Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition

Krehel, O Oleh; Muntean, Adrian; Knabner, Peter

doi:10.1016/j.advwatres.2015.10.005

Cited by 32 publications

(39 citation statements)

References 38 publications

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“…The situation remotely resembles the filter blockage case discussed in [11]. Using a similar methodology as in [20], one can also point out the effect of a nonlinear dynamic blocking function on the colloidal deposition.…”

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confidence: 82%

“…, u N ). Also β i,j is the collision kernel -rate constant determined by the transport mechanism that bring the particles in close contact, α i,j ∈ [0, 1] is the collision efficiency, the fraction of collision that finally form an aggregate ( [20]). Note that if we consider only one colloidal species, then this reduces to R(u) = −cu 2 , with a suitable reaction constant c > 0.…”

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confidence: 99%

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Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

Muntean¹,

Nikolopoulos²

2020

SIAM J. Appl. Math.

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We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow reducing therefore the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and therefore, can provide estimates on the storage capacity of the porous matrix.

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confidence: 82%

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confidence: 99%

Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

Muntean¹,

Nikolopoulos²

2020

SIAM J. Appl. Math.

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“…This problem is connected to the Smoluchowski-Soret-Dufour modeling of the evolution of temperature and colloid concentrations [3,10]. Here, u ε := (u ε 1 , ..., u ε N ) denotes the vector of the concentrations, d ε i represents the molecular diffusion with R i being the volume reaction rate and a ε i , b ε i are deposition coefficients, whilst F i indicates a surface chemical reaction for the immobile species.…”

Section: Problem Settingsmentioning

confidence: 99%

“…In [7], the investigated microscopic semi-linear system resembles a steady state-type of thermo-diffusion systems ( [10,9]). Essentially, we have analyzed the solvability of the microscopic system in [7], derived the upscaled equations as well as the corresponding effective coefficients, and proved the high-order corrector estimates for the differences of concentrations and their gradients in which the standard energy method has been used.…”

Section: Introductionmentioning

confidence: 99%

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

Khoa¹

2017

Comptes Rendus. Mécanique

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We derive in this note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates. This type of correctors justifies mathematically the convergence rate of formal asymptotic expansions for the two-scale homogenization settings. As main tool, we follow the standard approach by the energy-like method to investigate the error estimate between the micro and macro concentrations and micro and macro concentration gradients. This work aims at generalizing the results reported in [2,7].

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“…Our results might find some applicability also in the case of a porous medium in which various chemical substances are allowed to diffuse and to react inside and on the walls of the porous medium and in multiscale modeling of colloidal dynamics in porous media (see, for instance, [33] and [39]).…”

Section: Introductionmentioning

confidence: 95%

Homogenization results for a coupled system of reaction–diffusion equations

2019

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The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic processes taking place in living cells, in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes. The coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms. These nonlinearities, which model, at the microscopic scale, various volume or surface reaction processes, give rise in the macroscopic model to different effects, such as the appearance of additional source or sink terms or of a non-standard diffusion matrix.

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Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition

Cited by 32 publications

References 38 publications

Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

Colloidal Transport in Locally Periodic Evolving Porous Media---An Upscaling Exercise

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

Homogenization results for a coupled system of reaction–diffusion equations

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