Critical trajectories for aerosol particles: their determination for impaction in fibrous filters and in oscillating bubbles

Critical trajectories for aerosol particles in a gas flow are ones which divide an aerosol flux into different parts, for example aerosol which is, and is not deposited. They can exist in all gas flows in which aerosol motion is governed by gas velocity rather than by diffusion and we describe two mathematical methods for their calculation. For deposition by impaction on a filter fibre it is necessary to solve the differential equations for particle motion and an efficient iterative procedure is used to obtain the critical trajectories. Jonas and Schütz (1988) have shown that aerosol impaction is an important mechanism for the removal of aerosol from an oscillating sodium vapour bubble formed during a hypothetical core disruptive accident in a fast reactor. For these one-dimensional oscillations, when the gas velocity within a bubble is a linear function of position, we extend their work by calculating critical trajectories directly from the integral equation describing a depositing particle for two models with different initial conditions. With initially entrained uniform aerosol, the percentage impacted is independent of the inclusion of gravity in the calculations as long as regions empty of aerosol do not appear in the bubbles. Numerical results are obtained for a wide range of amplitudes of bubble oscillations and aerosol in the size range 1-30 m. In agreement with Jonas and Schütz, we find that a considerable fraction of the aerosol at larger sizes is removed by impaction. For aerosol below 20 m in size, the removal fraction does not always increase with the oscillation amplitude, but appears to peak at a certain value of the amplitude. This could indicate a kind of resonant behaviour coupling aerosol entrainment to oscillations in the gas velocity. The theory is applicable to different types of bubble oscillation.