Numerical Simulation of the Motion of Inextensible Capsules in Shear Flow Under the Effect of the Natural State

Abstract

The effect of the nature state on the motion of an inextensible capsule in simple shear flow has been studied in this paper. Besides the viscosity ratio of the internal fluid and external fluid of the capsule, the nature state effect also plays a role for having the transition between two well known motions, tumbling and tank-treading (TT) with the long axis oscillating about a fixed inclination angle (a swinging mode), when varying the shear rate. The intermittent region between tumbling and TT with a swinging mode of the capsule with a biconcave rest shape has been obtained in a narrow range of the capillary number. In such region, the dynamics of the capsule is a mixture of tumbling and TT with a swinging mode; when having the tumbling motion, the membrane tank-tread backward and forward within a small range. As the capillary number is very close to and below the threshold for the pure TT with a swinging mode, the capsule tumbles once after several TT periods in each cycle. The number of TT periods in one cycle decreases with respect to the decreasing of the capillary number, until the capsule has one tumble and one TT period alternatively and such alternating motion exists over a range of the capillary number; and then the capsule performs more tumbling between two consecutive TT periods when reducing the capillary number further, and finally shows pure tumbling. The critical value of the swelling ratio for having the intermittent region has been estimated.

Numerical simulation on the effects of the viscosity contrast of a soft particle at the transition between tank-treading and tumbling motions

“…The dependences of membrane velocity and inclination angle on the reduced area are shown in Fig. 7 and are subsequently compared with the results of previous studies (Niu et al, 2015;Kaoui et al, 2011). The membrane velocity was non-dimensionalised by 𝛾ṙ 0 /2, which is the theoretical value of the rotation velocity with a soft particle in shear flow, and similarly, the tumbling frequency by 𝛾/4𝜋 (Kaoui et al, 2012), where 𝑟 0 = 2.8 × 10 −6 [m] is the initial radius.…”

Shape Memory of Elastic Capsules Under the Effect of Spontaneous Shape

“…The biconcave shape developed by Evans and Fung [12] has been adopted by many researchers as the spontaneous shape of RBC [2,8,9]. Capsules and vesicles composed of lipid bilayer only can also possess shape memory due to biconcave spontaneous shape [19,27].…”