Shape transitions of fluid vesicles and red blood cells in capillary flows

Noguchu and Gompper. 10.1073/pnas.0504243102.

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Fig. 7. Dependence of the rear (dimple) curvatures of parachute-shaped elastic vesicles on the elastic parameters m and k at v_mt/R_cap = 218. All data are found to fall onto a single scaling curve when plotted against the ratio mR₀²/k, or equivalently the Föppl–von Kármán number. The green triangles and red circles represent data for k/k_BT = 10 and 20 with various m, respectively. The blue squares represent data for mR₀²/k_BT = 110 with various k.

Movie 1. Dynamics of an elastic vesicle with bending rigidity k/k_BT = 20 and shear modulus mR₀²/k_BT = 110 in capillary flow at v_mt/R_cap = 107 (somewhat larger than the transition velocity v_mt/R_cap = 80 ± 26) for 0 ≤ t/t ≤ 2.4. The initial state is the steady discocyte at the mean fluid velocity v_mt/R_cap = 52. The vesicle transforms from the discocyte into a parachute shape by means of a transient slipper-like shape. The vesicle is rotated around the z axis at t/t = 0 to illustrate the nonaxisymmetric shape of the discocyte. A coordinate system is indicated to guide the eye during the axis rotation. Thick black lines show the location of the walls of the cylindrical capillary.

Movie 2. Dynamics of a fluid vesicle with bending rigidity k/k_BT = 20 in capillary flow at v_mt/R_cap = 13, for 0 ≤ t/t ≤ 3.5. The initial state is the steady prolate at the mean fluid velocity v_mt/R_cap = 110. The vesicle transforms from the prolate into a discocyte shape by means of a transient V-shaped conformation. Thick black lines show the location of the walls of the cylindrical capillary.

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