球形胶囊的渗透屈曲
Osmotic buckling of spherical capsules
摘要：
本文研究了弹性球壳在渗透压作用下的屈曲问题。我们比较我们的结果的分叉行为与结果的机械压力控制下的屈曲，也就是说，与空胶囊内部。我们发现渗透和机械屈曲的屈曲状态之间的显着差异。机械压力控制总是导致相对侧接触的完全塌陷状态，而具有单个有限凹坑的未塌陷状态对于渗透压控制是通用的。对于足够大的内部渗透剂浓度，渗透压控制在质量上类似于体积控制下的屈曲，其中体积由壳内外的渗透剂浓度规定。我们提出了一个定量的理论，它也捕捉壳的弹性渗透压和体积之间的关系的影响。这些发现是相关的屈曲形状的控制在应用中。我们展示了如何渗透浓度可以用来控制屈曲壳的体积。导出了渗透压、弹性模量与胶囊体积之间关系的精确解析式。这也允许使用弹性胶囊作为渗透压传感器或从响应于渗透压变化的形状变化推断弹性性质和内部渗透剂浓度。我们将我们的研究结果应用于已发表的实验数据。
英文摘要：
We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as 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 qualititatively 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 relation 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 analytic formula is derived for the relation between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows to use elastic capsules as osmotic pressure sensors or to deduce 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.
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