Let's hypothesize there is a flat ballon in space (vacuum, no gravity and no external pressure), which is connected to a gas pump. The gas and the material of the balloon doesn't interact. At a certain time, a valve opens the tank, and some gas inflates towards the flat balloon. The Ballon has a perfect spherical shape if inflated. The material of the balloon is particular, for example some combination of Mylar and Aluminium foil, so it will not burst in space (see ECHO I & II, as example). Let's suppose we know all about the material and the balloon geometry (initial radius, and infltated radius, thickness, elastic modulus, Poisson ratio, etc...) and the gas (density, attractive and repulsive forces between atoms, and so on...).
How can we model the inflation of the balloon in space? how much pressure is needed?
This question comes to me after reading about ECHO missions in wikipedia that: " During ground inflation tests, 18,000 kg (40,000 lb) of air were needed to fill the balloon, but while in orbit, several pounds of gas were all that was required to fill the sphere." [Thermal related problems are avoided for now :) ]