Simulations of Odd Microswimmers Akira Kobayashi1Kento Yasuda2Li-Shing Lin1Isamu Sou1Yuto Hosaka3and Shigeyuki Komura4 5 1 1Department of Chemistry Graduate School of Science

2025-05-03 0 0 520.82KB 5 页 10玖币

侵权投诉

Simulations of Odd Microswimmers

Akira Kobayashi,1Kento Yasuda,2Li-Shing Lin,1Isamu Sou,1Yuto Hosaka,3and Shigeyuki Komura4, 5, 1, ∗

1Department of Chemistry, Graduate School of Science,

Tokyo Metropolitan University, Tokyo 192-0397, Japan

2Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

3Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 G¨ottingen, Germany

4Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325001, China

5Oujiang Laboratory, Wenzhou, Zhejiang 325000, China

We perform numerical simulations of odd microswimmers consisting of three spheres and two odd

springs. To describe the hydrodynamic interaction, both the Oseen-type and the Rotne-Prager-

Yamakawa (RPY)-type mobilities are used. For the Oseen-type mobility, the simulation results

quantitatively reproduce the asymptotic expression of the average velocity. For the RPY-type

mobility, on the other hand, the average velocity is smaller than that of the Oseen-type mobility and

the deviation is more pronounced for larger spheres. We also perform simulations of microswimmers

having diﬀerent sphere sizes and show that the average velocity becomes smaller than that of the

equal size case. The size of the middle sphere plays an important role in determining the average

velocity.

I. INTRODUCTION

Recently, Scheibner et al. introduced the concept of

odd elasticity that is useful to characterize nonequilib-

rium active systems [1, 2]. Odd elasticity arises from anti-

symmetric (odd) components of the elastic modulus ten-

sor that violates the energy conservation law and thus can

exist only in active materials [3] or biological systems [4].

Unlike passive materials, a ﬁnite amount of work can

be extracted in odd elastic systems through quasi-static

cycle of deformations [1, 2]. It was also shown that anti-

symmetric parts of the time-correlation functions in odd

Langevin systems are proportional to the odd elastic-

ity [5]. The concept of odd elasticity can be further

extended to quantify the nonreciprocality of active mi-

cromachines (such as enzymes or motor proteins) and

microswimmers [6, 7]. According to Purcell’s scallop the-

orem for microswimmers [8], nonreciprocal body motion

is required for locomotion in a Newtonian ﬂuid. Within

the Onsager’s variational principle [9], it was shown that

odd elastic moduli are proportional to the nonequilibrium

force [10].

Moreover, we have proposed a model of a thermally

driven microswimmer in which three spheres are con-

nected by two springs having odd elasticity [11]. It was

theoretically shown that the presence of odd elasticity

leads to a directional locomotion of the stochastic mi-

croswimmer. We have analytically obtained the average

velocity under the assumption that the sphere size and

the spring extensions are small enough compared to the

natural length of the spring. As we show later again, the

average velocity is proportional to the odd elastic con-

stant whose sign determines the swimming direction.

In this paper, we report the results of numerical

simulations of odd microswimmers to check the va-

∗komura@wiucas.ac.cn

lidity of our analytical prediction [11]. For compari-

son, we use both the Oseen-type and the Rotne-Prager-

Yamakawa (RPY)-type hydrodynamic mobilities in our

simulations [12, 13]. To numerically integrate the multi-

plicative Langevin equations, we also employ the previ-

ously suggested formulation that assures the equilibrium

distribution [14, 15]. Although our previous work consid-

ered only the case when the sphere size is identical [11],

we also perform the simulations for odd microswimmers

having diﬀerent sphere sizes.

II. MODEL

Let us ﬁrst review the model of an odd microswim-

mer [11]. As depicted in Fig. 1, we consider a three-

sphere microswimmer in which the positions of the three

spheres of radius aiare given by xi(i= 1,2,3) in a

one-dimensional coordinate system [16, 17]. These three

spheres are connected by two springs that exhibit both

even and odd elasticities [1, 2]. We denote the two spring

extensions by uA=x2−x1−`and uB=x3−x2−`,

where `is the natural length. Then the forces FAand

FBconjugate to uAand uB, respectively, are given by

Fα=−Kαβ uβ(α, β = A,B). For an odd spring, the

elastic constant Kαβ is given by [5–7, 11]

Kαβ =Keδαβ +Koαβ ,(1)

where Keand Koare even and odd elastic constants

in the two-dimensional conﬁguration space, δαβ is the

Kronecker delta, and αβ is the 2D Levi-Civita tensor.

The forces fiacting on each sphere are given by f1=

−FA,f2=FA−FB, and f3=FB. We note that these

forces satisfy the force-free condition, i.e., f1+f2+f3= 0.

The above odd microswimmer is immersed in a ﬂuid of

shear viscosity ηand temperature T. Then the Langevin

equation of each sphere is given by

˙xi=Mij fj+ξi,(2)

arXiv:2210.12987v2 [cond-mat.soft] 23 Jan 2023

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

SimulationsofOddMicroswimmersAkiraKobayashi,1KentoYasuda,2Li-ShingLin,1IsamuSou,1YutoHosaka,3andShigeyukiKomura4,5,1,1DepartmentofChemistry,GraduateSchoolofScience,TokyoMetropolitanUniversity,Tokyo192-0397,Japan2ResearchInstituteforMathematicalSciences,KyotoUniversity,Kyoto606-8502,Japan3MaxPlanckI...

展开>> 收起<<

Simulations of Odd Microswimmers Akira Kobayashi1Kento Yasuda2Li-Shing Lin1Isamu Sou1Yuto Hosaka3and Shigeyuki Komura4 5 1 1Department of Chemistry Graduate School of Science.pdf

共5页,预览1页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Simulations of Odd Microswimmers Akira Kobayashi1Kento Yasuda2Li-Shing Lin1Isamu Sou1Yuto Hosaka3and Shigeyuki Komura4 5 1 1Department of Chemistry Graduate School of Science

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: