Sculpting Liquids with Ultrathin Shells

Pattern Formation in Confined Core‐Shell Structures: Stiffness, Curvature, and Hierarchical Wrinkling

“…Despite the system containing uncured oligomers in the liquid state, we chose to utilize a Winkler substrate with stiffness ($$K_s ={E_s}{\sqrt {Rt}}$$), [ 40 ] as opposed to previous studies applying Laplace pressure for P (=2γ/ R ). [ 17,20 ] The rationale behind this choice is that the key scaling results of the sheet‐on‐liquid drop problem exhibit distinct deviations compared to the morphological changes in our system (refer to ‘ p evaluation’ section of the Supporting Information for related discussion). Furthermore, our system is situated within the domain of high bendability, as indicated by the condition ϵ −1 = γ W 2 / B ≫ 1, [ 17 ] rendering the bending term negligible in the force balance of the dominant terms.…”

“…These results align remarkably well with previous sheet‐on‐droplet problems. [ 20,37 ] For oligomer droplets, even slight progress in curing induces a rapid escalation in E s , leading to a corresponding significant increase in α. This incremental shift causes $$\tilde{L}\rightarrow 0$$, as deduced from Equation (), which also aligns well with the previously observed outcomes of pattern formation in the microspheres (with large κ).…”

“…[14][15][16] For flat disks, efforts have focused on determining the extent of the wrinkled region and using the degree of confinement as a key metric to clarify the compatibility problem. In particular, the investigations conducted so far have focused primarily on specific scenarios, such as when the substrate is either in a liquid state, such as in the sheeton-droplet problem, [17][18][19][20] or when the substrate is highly rigid and experiences minimal deformation. [21][22][23] However, this narrow focus has neglected a wider range of substrate mechanical properties that could be exploited in practical applications.…”

Cross-sections of doubly curved sheets as confined elastica

“…These microstructures arise to solve a geometric problem: they take up excess length at a small scale to facilitate changes in length imposed at a larger scale, by boundary conditions at the edges or by an imposed metric in the bulk. When the confining potential is sufficiently soft, like that presented by a liquid, the sheet can have significant freedom to select the overall response that the small-scale features decorate ( 11 , 14 – 21 ). Understanding how gross and fine structures are linked, especially in situations with large curvatures and compression, remains a frontier in the mechanics and geometry of thin films.…”