Instabilities of soft elastic microtubes filled with viscous fluids: pearls, wrinkles, and sausage strings

Abstract

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro- or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y=γ/(GeR)>6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y>2, where γ, G_e, and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.