Boundary element methods for particles and microswimmers in a linear viscoelastic fluid
Boundary element methods for particles and microswimmers in a linear viscoelastic fluid
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DOI：
10.1017/jfm.2017.636
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发表时间：
2017-11-25
影响因子：
3.7
通讯作者：
Gaffney, Eamonn A.
中科院分区：
文献类型：
--
作者：
Ishimoto, Kenta;Gaffney, Eamonn A.
在流体动力学边界元法中考虑粘弹性，传统上要求在整个流动域上进行网格划分。反过来，边界元法的一个主要优点，即只需要考虑表面边界积分丢失。在这里，使用广义互易关系和粘弹性力奇异性，边界元法开发的线性粘弹性流动。我们继续探讨有限变形微游动线性麦克斯韦流体。我们首先推导出一个有限振幅的概括以前报道的结果，牛顿流体和线性麦克斯韦流体之间的流场是不变的规定的小振幅变形。因此，珀塞尔定理对线性麦克斯韦流体成立。我们接着考虑在外力作用下线性麦克斯韦流体中游动的变形。边界散射轨迹的一个范例蠕动接近表面观察到表现出弱依赖于德博拉数，而表面附近的精子和monotrichous细菌的轨迹预测基本上不受影响，在温和的德博拉数。反过来，后者支持使用牛顿斯托克斯流研究鞭毛虫游泳线性麦克斯韦媒体的共同简化。此外，被认为是一个外部磁场的影响下的磁性螺旋的运动，并强调线性粘弹性可以显着影响螺旋的传播，反过来证明，即使是线性流变学是重要的考虑强迫游泳。最后，所提出的框架需要最低限度的调整牛顿边界元代码，使快速实施，是更普遍适用的，例如在微尺度上的主动线性流变学的粒子相互作用的研究。
The consideration of viscoelasticity within fluid dynamical boundary element methods has traditionally required meshing over the whole flow domain. In turn, a major advantage of the boundary element method is lost, namely the need to consider only surface boundary integrals. Here, using a generalised reciprocal relation and viscoelastic force singularities, a boundary element method is developed for linear viscoelastic flows. We proceed to explore finite-deformation microswimming in a linear Maxwell fluid. We firstly deduce a finite-amplitude generalisation of a previously reported result that the flow field is unchanged between a Newtonian and linear Maxwell fluid for prescribed small-amplitude deformations. Hence Purcell's theorem holds for a linear Maxwell fluid. We proceed to consider deformation swimming in a linear Maxwell fluid given an external forcing. Boundary scattering trajectories for an exemplar squirmer approaching a surface are observed to exhibit a weak dependence on the Deborah number, while the trajectories of a sperm and monotrichous bacterium near a surface are predicted to be essentially unaffected at moderate Deborah number. In turn, the latter supports the common simplification of using Newtonian Stokes flows for studying flagellate swimming in linear Maxwell media. In addition, the motion of a magnetic helix under the influence of an external magnetic field is considered, and highlights that linear viscoelasticity can significantly impact the propagation of the helix, in turn demonstrating that even linear rheology is important to consider for forced swimmers. Finally, the presented framework requires minimalistic adjustments to Newtonian boundary element codes, enabling rapid implementation, and is more generally applicable, for instance to studies of particle interactions in active linear rheology on the microscale.