Is there any halachik problem with blowing bubbles on Shabbos? If so what melacha categories does it fall under? Does the age of the blower matter?
I am quoting you Rabbi Ribiat The 39 Melachos:
Some Poskim advise that one should not blow soap bubbles on Shabbbos because this entails a semblance of creating,which should be avoided.(One should also not deliberately form bubbles from bubble gum.)Nevertheless,one need not restrict young children from blowing the bubbles on SHABBOS.
The Rivevos Ephraim Chelek 8:564:1 was asked if one can blow bubbles from chewing gum(bazuka). He writes that making bubbles from soap was discussed in Shmiras Shabbas Kehilchasa perek 17:30 and says that one shouldn't make them. However, he writes that one shouldn't refrain a child from doing so,and the reason written in the name of Rav Shlomo Zalamn Aurbach is that the bubble inst permanent(no kiyum).
The Rivevos EPhraim uses this logic by gum and writes that making a bubble from gum lasts for a moment and then rips and has no permanence(kiyum). Therefore he writes that it should be permitted. However,he adds that bnei Torah and their children should be machmir. He ends off by saying that in genreal chewing gum isn't a nice thing for a bnei Torah and should be avoided even during the week.
Rav Abadi in his Ohr Yitzchak 1:192 writes:
Shmirat Shabbat Kehilchatah 16:30:
Although adults should not blow soap bubbles, one need not stop children from doing so.
He adds in a footnote that he heard the leniency (of allowing children to blow bubbles) from Shlomo Zalman Auerbach ZTL. The reason was due to the impermanence of the bubbles.