Effect of the finite width of the temperature transition in diffusive condensation particle counters

Abstract

The fluid streamlines w moving near the hot-cold wall junction in diffusive condensation particle counters (DCPCs) experience close to unit saturation ratio (S ¼ 1), being ineffective for nucleation. Nevertheless, when the wall temperature changes discontinuously, the maximal saturation ratio sensed along all near-wall streamlines S max (w) is well above unity, and is the same for all near-wall streamlines. This property greatly reduces the range of effective values of S max (w) present within the CPC. When the ratio of heat and mass diffusivities Le ¼ a/D approaches unity, S max (w) becomes constant also for streamlines far from the wall, enabling in principle the use of DCPCs for basic heterogeneous nucleation studies and for high resolution particle sizing. Here we consider theoretically the near-wall structure of the saturation ratio profile in the more realistic case when the temperature change takes place linearly over an insulating strip of finite length D placed between two metallic wall segments held at different uniform temperatures. A thin boundary layer forms then near the wall, over which S max (w) transitions from unity at the wall to the uniform value expected in the idealized temperature jump case. This boundary layer is unavoidable at all Le, including Le ¼ 1. However, simple scaling laws are provided for its width, showing that it may be relatively thin, and its effects may be removed by using sheath gas.