Robert Evans is distinguished for his contributions to the statistical physics of bulk liquids and liquids at interfaces. In the 1970s, he developed theories for the electrical properties and structure of liquid metals. In 1979, he introduced the systematic formulation of classical density functional theory (DFT) for atomic fluids, showing how this can be used to derive tractable approximations for interfacial density profiles, correlation functions and surface tension.

In the 1980s, he employed DFT methods to uncover the nature of wetting transitions (partial to complete wetting for a fluid at a flat substrate) and the phase behaviour of fluids in simple confining geometries. Novel transitions, unrelated to bulk, occur in both. Later Robert developed powerful analytic methods to probe the large distance decay of pair correlation functions whose predictions were borne out later in computer simulation and experiment.

From 1998, Robert investigated solvent mediated interactions — the effective interaction between big particles immersed in a reservoir of smaller ones. His work has shed fundamental insight into the nature of depletion and Casimir interactions in colloidal fluids.