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Minimal model for transient swimming in a liquid crystal

机译:液晶瞬态游动的最小模型

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When a microorganism begins swimming from rest in a Newtonian fluid such as water, it rapidly attains its steady-state swimming speed since changes in the velocity field spread quickly when the Reynolds number is small. However, swimming microorganisms are commonly found or studied in complex fluids. Because these fluids have long relaxation times, the time to attain the steady-state swimming speed can also be long. In this article we study the swimming startup problem in the simplest liquid crystalline fluid: a two-dimensional hexatic liquid crystal film. We study the dependence of startup time on anchoring strength and Ericksen number, which is the ratio of viscous to elastic stresses. For strong anchoring, the fluid flow starts up immediately but the liquid crystal field and swimming velocity attain their sinusoidal steady-state values after a time proportional to the relaxation time of the liquid crystal. When the Ericksen number is high, the behavior is the same as in the strong-anchoring case for any anchoring strength. We also find that the startup time increases with the ratio of the rotational viscosity to the shear viscosity, and then ultimately saturates once the rotational viscosity is much greater than the shear viscosity.
机译:当微生物在诸如水的牛顿流体中从静止状态开始游动时,由于雷诺数较小时速度场的变化会迅速扩散,因此它会迅速达到稳态游动速度。但是,游泳微生物通常是在复杂的液体中发现或研究的。由于这些流体的弛豫时间长,因此达到稳态游泳速度的时间也可能会很长。在本文中,我们研究了最简单的液晶流体:二维六面体液晶薄膜中的游泳启动问题。我们研究了启动时间对锚固强度和埃里克森数的依赖性,埃里克森数是粘性应力与弹性应力之比。对于牢固的锚固,流体流动立即开始,但是在与液晶的弛豫时间成比例的时间之后,液晶场和游泳速度达到其正弦稳态值。当埃里克森数高时,对于任何锚固强度,其行为与在强锚固情况下相同。我们还发现启动时间随旋转粘度与剪切粘度之比的增加而增加,然后一旦旋转粘度远大于剪切粘度,则最终饱和。

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