Roy Jackson conducts seminal research on the stability of a dispersion of particles supported by up-flowing gas. This work led to the prediction of voidage waves, subsequently observed in fluidised beds. He also pioneered theory describing the flow of particles round a gas bubble rising in a fluidised bed and gave the first proper analysis of densely packed particle flow down a vertical standpipe. His work on upward motion of a gas–particle mixture in a pipe provides a rational explanation of particle accumulation near the walls.

More recently, he has taken up the general problem of the mechanics of the motion of gas-free granular material. He has also made notable contributions to the dynamics of chemically reacting systems, the interplay of reactions and diffusion in porous catalysts, and optimisation of the design and operation of chemical process plants.