# Diffusiophoresis in porous media for groundwater remediation

Florian Cajot, Cyprien Soulaine, Sophie Roman

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To cite this version:

Florian Cajot, Cyprien Soulaine, Sophie Roman. Diffusiophoresis in porous media for groundwater remediation. FOAMU2025, Apr 2025, Bruxelles, Belgium., 2025. [hal-05038840](https://hal.science/hal-05038840v1)

HAL Id: hal-05038840

https://hal.science/hal-05038840v1

Submitted on 18 Apr 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Diffusiophoresis in porous media for groundwater remediation

Florian Cajot, Cyprien Soulaine and Sophie Roman

florian.cajot@univ-orleans.fr, cyprien.soulaine@cnrs-orleans.fr, sophie.roman@univ-orleans.fr

ISTO, UMR 7327, Orléans, France

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A novel approach considers the concentration gradient generated by pollutants to drive particles toward contaminated zones for remediation.

This particle transport driven by **concentration gradients** is known as **diffusiophoresis**.

Diffusiophoresis remains poorly studied in porous media, and existing models are largely limited to simplified cases.

A key question is how to incorporate diffusiophoresis into particle transport mechanisms within porous media.

We propose a pore-scale model and OpenFOAM simulations to study particle movement in porous media under solute concentration gradients.

This work improves our understanding of how to model diffusiophoresis in porous media.

## 1) Introduction

The presence of pollutants in soils and subsurface geological formations poses a serious threat to groundwater quality, often leading to

contamination that renders the resource unusable. Effective remediation requires strategies capable of reaching the most isolated zones within the porous matrix. One approach is to use particles as decontaminants. In this context, we explore **diffusiophoresis**—the directed movement of particles under solute concentration gradients—as a promising mechanism to enhance particle transport in contaminated porous media. In particular how can diffusiophoresis be effectively incorporated into models of transport particle movement in complex porous media for groundwater remediation?

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## 2) Modelling

### Diffusiophoresis

Diffusiophoresis refers to the motion of microscopic colloidal particles driven by local solute concentration gradients, as first described by Derjaguin et al. (1947). For instance, trapped NAPL (Non-Aqueous Phase Liquid) within porous media can release chemical compounds, creating local concentration gradients that influence the movement of colloidal particles.

The phoretic motion of particle are physically given by two components

Velegol et al. (2016)

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Electrophoresis is the migration of charged particles suspended in a solution of fluid under the influence of a local electric field, which exerts a force on the surface of the charged particle.

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Chemiphoresis is the movement of particles induced by a solute concentration gradient that generates an osmotic pressure gradient along the particle surface.

The phoretic motion is proportional to a mobility $\Gamma_d$ and a solute concentration $C_s$

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$$ \mathbf{u}_{dp} = \Gamma_d \nabla \ln C_s $$

### Governing equation of fluid velocity

$$ \partial_t \mathbf{u} + (\mathbf{u} \cdot \nabla \mathbf{u}) = -\nabla \frac{p}{\rho_w} + \nu \Delta \mathbf{u} - \frac{\nu}{k} \mathbf{u} $$

u: fluid velocity

v: kinematic viscosity

p: pressure

k: permeability

### Governing equation of particle concentration

$$ \partial_t C_p + \nabla \cdot ([\mathbf{u} + \mathbf{u}_{dp}] C_p) = D_p \Delta C_p $$

$$ n \cdot \nabla C_p = 0 \quad (\text{Boundary condition}) $$

$C_p$: particle concentration

$D_p$: particle diffusivity

## References

Battat et al, (2019). Particle entrainment in dead-end pores for diffusiophoresis.

Cajot et al, (2025a). A free energy based model for water transfer in amphiphilic soils.

Cajot et al, (2025b). Model of drop infiltration into a thin amphiphilic porous medium.

Derjaguin et al, (1947). Kinetic Phenomena in the boundary layers of liquids 1. the capillary osmosis.

Shin, (2020). Diffusiophoretic separation of colloids in microfluidic flows.

Velegol et al, (2016). Origins of concentration gradients for diffusiophoresis.

## 3) Modelling results

### Comparison with literature experiment

Experimental set-up:

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We compare our OpenFOAM simulations with experimental results from the literature under two conditions: (i) without a concentration gradient and (ii) with a concentration gradient.

### No solute concentration gradient

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### Solute concentration gradient in dead-end pore

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The model capture diffusiophoresis in presence of solute concentration gradient.

## 4) Conclusion

This modelling framework highlights the influence of solute concentration gradients on particle migration within dead-end pores via diffusiophoresis.

This approach will be extended to more complex porous media, including systems with reactive substrates, and validated through laboratory experiments. Furthermore, it provides a foundation for upscaling to the continuum scale by incorporating thermodynamic principles, such as free energy Cajot et al 2025a,b.

## Acknowledgement

This work is funded by the European Union (ERC, TRACE-it, 101039854).