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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.

Original languageEnglish (US)
Pages (from-to)950-975
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • discrete calculus
  • filtration
  • fluid mechanics
  • graph theory
  • networks


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