The paper deals with a method to characterize the membrane mechanical properties of microcapsules. The technique consists in flowing microcapsules into a microchannel of comparable dimensions, observing the deformation as a function of the flow rate, and deducing the membrane elastic modulus by means of an inverse method based on a numerical model of the flowing capsule. The method is tested on liquid-filled microcapsules (average diameter of 67 μm) with a membrane made of crossed-linked ovalbumin flowing inside a cylindrical channel. For a neo-Hookean constitutive law, the method yields a constant value for the membrane shear elastic modulus independently of capsule size or deformation. When the capsules are flowed into a square-section microchannel, an approximate analysis of the deformation yields the same value of the membrane shear modulus provided that the size ratio between the capsule and the channel is of order unity.

We present a numerical model of the axisymmetric flow of an initially spherical capsule in a co-axial cylindrical tube. The capsule consists of a liquid droplet enclosed by a thin hyper-elastic membrane that is assumed to obey different membrane constitutive equations such as Mooney–Rivlin, Skalak et al. (1973) or Evans & Skalak (1980) laws. It is further assumed that the capsule may be subjected to some isotropic pre-stress due to initial swelling. We compute the steady flow of the capsule inside the tube as a function of the size ratio between the capsule and tube radii, the amount of pre-swelling and the membrane constitutive law. We thus determine the deformed profile geometry and specifically the onset of the curvature inversion at the back of the particle. We show that for a given size ratio, the critical flow rate at which the back curvature changes is strongly dependent on pre-inflation. The elastic tension level in the membrane as well as the additional pressure drop created by the presence of the particle are also computed. The numerical results are then compared to experimental observations of capsules with alginate membranes as they flow in small tubes (Risso. et al. 2006). It is found that the experimental capsules were probably pre-inflated by about 3% and that their membrane is best modelled by the Skalak et al. law.

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