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arXiv 1908.10631cond-mat.soft
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推进式微型游泳器的渗流转捩

Percolation transition of pusher-type microswimmers

Fabian Jan Schwarzendahl, Marco G. Mazza

摘要:

我们确定了一个连续的渗流过渡模型悬浮液中的推型microswimmer的存在。团簇的动态聚集和解聚是由吸引力和排斥力以及空间相互作用的竞争引起的。随着微游泳者填充率的增加,团簇尺寸分布接近无标度形式,并且出现跨越整个系统的大团簇。我们通过与团簇尺寸分布$τ$、相关长度$ν$、平均团簇尺寸$γ$和团簇分形维数$d_f$相关的临界指数来表征这种微游泳者渗流转变。我们能够表明,两个标度关系,从渗滤理论,也为我们的微泳。实空间重整化群变换可以近似地预测指数$ν$的值。这一发现为微泳者的聚集过程开辟了新的前景。

英文摘要:

We identify the presence of a continuum percolation transition in model suspensions of pusher-type microswimmers. The clusters dynamically aggregate and disaggregate resulting from a competition of attractive and repulsive hydrodynamic and steric interactions. As the microswimmers' filling fraction increases, the cluster size distribution approaches a scale-free form and there emerge large clusters spanning the entire system. We characterize this microswimmer percolation transition via the critical exponents associated to cluster size distribution $τ$, correlation length $ν$, mean cluster size $γ$, and clusters' fractal dimension $d_f$. We are able to show that two scaling relations, known from percolation theory, also hold for our microswimmers. A real-space renormalization group transformation can approximately predict the value of the exponent $ν$. This finding opens new vistas on microswimmers' congregative processes.

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