Effect of membrane bending stiffness on the axisymmetric deformation of capsules in uniaxial extensional flow

The effect of interface bending stiffness on the axisymmetric deformation of liquid capsules enclosed by elastic membranes subject to uniaxial extensional flow is considered. Flow-induced deformation causes the development of membrane in-plane elastic tensions and bending moments due to the noninfinitesimal thickness of the membrane or to a preferred equilibrium configuration of an interfacial molecular network, accompanied by transverse shear tensions. The elastic tensions are related to the surface deformation by means of Mooney's linear constitutive law for thin elastic sheets, and the bending moments are related to the membrane resting shape and to the instantaneous principal curvatures by means of constitutive equations. Interfacial force and torque balances are used to relate the jump in hydrodynamic traction across the interface to the elastic tensions and bending moments. A numerical procedure is implemented for simulating the capsule deformation in uniaxial extensional Stokes flow based on a boundary-integral method. Results on the transient and asymptotic deformation for capsules with spherical unstressed shapes illustrate the effect of bending stiffness expressed by an interface modulus of bending for a broad range of elasticity capillary numbers. It is shown that bending stiffness, however large, is not able to restrain continued deformation beyond a critical capillary number, and its main effect is to cause highly deformed capsules with pointed shapes to develop instead nearly cylindrical shapes with rounded caps. (C) 2001 American Institute of Physics.