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From:
Sebastian Knoche and Jan Kierfeld (Dept. of Physics, Technische Universität Dortmund, 44221 Dortmund, Germany),
“Osmotic buckling of spherical capsules”, Soft Matter, Issue 41, 2014, Advance Article,
DOI: 10.1039/C4SM01205D, Received 04 Jun 2014, First published online 18 Aug 2014
ABSTRACT: We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as a control parameter. We compare our results for the bifurcation behavior with results for buckling under mechanical pressure control, that is, with an empty capsule interior. We find striking differences for the buckling states between osmotic and mechanical buckling. Mechanical pressure control always leads to fully collapsed states with opposite sides in contact, whereas uncollapsed states with a single finite dimple are generic for osmotic pressure control. For sufficiently large interior osmolyte concentrations, osmotic pressure control is qualitatively similar to buckling under volume control with the volume prescribed by the osmolyte concentrations inside and outside the shell. We present a quantitative theory which also captures the influence of shell elasticity on the relationship between osmotic pressure and volume. These findings are relevant for the control of buckled shapes in applications. We show how the osmolyte concentration can be used to control the volume of buckled shells. An accurate analytical formula is derived for the relationship between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows use of elastic capsules as osmotic pressure sensors or deduction of elastic properties and the internal osmolyte concentration from shape changes in response to osmotic pressure changes. We apply our findings to published experimental data on polyelectrolyte capsules.
Figure caption (Fig. 1 in the paper):
Fig. 1 Bifurcation diagrams for buckling by mechanical pressure and volume control: (a) volume–pressure relationship, (b) enthalpy as a function of pressure, (c) elastic energy as a function of volume. The dotted blue line represents the spherical solution branch; the other colored lines represent buckled solution branches A, B, C and C' according to the labels and pictograms on the right. The insets in the energy diagrams in (b and c) show the differences between buckled and spherical branches. In all plots, the elastic moduli are EsubB(bar)= 0.0001 and Poisson ratio nu = 1/3, and the same qualitative behavior has been obtained for all bending stiffness under consideration, from EsubB(bar) = 0.000001 to 0.01, See also ref. 16. On the right, schematic diagrams clarify the qualitative course of the solution branches.
ref. 16: S. Knoche and J. Kierfeld, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2011, 84, 046608
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