Q. 2 shailos on liquid soap;
1 Is it muttar to use lkiquid soap on Shabbos
2. If yes what about liquid soap that changes from a liquid to a foam
Kol Toov

A.  Remoh (O.H. 326: 10) prohibits using solid soap that dissolves into the water used for washing since it involves creating a new presence and this constitutes “nolad,” (born.)
Nolad refers to things that come into existence on Shabbos, for example breaking ice in order to produce water prohibited by the Talmud (Shabbos 51b.) Sefer Hat’rumah and Remoh, (318: 16 – see M”B 320: 35) explain that the reason is creating a new being.
Other Poskim prohibit because of “memachek” or smoothing which is one of the thirty nine melochos or labours forbidden on Shabbos.
Yechave Daas (2:50 ) permits the use of a bar of soap, because the user has no intention of changing anything; he only intends to clean what he is washing. However, Igrois Moshe (O.H. 1: 113) is stringent in the use of even liquid soaps that can be further diluted.
Most Poskim maintain the prohibition on solid bar soaps but permit the use of free flowing liquid soaps, including the foam or bubbles unintentionally created.(Aruch Hashulchan 326: 11, Ketzos Hashulchan 146: 32, Bris Olam – Memachek 5, Beer Moshe 8: 248, Shemiras Shabbos Kehilchaso 14: 16, et. al.)
Horav Shlomo miller’s Shlit’a opinion is that free flowing or diluted liquid soap is permitted when needed.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a