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Abstract <p>A pore-scale model is developed to simulate homogeneous-heterogeneous reactive transport of a non-Newtonian fluid in porous media. The fluid’s behavior is described by the Carreau viscosity model. The heterogeneous reaction is governed by the Langmuir isotherm on adsorbent surfaces, while the homogeneous reaction follows a time fractional Gray-Scott model within the porous media. The governing system is splitted into the Stokes equations and convection-subdiffusion-reaction equations with specified boundary conditions. We consider the case when the fluid flow has a one-way influence on the species transport. Computational implementation is based on the Crank–Nicolson scheme with a standard linear approximation for time fractional derivative. Each process is spatially discretized using a variational formulation with suitable finite elements. We use Picard iterations for a stationary non-Newtonian fluid flow and Newton’s method to solve a non-linear problem for reactive mass transport. The numerical results for a two-dimensional model problem show that fractional order and fluid flow parameters significantly affect the breakthrough curves.</p>

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Fractional Time Derivative for Non-Newtonian Flow on Homogeneous–Heterogeneous Pore-Scale Reactive Transport

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • V. V. Grigoriev,
  • D. K. Ivanov,
  • A. V. Savvin

摘要

Abstract

A pore-scale model is developed to simulate homogeneous-heterogeneous reactive transport of a non-Newtonian fluid in porous media. The fluid’s behavior is described by the Carreau viscosity model. The heterogeneous reaction is governed by the Langmuir isotherm on adsorbent surfaces, while the homogeneous reaction follows a time fractional Gray-Scott model within the porous media. The governing system is splitted into the Stokes equations and convection-subdiffusion-reaction equations with specified boundary conditions. We consider the case when the fluid flow has a one-way influence on the species transport. Computational implementation is based on the Crank–Nicolson scheme with a standard linear approximation for time fractional derivative. Each process is spatially discretized using a variational formulation with suitable finite elements. We use Picard iterations for a stationary non-Newtonian fluid flow and Newton’s method to solve a non-linear problem for reactive mass transport. The numerical results for a two-dimensional model problem show that fractional order and fluid flow parameters significantly affect the breakthrough curves.