We analyze the performance of membrane filters represented by pore networks using two criteria: 1) total volumetric throughput of filtrate over the filter lifetime and 2) accumulated foulant concentration in the filtrate. We first formulate the governing equations of fluid flow on a general network, and we model transport and adsorption of particles (foulants) within the network by imposing an advection equation with a sink term on each pore (edge) as well as conservation of fluid and foulant volumetric flow rates at each pore junction (network vertex). Such a setup yields a system of partial differential equations on the network. We study the influence of three geometric network parameters on filter performance: 1) average number of neighbors of each vertex; 2) initial total void volume of the pore network; and 3) tortuosity of the network. We find that total volumetric throughput depends more strongly on the initial void volume than on average number of neighbors. Tortuosity, however, turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration in the filtrate shows an exponential decay as tortuosity increases.

翻译：我们用两个标准分析孔隙网络代表的膜过滤器的性能:1)过滤器生命周期过滤器的总量输送总量,2)过滤器中累积的污点浓度。我们首先在一般网络上制定流体流的调节方程式,然后对网络内颗粒(毛虫)的运输和吸附进行模型,方法是对每个孔径(顶)强制规定一个沉淀方程式,并保护每个孔口(网络脊椎)的流体和肮脏体积流率。这种设置在网络上产生一个部分差分方的系统。我们研究了三个几何网络参数对过滤性能的影响:1)每个顶端的邻居平均人数;2)孔径网络的初始完全空积;3)网络的不稳定性。我们发现,总体积通过量比平均邻里数更依赖初始无效的体积。然而,托尔蒂却是一个普遍参数,导致各种网络结构的所有结果几乎完全崩溃。我们研究了三个几何参数对过滤器性参数的影响:(1)每个顶端的顶端;(2)孔形网际网络的加速度显示,特别是不断积累的腐化的腐化浓度。