Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

• Published in: Journal of fluid mechanics Vol. 440; pp. 269 - 291
• Main Author: POZRIKIDIS, C.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.08.2001
• Subjects: Biological and medical sciences; Biomechanics. Biorheology; Exact sciences and technology; Fluid dynamics; Fundamental and applied biological sciences. Psychology; Fundamental areas of phenomenology (including applications); Haemodynamics, pneumodynamics; Laminar flows; Laminar flows in cavities; Laminar suspensions; Membranes; Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Tissues, organs and organisms biophysics; Constitutive equation; Stress analysis; Thin shell; Shear flow; Red blood cell; Capsule; Fluid structure interaction; Particle suspension; Blood; Membrane; Numerical simulation; Circulatory system; Hemodynamics; Boundary element method; Stokes flow
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112001004657

The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.