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arXiv 2104.11972physics.flu-dyn
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粘弹性流体表面模拟的一种数值方法

A numerical method for the simulation of viscoelastic fluid surfaces

Eloy de Kinkelder, Leonard Sagis, Sebastian Aland

摘要:

粘弹性表面流变学在多相体系中起着重要的作用。一个典型的例子是围绕着大多数动物细胞的肌动蛋白皮层。它在短时间尺度上表现出弹性,在长时间尺度上表现出粘性。因此,细胞形状动力学的真实模拟需要捕获整个弹性到粘性光谱的模型。然而,目前还没有数值方法来模拟变形粘弹性表面。因此,细胞皮层或其他粘弹性表面的模型通常基于限制其适用性的假设或简化。在本文中,我们开发了第一个数值方法模拟变形粘弹性表面。为此,我们推导出表面等效的上随体麦克斯韦模型使用非平衡态热力学的GENERIC制定。该模型区分了剪切动力学和界面动力学。粘弹性表面嵌入在由纳维-斯托克斯方程建模的粘性流体中。这两个系统都使用有限元求解。流体和曲面使用任意拉格朗日-欧拉(ALE)方法组合,该方法在曲面的旋转和平移期间保持曲面网格间距。我们验证了这个数值实现对解析解,并找到很好的协议。为了证明它的潜力,我们模拟实验观察到的翻滚和坦克踩踏的小泡在剪切流。我们还提供了一个相图来证明的粘弹性参数的影响的行为上的囊泡在剪切流。最后,我们探讨胞质分裂作为未来的应用程序的数值方法,通过模拟胞质分裂的开始使用空间依赖函数的表面张力。

英文摘要:

Viscoelastic surface rheology plays an important role in multiphase systems. A typical example is the actin cortex which surrounds most animal cells. It shows elastic properties for short time scales and behaves viscous for longer time scales. Hence, realistic simulations of cell shape dynamics require a model capturing the entire elastic to viscous spectrum. However, currently there are no numerical methods to simulate deforming viscoelastic surfaces. Thus models for the cell cortex, or other viscoelastic surfaces, are usually based on assumptions or simplifications which limit their applicability. In this paper we develop a first numerical approach for simulation of deforming viscoelastic surfaces. To this end, we derive the surface equivalent of the upper convected Maxwell model using the GENERIC formulation of nonequilibrium thermodynamics. The model distinguishes between shear dynamics and dilatational surface dynamics. The viscoelastic surface is embedded in a viscous fluid modelled by the Navier-Stokes equation. Both systems are solved using Finite Elements. The fluid and surface are combined using an Arbitrary Lagrange-Eulerian (ALE) Method that conserves the surface grid spacing during rotations and translations of the surface. We verify this numerical implementation against analytic solutions and find good agreement. To demonstrate its potential we simulate the experimentally observed tumbling and tank-treading of vesicles in shear flow. We also supply a phase-diagram to demonstrate the influence of the viscoelastic parameters on the behaviour of a vesicle in shear flow. Finally, we explore cytokinesis as a future application of the numerical method by simulating the start of cytokinesis using a spatially dependent function for the surface tension.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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