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

Published online by Cambridge University Press:  14 September 2015

Xiting Niu ,
Lingling Shi ,
Tsorng-Whay Pan  and
Roland Glowinski
Xiting Niu
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA
Lingling Shi
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA
Tsorng-Whay Pan*
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA
Roland Glowinski
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, USA
*
*Corresponding author. Email addresses: xiting@math.uh.edu (X. Niu), lingling@math.uh.edu (L. Shi), pan@math.uh.edu (T.-W. Pan), roland@math.uh.edu (R. Glowinski)
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Abstract

In this paper, a computational model for the natural state of an inextensible capsule has been successfully combined with a spring model of the capsule membrane to simulate the motion of the capsule in two-dimensional shear flow. Besides the viscosity ratio of the internal fluid and external fluid of the capsule, the natural state also plays a role for having the transition between two well known motions, tumbling and tank-treading (TT) with the long axis oscillates about a fixed inclination angle (a swinging mode), when varying the shear rate. Between tumbling and tank-treading, the intermittent behavior has been obtained for the capsule with a biconcave rest shape. The estimated critical value of the swelling ratio for having the intermittent transition behavior is less than 0.7, i.e., the capsules with rest shape closer to a full disk do not have the intermittent behavior in shear flow. The intermittent dynamics of the capsule in the transition region is a mixture of tumbling and TT with a swinging mode. Just like the motion of TT with a swing mode, which can be viewed as a tank-treading with an incomplete tumbling, the membrane tank-treads backward and forward within a small range during the tumbling motion.

Keywords

76M1076Z0576D0592C05Natural statetumblingtank-treading with a swinging modeintermittent regioncapsuleshear flow
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 787 - 807
Copyright
Copyright © Global-Science Press 2015 

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