What is the smallest pressure differential that humans can detect?
Short answer
The sensitivity to pressure differences highly depends on the study setup used. A paper resembling the conditions in your kitchen experiment concludes that the just noticeable difference ranges from 19 to 35 kPa.
Background
The smallest difference that can be perceived between two stimulus levels is called the just noticeable difference, or JND. The issue with determining pressure difference JNDs is that it may be dependent on many things. To name a few important factors are the place on the body and the type of stimulus used. The fingertips and tongue are among the most sensitive parts of the body, while the back is way less sensitive to mechanical stimulation. The type of stimulus may also dramatically affect the findings, because vibratory stimuli are sensed by other types of mechanoreceptors than static pressure stimuli.
Having said that, I found a paper describing an experiment that resembled your kitchen experiment pretty well . The authors used air puffs applied to the fingertips. They used an apparatus where the nozzle could be adjusted to accommodate different aperture sizes. The authors tested 10 normal, right handed controls and used a standard 2 alternative forced choice (2AFC) task applied as a method of constant stimuli. Personally I would have adopted an adaptive 2AFC task, but both methods are valid. The authors conclude that

Subject-averaged pressure JND values ranged from 19.4 – 24.7 kPa, with no statistical differences observed between aperture sizes.

Reference
- 33rd Bianchi et al., Annual International Conference of the IEEE EMBS Boston, Massachusetts USA, August 30 - September 3, 2011