Phase separation in mixtures of polymers and alkanes is investigated with the aid of a recently developed lattice model, based on the Born-Green-Yvon (BGY) integral equation approach to fluids. The system-dependent parameters of the BGY lattice model for binary mixtures are deduced from those of its pure components, which in turn are determined from a comparison with experimental data. The lower critical solution temperatures (LCSTs) for polyethylene (PE) in various n-alkanes were predicted from the BGY lattice model and compared with experimental data. While the model underestimates the LCSTs for the smaller alkanes, it reproduces the experimental values very well for the higher alkanes (decane through tridecane), The effect of the chain length of the polymer on the solubility is investigated for the case of decane as a solvent. (C) 1998 Elsevier Science B.V. All rights reserved.