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arXiv 1607.03532cond-mat.soft
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拥挤混合物中的扩散和斑图形成

Gradient-driven diffusion and pattern formation in crowded mixtures

Prithviraj Nandigrami, Brandy Grove, Andrew Konya, Robin L. B. Selinger

摘要:

拥挤的,多组分混合物中的粘性驱动扩散是一个非常感兴趣的话题,因为它在生物过程中的作用,如在细胞膜中的运输。在部分相分离的解决方案中,梯度驱动的扩散影响微观结构,这反过来又影响扩散率;一个关键问题是这种复杂的耦合如何控制传输和斑图形成。为了研究这些机制,我们研究了一个二维的多组分格子气模型,其中“示踪剂”分子扩散之间的源和汇分离的解决方案的粘性“拥挤”的分子,集群形成动态演变的障碍。在高温极限下,拥挤剂和示踪剂是可混溶的,并且可以通过分析预测运输。在中等温度下,拥挤相分离成向示踪剂汇漂移的簇。其结果是,稳态示踪剂的扩散系数依赖于非单调的温度和拥挤的密度,我们观察到各种复杂的微观结构。在低温极限,拥挤迅速聚集,形成动力学逮捕的障碍,如果拥挤的密度是渗流阈值附近,所产生的示踪剂扩散率显示标度行为与随机电阻网络模型相同的标度指数。虽然高度理想化,这个简单的模型揭示了基本机制,耦合梯度驱动的扩散,相分离,和微观结构的演变拥挤的解决方案。

英文摘要:

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multi-component lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high temperature limit, crowders and tracers are miscible and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends non-monotonically on both temperature and crowder density and we observe a variety of complex microstructures. In the low temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded solutions.

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