Mixed-wet percolation on a dual square lattice

IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Jnana Ranjan Das , Santanu Sinha , Alex Hansen , Sitangshu B. Santra
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Abstract

We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual lattice where the sites on the primal lattice represent the grains of the porous medium, and the bonds on the dual lattice represent the pores in between the grains. The bonds on the dual lattice are occupied based on the two adjacent sites on the primal lattice, which represent the pores where the capillary forces average to zero. The spanning cluster of the bonds, therefore, represents the flow network through which the two immiscible fluids can flow without facing any capillary barrier. It turns out to be a percolation transition of the perimeters of a site percolation problem. We study the geometrical properties at the criticality of the perimeter system numerically. A scaling theory is developed for these properties, and their scaling relations with the respective density parameters are studied. We also verified their finite-size scaling relations. Though the site clusters and their perimeters look very different compared to ordinary percolation, the singular behaviour of the associated geometrical properties remains unchanged. The critical exponents are found to be those of the ordinary percolation.
双方晶格上的混合湿渗透
我们提出了一个渗透模型,其灵感来自于最近关于混合湿多孔介质中具有两种不同润湿性的颗粒混合物的非混相两相流的研究。渗流模型建立在一个对偶晶格上,其中原始晶格上的位置代表多孔介质的颗粒,对偶晶格上的键代表颗粒之间的孔隙。双晶格上的键是基于原始晶格上相邻的两个位置来占据的,这两个位置代表毛细力平均为零的孔。因此,键的跨越簇代表了流动网络,通过该网络,两种不混溶的流体可以在没有任何毛细管屏障的情况下流动。结果表明,这是一个场址周界的渗流过渡问题。本文用数值方法研究了周长系统临界时的几何性质。建立了这些性质的标度理论,并研究了它们与各自密度参数的标度关系。我们还验证了它们的有限尺度关系。虽然与普通的渗透相比,站点集群及其周长看起来非常不同,但相关几何性质的奇异行为保持不变。发现临界指数为普通渗流的临界指数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
7.20
自引率
9.10%
发文量
852
审稿时长
6.6 months
期刊介绍: Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.
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