Hypothesis: While the lack of efficient tools yielding controllable uniform supersaturations (S) has delayed basic experimental heterogeneous nucleation studies, common diffusive condensation particle counters (DCPCs) would fill this gap if their present substantial S-variation could be minimized. Analysis: For an initially saturated vapor in two-dimensional (2D) parabolic flow, with discontinuous wall temperature change from T-s to T-c, we calculate the spatial S(x, y) distribution, including the curve S-max(Psi) of maximal supersaturations versus streamline Psi. Activation probability curves P(T-s, T-c) are also calculated assuming that nucleation goes from zero to 100% at a critical supersaturation S*. Findings: Two new approaches to achieve a nearly constant S-max(Psi) are discovered. (i) Sampling only the central 50% of the flow is most effective because the [dS(max)(Psi)/D psi](Psi=0) = 0. This advantage is lost in the more common axisymmetric configuration. (ii) When the ratio Le = alpha/D between gas-vapor heat and mass diffusivities is unity, we find the quite general property that S-max(Psi) is exactly constant. This singular condition may be achieved in special vapor/gas mixtures (ethanol/CO2; methanol/CO2; H2O/air, all seeded with lighter or heavier gases). With greater generality, Le = 1 also in turbulent flows. Therefore, basic heterogeneous nucleation studies with newly available seed particles of fixed size and composition are viable in DCPCs. (C) 2020 Elsevier Inc. All rights reserved.