Mathematical model for filtration and drying in filter membranes

Ji, Hangjie; Sanaei, Pejman

doi:10.1103/physrevfluids.8.064302

Cited by 1 publication

(17 citation statements)

References 44 publications

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“…Our homogenised model (2.20) is similar in structure to those proposed in Breward et al (2020), Sanaei et al (2022) and Ji & Sanaei (2023), with the suspended dirt satisfying a reaction-diffusion equation ahead of a moving evaporation front. However, through the systematic homogenisation analysis, we have found the correct form for the diffusion term in (2.20b), which was erroneously given as (D(φθ ) Y ) Y (in our notation) by Ji & Sanaei (2023). Additionally, we have quantified the effective parameters D, C and φ, which all vary with the deposited dirt-layer thickness R. We also impose different boundary conditions to Ji & Sanaei (2023), which will result in different drying behaviours, as discussed in § 3 below.…”

Section: Summary Of the Homogenised Drying Modelmentioning

confidence: 76%

“…(We note that therefore f (0) = 1.) The presence of particles at the interface are expected to hinder the vaporisation; in both Ji & Sanaei (2023) and Karapetsas et al (2016) the evaporative flux is modelled as decreasing with increased particles on the fluid surface. We keep f (θ ) general as far as possible, and in § 5 we investigate the effect of different functional dependencies f (θ ) on the drying rate.…”

Section: Pore-scale Modelmentioning

confidence: 99%

“…Drying-driven redistribution of dirt within filters and textiles is a common problem, with practical industrial importance. For instance, after the rinsing of filters used in vacuum cleaners or washing machines, the filter dries and any remaining dirt or cloth fibres are left in the filter (Ji & Sanaei 2023), reducing its capacity for the next filtration cycle. Waterproof clothing such as coats and boots will dry after use, and impurities or dirt may similarly be left within the pores of the textile and waterproof membrane (Breward et al 2020;Sanaei et al 2022).…”

Section: Introductionmentioning

confidence: 99%

“…One benefit of the homogenisation approach is that the pore-scale behaviour is included in the homogenised model through averaged terms. This ensures that the model conserves mass of all species, and also results in a different diffusive term in the homogenised equations compared with the model posed by Ji & Sanaei (2023). For simplicity, as in both Luckins et al (2023) and Ji & Sanaei (2023), we assume that capillary flows are negligible and a sharp evaporating interface moves into the porous material.…”

Section: Introductionmentioning

confidence: 99%

“…This ensures that the model conserves mass of all species, and also results in a different diffusive term in the homogenised equations compared with the model posed by Ji & Sanaei (2023). For simplicity, as in both Luckins et al (2023) and Ji & Sanaei (2023), we assume that capillary flows are negligible and a sharp evaporating interface moves into the porous material. In practice, such systems would be valid when viscous or gravitational forces dominate over surface tension, for instance, if the solid is hydrophobic (Shokri, Lehmann & Or 2008) or the pores are sufficiently large relative to the capillary length scale (Lehmann et al 2008).…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling of impurity deposition during evaporation of dirty liquid in a porous material

Luckins,

Breward,

Griffiths

et al. 2024

J. Fluid Mech.

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When a contaminated liquid evaporates from within a porous material, the impurities or dirt accumulate and deposit within the pore space. This occurs during the cleaning of filters and fouling of textiles, and is related to the ‘coffee-ring’ problem. To investigate how and where dirt is deposited in the pore space, we present a model for the motion of an evaporation front through a porous material, and the related accumulation, transport, and deposition of dirt, assuming that the liquid remains stationary. For physically relevant parameters, vapour transport out of the porous material is quasi-steady and we derive a single ordinary differential equation describing the motion of the evaporation front in time. Model solutions exhibit spatially non-uniform profiles of the deposited dirt-layer thickness through the porous material. The dirt accumulation and evaporation problems are coupled: deposited dirt hinders vapour transport through the porous material, slowing the evaporation. We identify two scenarios in which the porous material becomes clogged with dirt. Accumulation of suspended dirt at the evaporating interface along with slow dirt diffusion results in the deposited dirt layers clogging the pores at the evaporating interface, halting the drying and trapping liquid in the porous material. Alternatively, slow dirt deposition results in the suspended dirt being pushed far into the porous material by the evaporation, eventually leaving only dirt (with no liquid) in the pore space. We investigate the dynamics of both clogging scenarios, characterising the parameter regimes for which each occurs. Both clogging scenarios must be avoided in practice since they may be detrimental to future filter efficacy or textile breathability.

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