A more complete combustion and a decrease in particulate emissions in the burning of a heavy fuel oil in an industrial boiler or similar combustion device is obtained by first heating the oil to a temperature sufficient to significantly lower its viscosity and continuously mixing a fuel additive containing a solution of a high molecular weight, substantially linear, viscoelastic polymer to the heated oil flowing to the combustion device by mechanically stirring the oil and additive at conditions that do not cause degradation of the viscoelastic polymer through rupture and breakage of polymer molecules.