# Geometric Confinement of 3D Smectic Liquid Crystal Foams
## 4 Discussion  
Based on the experimental results presented in the previous section, we concluded that the properties of SDS and LC foams are significantly affected by the geometry of the boundaries, the flow rate of the injected air, and the drainage properties of the foam. For example, we found that we could improve the foam structures and their stability by changing the shape of their container from rectangular and square to cylindrical. This is because the confining forces in the cylindrical geometries are radial and symmetric, unlike the anisotropic ones in rectangular and square containers. These radial forces apply uniform pressure that helps support the foams at high airflow rates while organizing and stabilizing them. We also found that the material's elastic properties can play an essential role in foam fabrication and assembly processes. When the air is injected into the LC, it induces a deformation of the smectic film to generate a bubble. This deformation is usually energetically expensive. To minimize the excess of the free energy, the elasticity of the LC (bulk effect) and its surface tension (at the smectic-air interface) resist the forces produced by the air and balance them. This is why the size of 8 CB cells is smaller than that of SDS because the elasticity of SDS is negligible compared to that of LC (Figures 2e and 3g). This is also why the smectic cells are deformed at high airflow rates and why we cannot create foams above 38 mL/min in rectangular containers (Figure 2d). However, it is essential to mention that the size effect is valid only for rectangular and square confinements where the pressure forces are anisotropic. In the case of cylindrical boundaries, the opposite behavior is observed: the LC cells are larger than those of SDS (Figure 4g). We believe that this is due to the interplay between the radial confining forces and the elastic ones that create a resultant force that supports the cells, stabilizes them, and helps them to grow, unlike rectangular and square containers, where the confining pressures and elastic forces are anisotropic, causing the bubbles to bump and collapse. The LC bubbles can then support a larger volume of air, while the SDS ones can be created with a lower air volume, which explains why these cells are smaller than the LC ones in cylindrical containers. By analyzing the effect of the airflow rate and the geometry of confinement, and by comparing the smectic foam to SDS, we concluded that the best parameters to fabricate stable and ordered LC foam are in a cylindrical container at an airflow rate of 2 mL/min. We next focused on the 3D structure of the foams and the assembly of their cells. Figure 5 shows the different 3D assemblies of the SDS and LC foams under different geometric confinements. Our results indicate that the structure of foams depends on three parameters: The first one is the drainage of the foam that affects their cell thicknesses and shapes. The second one is the confinement conditions. The third one is the elastic properties of the materials. To better understand the drainage effect due to gravity, we measured the change in foam-cell thickness between the upper layer (in contact with the air) and the lower one (in contact with the material reservoir), as shown in Supplementary Figure S4. We found that the change in cell thickness within rectangular geometries is more significant for the SDS (57 \(\pm\) 2%) than the LC (40 \(\pm\) 1%) (Supplementary Figure S4a). We also noticed that the drainage does not depend on the flow rate of the injected air. In rectangular confinement, all cells have a polyhedral shape and present BCC symmetry (Figure 5d) in the case of SDS and FCC (Figure 5f) in the case of LC (Figure 5a). When the geometry of confinement was changed to a square (Figure 5b), we noticed that the shape and the arrangement of SDS cells were affected by the drainage of the foam.