Buckling of spherical shells adhering onto a
rigid substrate |
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Authors: | Email author" target="_blank">S?KomuraEmail author K?Tamura T?Kato |
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Institution: | (1) Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan |
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Abstract: | Deformation of a spherical shell adhering onto a rigid substrate
due to van der Waals attractive interaction is investigated by
means of numerical minimization (conjugate gradient method) of
the sum of the elastic and adhesion energies.
The conformation of the deformed shell is governed by two
dimensionless parameters, i.e., Cs/epsilon and
Cb/epsilon where Cs and Cb are
respectively the stretching and the bending constants, and
epsilon is the depth of the van der Waals potential between
the shell and substrate.
Four different regimes of deformation are characterized as
these parameters are systematically varied:
(i) small deformation regime, (ii) disk formation regime,
(iii) isotropic buckling regime, and (iv) anisotropic buckling
regime.
By measuring the various quantities of the deformed shells,
we find that both discontinuous and continuous bucking transitions
occur for large and small Cs/epsilon, respectively.
This behavior of the buckling transition is analogous to van der
Waals liquids or gels, and we have numerically determined the
associated critical point.
Scaling arguments are employed to explain the adhesion induced
buckling transition, i.e., from the disk formation regime to
the isotropic buckling regime.
We show that the buckling transition takes place when the
indentation length exceeds the effective shell thickness which
is determined from the elastic constants.
This prediction is in good agreement with our numerical results.
Moreover, the ratio between the indentation length and its
thickness at the transition point provides a constant number
(2–3) independent of the shell size.
This universal number is observed in various experimental systems
ranging from nanoscale to macroscale.
In particular, our results agree well with the recent compression
experiment using microcapsules. |
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Keywords: | |
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