Breath Figure Spot: a Recovery Concentration Manifestation

Directing a jet of humid air to impinge on a surface that is cooled below the dew point results in micro-sized water droplets. Lord Rayleigh discussed the phenomenon by contrasting clean to flame-exposed glass and called such behaviour Breath Figures (BF). Historically, utilizing dew as a water source was investigated by several scientists dating back to Aristotle. However, due to the degrading effects of air as a non-condensable gas (NCG) such efforts are limited to small scale water production systems and exhaled breath condensate (EBC) technology, to name a few. Recently, the concept of BF has been utilized extensively in the generation of micro-scale polymer patterns as a self-assembly process. However, the generation of BF on surfaces while being impinged by a humid air jet has not been quantified. In this work, we illustrate that a BF spot generated on a cooled surface is a manifestation of a recovery concentration. The concept is analogous to the concept of adiabatic-wall temperature defined for heat transfer applications. Upon closer examination of the vapor concentration distribution on a cooled impinged surface, we found that the distribution exhibits distinct regimes depending on the radial location from the center of the impingement region. The first regime is confined within the impingement region, whereas the second regime lies beyond this radial location including the wall jet region. Scaling analysis as well as numerical solution of the former regime shows that the maximum concentration on the surface is equivalent to its counterpart of a free unbounded jet with similar geometrical conditions. Additionally, the scaling analysis of the latter regime reveals that the jet speed and standoff distance are not important in determining the recovery concentration. However, the recovery concentration is found to vary monotonically with the radial location. Our conclusions are of great importance in optimizing jet impingement where condensation phase change is prevalent.