A novel concept of effectiveness factor dependence on the length of a catalyst particle is suggested. Such behaviour emerges in sufficiently long catalysts when an inhomogeneous state is established in the uniformly exposed particle. The source of instability considered here is an endothermic reaction with reactant inhibition (e.g. a Langmuir-Hinshelwood expression). The asymmetry results from the large thermal to mass diffusivities ratio. The observable constant-length bifurcation diagrams are indistinguishable from those of lumped systems. Singular points in the two-dimensional bifurcation map may reveal the asymmetric nature of the solution. The identification of such points is of importance in the analysis of experiments. The assumptions made in the model can be justified on physicochemical grounds. That and the wide domain of stability of the inhomogeneities make the phenomenon a likely candidate for experimental verification.