A GRAPHICAL REPRESENTATION OF MEMBRANE FILTRATION

Document Type

Article

Publication Date

1-1-2022

Abstract

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.

Identifier

85132229806 (Scopus)

Publication Title

SIAM Journal on Applied Mathematics

External Full Text Location

https://doi.org/10.1137/21M1424743

ISSN

00361399

First Page

950

Last Page

975

Issue

3

Volume

82

Grant

DMS-1615719

Fund Ref

National Science Foundation

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