交变电场中囊泡变形的电流体动力学模型
Electrohydrodynamic model of vesicle deformation in alternating electric fields
摘要：
我们发展了一种分析理论来解释实验观察到的由AC电场诱导的巨囊泡的形态转变（1）。该模型将内部和悬浮介质视为有耗介质，而膜视为不渗透离子的柔性不可压缩流体片。囊泡形状通过平衡施加在膜上的电应力、流体动力应力和弯曲应力而获得。考虑到一个近似球形的囊泡，电流体动力学问题的解作为一个规则的摄动展开在多余的区域。该理论预测，固定囊泡变形取决于场频率和电导率条件。如果内部流体比悬浮介质更导电，则囊泡总是采用扁长的形状。在相反的情况下，囊泡在临界频率下经历了从长椭圆体到扁椭圆体的转变，该理论与膜充电时间的倒数一致。在高于逆麦克斯韦-瓦格纳极化时间的频率下，电流体动力学应力变得太小而不能改变囊泡的准球形静止形状。分析表明，向静止囊泡变形的演变强烈依赖于膜的性质，如粘度。该模型可用于合理化生物细胞在电场中的瞬态和稳态变形。
英文摘要：
We develop an analytical theory to explain the experimentally-observed morphological transitions of giant vesicles induced by AC electric fields (1). The model treats the inner and suspending media as lossy dielectrics, while the membrane as an ion-impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, and bending stresses exerted on the membrane. Considering a nearly spherical vesicle, the solution to the electrohydrodynamic problem is obtained as a regular perturbation expansion in the excess area. The theory predicts that stationary vesicle deformation depends on field frequency and conductivity conditions. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicle's quasi-spherical rest shape. The analysis shows that the evolution towards the stationary vesicle deformation strongly depends on membrane properties such as viscosity. The model can be applied to rationalize the transient and steady deformation of biological cells in electric fields.
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