AbstractCapsules with a thin aerogel shell were prepared by the OO/W/OIemulsion process. (Phloroglucinol carboxylic acid)/formaldehyde (PF) was used as the water phase (W) solution to form the shell of the capsule. PF is a linear polymer prepared from phloroglucinol carboxylic acid. The viscosity of the PF solution can reach a high level of 9×10−5m2/s without gelation while resorcinol/formaldehyde (RF) gelates at ~3–4×10−5m2/s. Using the viscous PF solution, capsule with a 17 µm gel shell was fabricated. This thickness satisfies the specification of the first phase of Fast Ignition Realization Experiment (FIREX-I) at Osaka University. When PF gel was extracted to remove the organic solvent, shrinkage of 9% occurred. The final density of the PF aerogel was 145 mg/cm3. Both the shell thickness and density can satisfy the specification of FIREX-I. The pore size of the PF aerogel was less than 100 nm while that of RF was 200–500 nm. The SEM showed that PF had particle-like foam structure while RF had fibrous-like foam structure.
AbstractIt is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in \mathbb{R}^{n} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n\nearrow\infty.
Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach space theory, combinatorics, probability, discrete geometry, etc.
In this note, we give yet another two proofs via the regularity theory of elliptic partial differential equations and calculus of variations.
Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.
Thin shell aerogel fabrication for FIREX-I targets using high viscosity (phloroglucinol carboxylic acid)/formaldehyde solution
