INTRODUCTIONConsider a gas stream approaching an obstacle with a constant velocity U ∞ . For laminar flows at high Reynolds number, the potential region where the flow is deflected by the obstacle is much larger than the viscous boundary layer. In that potential region, the particle trajectories depart from the gas streamlines because the particles cannot follow the gas velocity changes. In this work, the dynamical behaviour of the particles is analysed accounting for particle inertia.For a circular cylinder of radius R transverse to the mainstream, and along the central streamline ending in the forward stagnation point, the dimensionless gas radial velocity u ≡ υ g /U ∞ is given by u = -1 + 1 / z 2 . Here z ≡ r / R and r is the radial coordinate measured from the cylinder centre. When particle inertia is taken into account, along this streamline the dimensionless particle radial velocity w ≡ υ P / U ∞ is governed by the following ordinary differential equation: Where St ≡ U ∞ τ / R is the particle Stokes number with τ being the characteristic particle relaxation time. Far away from the cylinder the particles move with the gas velocity. Then, the initial condition is w(u = -1) = -1.NUMERICAL INTEGRATIONThe integration of the previous equation leads to the results depicted in Figures 1 and 2. In Fig. 1 the particle velocity (w) is plotted versus the gas velocity (u), for different Stokes numbers. Dashed line in Fig. 1 corresponds to the absence of inertia (St=0) when the particles follow the gas velocity. For relatively small inertia (St<St c ) particles depart from the gas velocity, but approaching the cylinder the velocities becomes very small and the particles accommodate again to the gas, reaching a vanishing velocity at the surface. Therefore, particle impaction only occurs for St>St c when the particles cannot reach the accommodation with the gas near the stagnation point and they attain the surface with a non-vanishing velocity, w 0 . The value of w 0 (plotted in Fig. 2 as a function of the difference St-St c ) tends to zero with vanishing slope when St tends to St c . Thus, it is hard to obtain the value of St c directly from the numerical integration. However, integration. However, St c can easily been obtained by analysing the particle trajectories near the stagnation point.LINEAR REGIONFrom Eq. 1, in the vicinity of the stagnation point (z = 1 + x with x 1), the particle trajectory x(t), is approximately governed by the differential equation for a harmonic damped oscillator Eq. 2 is exact for particles in the two-dimensional stagnation flow with a gas velocity u = -2x.For St<18 the roots of the characteristic polynomial of Eq. 2 are real and the particles need and infinite time to reach the stagnation point where they arrive with a vanishing velocity. On the other hand, for St>18 these roots become imaginary and the particle trajectories are Moreover, the stagnation point corresponds to ωt + φ=π/2 and there the particle velocity is This exponential dependence is responsible for the behaviour of w 0 indicated in Fig. 2. The constants A and φ should be such as to match with the trajectories resulting from the numerical integration near z=1.