Figure 4: Insensitivity of the coating mechanism to the initial conditions. | Nature Communications

Figure 4: Insensitivity of the coating mechanism to the initial conditions.

From: Fabrication of slender elastic shells by the coating of curved surfaces

Figure 4

(a) Time-series of the normalized film thickness, h(φ,t)/hi, with a constant viscosity, at , and 30. Dashed lines correspond to the numerically computed evolution of an initially sinusoidal thickness profile of the form h(φ,t=0)/hi=1+0.375 cos (10φ) (see Methods and Supplementary Fig. 7). Solid lines are the theoretical prediction, equation (2), with uniform initial thickness profile, h(φ,t=0)/hi=1. The various parameters are: average initial film thickness hi=0.2 mm, sphere radius R=20 mm, and material properties for VPS-32. (b) Shell thickness, hf, obtained for different pouring conditions: pouring height, H, and volume, V, poured onto a spherical mold with R=20 mm using VPS-32. (c) Four different initial conditions used in the numerics converge to the same final thickness, hf, and agree well with equation (6) (black dashed line). The simulation parameters are: hi=2 mm, R=38 mm, hi,1/hi=1, hi,2/hi=1−0.475 cos(2φ), hi,3/hi=1+0.475 cos(2φ), hi,4/hi=1−0.475 cos(10φ), all with the material properties of VPS-32.

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