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The dynamic characteristics of a two-dimensional deformable capsule in a simple shear flow are studied with an immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the Reynolds number (Re) from 0.0125 to 2000 and the dimensionless shear rate (G) from 0.001 to 0.5. The G-Re plane can be divided into four regions according to the deformation dependence on the parameters considered: viscous dominant, inertia dominant, transitional and anomalous regions. There are four typical dynamic behaviours over the G-Re plane: steady deformation, pre-rupture state, quasi-steady deformation and continuous elongation. Analysis indicates that the pressure distribution and its variations due to the interplay of the fluid inertia force, the viscous shear stress and the membrane elastic force determines the complex behaviours of the capsule. The effects of the bending rigidity and the internal-to-external viscosity ratio on the dynamics of the capsule are further studied. It is found that the capsule experiences smaller deformation when the higher bending rigidity is included, and the low bending rigidity does not have a remarkable influence on the capsule deformation. The capsule normally experiences smaller deformation due to the increase of the internal-to-external viscosity ratio.

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