Transient deformation of elastic capsules in shear flow: Effect of membrane bending stiffness

The transient deformation of liquid capsules enclosed by elastic membranes with bending rigidity in shear flow has been studied numerically, using an improved immersed boundary-lattice Boltzmann method. The purpose of the present study is to investigate the effect of interfacial bending stiffness on the deformation of such capsules. Bending moments, accompanied by transverse shear tensions, usually develop due to a preferred membrane configuration or its nonzero thickness. The present model can simulate flow induced deformation of capsules with arbitrary resting shapes (concerning the in-plane tension) and arbitrary configurations at which the bending energy has a global minimum (minimum bending-energy configurations). The deformation of capsules with initially circular, elliptical, and biconcave resting shapes was studied; the capsules' minimum bending-energy configurations were considered as either uniform-curvature shapes (like circle or flat plate) or their initially resting shapes. The results show that for capsules with minimum bending-energy configurations having uniform curvature (circle or flat plate), the membrane carries out tank-treading motion, and the steady deformed shapes become more rounded if the bending stiffness is increased. For elliptical and biconcave capsules with resting shapes as minimum bending-energy configurations, it is quite interesting to find that with the bending stiffness increasing, the capsules' motion changes from tank-treading mode to flipping mode, and resembles Jeffery's flipping mode at large bending stiffness.