## 3 Neutron Test Measurements  
Test measurements with a single foam cell were carried out at the KWS-1 small angle scattering diffractometer at the Heinz Maier-Leibnitz-Zentrum (MLZ, Garching, Germany) [40; 41]. Figure 6a shows the foam cell at the beamline. All measurements were performed at a wavelength of 4.92 A with a 10% wavelength resolution (FWHM), a squared neutron beam of \(10\times 10\) mm, and a data acquisition time of 5 min. Scattering patterns were recorded with a \({}^{6}\)Li-scintillation detector with photomultiplier tubes and a spatial resolution of \(5.3\times 5.3\) mm\({}^{2}\). All measurements were background corrected due to dark current. The foam measurements were also corrected for the scattering by the empty cell. The sample-detector distance was determined using an optical theodolite. Figure 6b shows the 2D detector image of the empty foam cell recorded at a sample-detector distance of 7.615 m. As expected, the empty quartz cylinder provides a low background with no significant secondary scattering. Test measurements were conducted with a foam stabilized by 25 g L\({}^{-1}\) (86.7 mM) sodium dodecyl sulfate (SDS), which is well above the critical micelle concentration of 8 mM [42], at different foam heights. This system was chosen because of the high foam stability and the fact that the first study ever performed on SANS on foams also used a SDS foam at this concentration, making it a reference system [26]. 12 mL of the surfactant solution were initially foamed with a nitrogen gas flow rate of 10 mL min\({}^{-1}\). After the foam level reached a height of around 18 cm, the gas flow was reduced to 1 mL min\({}^{-1}\). At this flow rate the foam height does not change anymore, meaning that the foam formation at the  
Figure 6: **(a)** Single foam cell installed at the KWS-1 beamline at the MLZ. **(b)** 2D SANS data of an empty quartz foam cylinder. **(c–e)** 2D SANS data of a steady-state foam produced from a 25 g L\({}^{-1}\) SDS solution at 16 cm **(c)**, 9.5 cm **(d)**, and 2 cm **(e)** foam height above the foaming solution. All experiments were carried out at a sample–detector distance of 7.615 m. Data acquisition time was 5 min. bottom and the foam decay at the top of the column are balanced. This results in a steady-state foam, in which the foam height corresponds to the age of the foam (i.e., the time passed after its formation at the bottom of the cylinder) and therefore its drainage state. Figure 6c-e shows the corresponding 2D detector images recorded at 16 cm, 9.5 cm and 2 cm above the foaming solution. All images exhibit an isotropic scattering signal around the primary beam. This reveals that the neutron path length through the cell is long enough to average over all orientations of the foam structure, namely the liquid films, within the measuring window. The scattered intensity decreases with increasing measurement height. This is explained by the decreasing liquid volume fraction of the foam with increasing foam age (or height) and proves that different states of the foam can be accessed with a steady-state foam in one experiment. [PERSON] et al. studied the same system using a similar foam cell with a single quartz window for the neutron beam in the lower third of the cylinder and the reported values are shown for comparison (closed squares in Figure 7) [26]. They performed two types of measurements. The first type of measurement was a continuous foaming experiment, in which the SANS data were recorded while nitrogen was continuously bubbled through the foaming solution. This resulted in a wet foam at the measuring position. The second type of measurement was a drainage experiment, in which the gas flow was stopped after foam formation. After some time, this led to a dry foam at the measuring position at the bottom of the foam column. These two types of foams are related to different foam heights in a steady-state foam. Here, a wet and fresh foam is observed at the bottom while a dry and aged foam is observed at the top of the steady-state foam.