decaying boundary fields with various decay
exponents p. At the bulk critical point the solvation force acquires a
universal contribution which is long-ranged in L due to the critical
fluctuations, a phenomenon known as the critical Casimir effect. For p = 2, 3
and 50, we study the scaling behaviour of the solvation force along the
pseudo-phase coexistence and along the critical and sub-critical isotherms.
