Stretching of capsules in an elongation flow, a route to constitutive law

• Published in: Journal of fluid mechanics Vol. 767
• Main Authors: de Loubens, C., Deschamps, J., Boedec, G., Leonetti, M.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.03.2015; Cambridge University Press (CUP)
• Subjects: Biological Physics; Biomechanics; Condensed Matter; Fluid Dynamics; Fluid mechanics; Mechanics; Physics; Rapids; biological fluid dynamics; low-Reynolds-number flows; capsule/cell dynamics; Microcapsules; elasticity; Stokes flow
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2015.69

Soft bio-microcapsules are drops bounded by a thin elastic shell made of cross-linked proteins. Their shapes and their dynamics in flow depend on their membrane constitutive law characterized by shearing and area-dilatation resistance. The deformations of such capsules are investigated experimentally in planar elongation flows and compared with numerical simulations for three bidimensional models: Skalak, neo-Hookean and generalized Hooke. An original cross-flow microfluidic set-up allows the visualization of the deformed shape in the two perpendicular main fields of view. Whatever the elongation rate, the three semi-axis lengths of the ellipsoid fitting the experimental shape are measured up to 180 % of stretching of the largest axis. The geometrical analysis in the two views is sufficient to determine the constitutive law and the Poisson ratio of the membrane without a preliminary knowledge of the shear elastic modulus $G_{s}$ . We conclude that the membrane of human serum albumin capsules obeys the generalized Hooke law with a Poisson ratio of 0.4. The shear elastic modulus is then determined by the combination of numerical and experimental variations of the Taylor parameter with the capillary number.