Nitrogen oxides (NOx) emissions from diesel engines can profoundly be suppressed if a portion of exhaust gases is cooled through a heat exchanger known as exhaust gas recirculation (EGR) cooler and returned to the intake of the combustion chamber. One major hurdle though for the efficient performance of EGR coolers is the deposition of various species, i.e., particulate matter (PM) on the surface of EGR coolers. In this study, a model is proposed for the deposition and removal of soot particles carried by the exhaust gases in a tubular cooler. The model takes thermophoresis into account as the primary deposition mechanism. Several removal mechanisms of incident particle impact, shear force, and rolling moment (RM) have rigorously been examined to obtain the critical velocity that is the maximum velocity at which the particulate fouling can profoundly be suppressed. The results show that the dominant removal mechanism changes from one to another based particle size and gas velocity. Based on particle mass and energy conservation equations, a model for the fouling resistance has also been developed which shows satisfactory agreement when compared with the fouling experimental results.