The aspect of partial glazing of porcelain labware is not unique to Büchner funnels. This is typical of many porcelain items used in the lab. Other porcelain labware is also partly glazed. Check an evaporating dish. It is partially unglazed outside and completely glazed inside.
I do not know the exact reason for leaving the rim of this particular funnel unglazed but this has more to do with manufacturing rather than something fundamental to chemistry or filtration theory. As I recall damaged glazed porcelain funnels, it is possible that the rim is a high stress point. If the rim were also coated, cracks may start from the rim, they can propagate elsewhere, and this logic makes as to why one would leave the rim from glazing. It introduces a discontinuity. Porcelain does need glazing if it is to be used for reagents otherwise it is too porous and hence unwashable! Good for one use only.
Another reader (Snijderfrey) pointed out in the comments that during firing, the funnels have to sit somewhere and it is likely the reason that if the Büchner funnel is fired upside down, the rim does not get glazed.
Regardless, the rim not being glazed is a pretty old "tradition". One can see very old catalogues of the previous century with same specs. Today plastic Büchner, Pyrex funnels with sintered glass funnels are also very common, they do not need glazing and they are completely uniform.
I was able to access the first description of this funnel in the German chemical literature from 1888 by Eduard Büchner and an earlier description by Hirsch again in 1888. It is just a one paragraph description by Hirsch. His funnel is conical and Büchner simply made it flat. Nothing fundamental about porcelain or glazing is mentioned.
In the reports of the German Chem. Ges. 1886, p. 918, O. N. Witt
describes a filtration device consisting of a plate of glass, metal or
porcelain with multiple perforations, which is inserted into a funnel,
closed by a small filter disc and sealed against the funnel by a
larger one. This apparatus (Fig. 45), which is widely used in
thousands, especially in factory laboratories, often shows the defect
of not closing completely tightly, so that the filtrate is turbid,
especially at the beginning of the suction. To avoid this, I have had
porcelain funnels made in which the filter plate is firmly inserted.
Only one filter disc is then used for sealing, and the funnel can be
emptied and refilled without the plate moving and thus becoming leaky.
The apparatus is manufactured in the best quality by Max Kaehler
Martini, Berlin W, Wilhelmstr. 50. Huddersfield, March 3, 1888
Büchner simply changes the design...
Translated with www.DeepL.com/Translator (free version)
