  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 called such behavior 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.
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.
