In this letter, the structural stability of foam is investigated exper
imentally. We use crystalline foams (equi-sized gas bubbles confined i
n a cylindrical glass tube) under conditions of a steady-state drainag
e where soap solution is added onto the top of the foam at a constant
rate. By varying this how rate, we observe: 1) Reproducible structural
transitions that are induced when drainage exceeds a critical liquid
flow rate. The transition leads to a new ordered foam stable under the
flow. A structural diagram is defined, showing the boundary between t
he two structures for the whole range of existence of the initial stru
cture. 2) A deviation from the classical Poiseuille behavior of the dr
aining liquid, exhibited at low flow rates, is observed. 3) We propose
a simple model for the how into the foam, explaining both the deviati
on from the Poiseuille behavior and the stability boundary shown in th
e structural diagram.