Fractures are relatively planar discontinuities in rocks induced by the huge internal stresses which are created by the slow but constant motions of the underground masses. Deposition of a single solute in a single fracture is addressed in the limit where the geometrical changes are very slow compared to the average fluid velocity. The deposition fluxes are calculated by means of a finite-difference scheme which is much more efficient than random walks. Examples of deterministic fractures, random but uncorrelated fractures, Gaussian and self-affine fractures are studied for four different values of the Peclet and the Peclet-Damkohler numbers. Some general trends are discussed.