Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear |
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Authors: | Preston, S. P. Jensen, O. E. Richardson, G. |
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Affiliation: | (School of Mathematical Sciences, University Park, University of Nottingham, Nottingham NG7 2RD) |
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Abstract: | We consider the axisymmetric deformation of an initially spherical,porous vesicle with incompressible membrane having finite resistanceto in-plane shearing, as the vesicle is compressed between parallelplates. We adopt a thin-shell balance-of-forces formulationin which the mechanical properties of the membrane are describedby a single dimensionless parameter, C, which is the ratio ofthe membrane's resistance to shearing to its resistance to bending.This results in a novel free-boundary problem which we solvenumerically to obtain vesicle shapes as a function of plateseparation, h. For small deformations, the vesicle contactseach plate over a small circular area. At a critical value ofplate separation, hTC, there is a transcritical bifurcationfrom which a new branch of solutions emerges, representing buckledvesicles which contact each plate along a circular curve. Forthe values of C investigated, we find that the transcriticalbifurcation is subcritical and that there is a further saddle-nodebifurcation (fold) along the branch of buckled solutions ath = hSN (where hSN > hTC). The resulting bifurcation structureis commensurate with a hysteresis loop in which a sudden transitionfrom an unbuckled solution to a buckled one occurs as h is decreasedthrough hTC and a further sudden transition, this time froma buckled solution to an unbuckled one, occurs as h is increasedthrough hSN. We find that hSN and hTC increase with C, thatis, vesicles that resist shear are more prone to buckling. |
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