Guedda M
LAMFA, CNRS UMR 7352, Département de Mathématiques, Université de Picardie Jules Verne, Amiens, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012703. doi: 10.1103/PhysRevE.89.012703. Epub 2014 Jan 6.
We derive some analytical results of a well-known model for quasispherical vesicles in a linear shear flow at low deformability. Attention is focussed on the oscillatory regimes: the tumbling (TB) mode, vacillating-breathing (VB) mode, and the transition from vacillating-breathing to tumbling, depending on a control parameter Γ. It is shown that, during the VB-to-TB transition (Γ=1), the vesicle momentarily attains its maximal extension in the vorticity direction and transits through a circular profile in the shear plane for which the radius is exactly determined. In addition, we provide an explicit analytical expression for the effective membrane tension for different types of motions. We find a critical bending number below which the membrane undergoes compression at each instant and show that, during the VB-to-TB transition, a fourth-order membrane deformation is possible.
我们推导了一个著名的低变形性线性剪切流中准球形囊泡模型的一些分析结果。重点关注振荡状态：翻滚（TB）模式、摆动呼吸（VB）模式以及取决于控制参数Γ的从摆动呼吸到翻滚的转变。结果表明，在VB到TB转变期间（Γ = 1），囊泡在涡度方向上瞬间达到其最大伸展，并在剪切平面内通过一个半径精确确定的圆形轮廓。此外，我们给出了不同运动类型下有效膜张力的显式解析表达式。我们发现了一个临界弯曲数，低于该临界弯曲数时膜在每个瞬间都会受到压缩，并表明在VB到TB转变期间，可能会出现四阶膜变形。
