A three-dimensional lattice model of TIP4P water molecules in the presence of non-polar trimeric solute molecules against a charged wall is described. The statistical mechanical treatment of this model is carried out on the basis of a generalization of Barker's self-consistent field theory (J.A. Barker, J. Chem. Phys., 44 (1966) 4212), without introducing adjustable parameters to account for the behaviour of interfacial water molecules. With non-polar trimers which fit the three-dimensional lattice in such a way as to squeeze out water molecules completely from the adsorbed state when vertically oriented, the main features of two-dimensional condensation are predicted. To this end the presence of a van der Waals loop in the adsorption isotherms is eliminated by passing from the canonical to the grand canonical ensemble partition function on the basis of Hill's procedure (T.L. Hill, J. Chem. Phys., 23 (1955) 812).