# Geometric Confinement of 3D Smectic Liquid Crystal Foams
## 5 Conclusions  
In this work, we fabricated a new type of foam by using an ordered material, the smectic LC, and compared its behavior to the foam made with a simple fluid, the SDS. We reported the parameters that affect foam creation and assembly in 3D. We found that the geometry of confinement plays an essential role in the fabrication of LC foams. In particular, we demonstrated how radial forces within cylindrical boundaries could support and stabilize the foam, unlike rectangular and square confinements, where boundaries apply anisotropic forces that deform and disrupt the foam. We also discussed the impact of LC elasticity and the influence of the airflow rate and drainage in creating the foam and controlling its cell sizes. Our results show that the drainage effect due to gravity is weak in LCs compared to SDS soaps. Weakening the drainage effect helps the foam to maintain a similar volume fraction along the sample and preserve the ordering of its cells. This result is significant for industrial applications that require the fabrication of monodisperse foams with uniform structures. We are confident that our work will further stimulate theoretical, numerical, and experimental studies to better elucidate the 3D assembly of LC foams under confinement.  
Figure 5: Three-dimensional structure of SDS and LC foams under geometric confinement. (**a**) Rectangular confinement: The SDS cells have a BCC structure, while the LC cells present an FCC structure. (**b**) Square confinement: For the SDS foams, the 3D structure depends on their volume fraction. For low \(\varphi\), the cells have a BCC structure, and for high \(\varphi\), they present an FCC symmetry. The LC foam always shows an FCC structure, independently of \(\varphi\) or the geometry of confinement. (**c**) Cylindrical confinement: SDS foam presents a BCC structure at low \(\varphi\) and an FCC structure at high \(\varphi\). The LC structure presents an FCC structure for both high and low \(\varphi\). (**d**) Models of the dry polyhedral BCC structure in 2D and 3D. (**e**) Model of the wet spherical FCC structure (high \(\varphi\)). (**f**) Models of the dry polyhedral FCC structure in 2D and 3D (low \(\varphi\)). All scale bars are around 2 mm.  
**Supplementary Materials:** The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app13063414/s1](https://www.mdpi.com/article/10.3390/app13063414/s1)]([https://www.mdpi.com/article/10.3390/app13063414/s1](https://www.mdpi.com/article/10.3390/app13063414/s1)). Figure S1: SDS foam confined in rectangular containers. Figure S2: SDS foam confined in square containers. Figure S3: SDS foam confined in cylindrical containers. Figure S4: Drainage effect on the SDS and LC foams.  
**Author Contributions:** [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] performed the research; [PERSON] designed the experiments; [PERSON], [PERSON] and [PERSON] designed the 3D structures of the foam; [PERSON], [PERSON], [PERSON] and [PERSON] wrote the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the University of Massachusetts Boston. R.N.N. was supported by UMass Boston College of Science and Mathematics Dean's Research Fellowship from Oracle and The UMass Boston McNair fellowship.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data that support the findings of this study are included within the article.  
**Acknowledgments:** The authors thank [PERSON] for the helpful discussions and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.