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Numerical simulation of retention and release of colloids
in porous media at the pore scale
Nisrine Sefrioui, Azita Ahmadi, Aziz Omari, Henri Bertin
To cite this version:
Nisrine Sefrioui, Azita Ahmadi, Aziz Omari, Henri Bertin. Numerical simulation of retention and
release of colloids in porous media at the pore scale. Colloids and Surfaces A: Physicochemical and
Engineering Aspects, Elsevier, 2013, 427, pp.33-40. �10.1016/j.colsurfa.2013.03.005�. �hal-01081224�
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Handle ID: .http://hdl.handle.net/10985/8835
To cite this version :
Nisrine SEFRIOUI, Azita AHMADI, Aziz OMARI, Henri BERTIN - Numerical simulation of
retention and release of colloids in porous media at the pore scale - Colloids and Surfaces A:
Physicochemical and Engineering Aspects - Vol. 427, p.33-40 - 2013
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Numerical simulation of retention and release of colloids in porous
media at the pore scale
Nisrine Sefrioui, Azita Ahmadi, Aziz Omari, Henri Bertin
∗
I2M-TREFLE-UMR CNRS 5295, University of Bordeaux, Arts et Metiers ParisTech, Esplanade des Arts et Metiers, 33405, Talence, France
h i g h l i g h t s
•
Direct Numerical Simulation has
been performed.
•
Different roughness types have been
investigated.
•
Physicochemical interactions have
been included in the model.
•
Residence time depend on roughness,
hydrodynamics and physicochemical
interactions.
g r a p h i c a l a b s t r a c t
Flow structure and particle trajectory for a valley geometry roughness (dashed line corresponds to ideal
trajectory).
Keywords:
Colloid
Porous media
Rough surface
Retention
Numerical simulation
Ionic strength
a b s t r a c t
Transport of a solid colloidal particle was simulated at the pore scale in presence of surface roughness
and particle/pore physicochemical interaction by adopting a “one fluid” approach. A code developed in
our laboratory was used to solve equations of motion, while implementing additional modules in order
to take into account lubrication and physicochemical forces. Particles were recognized through a phase
indicator function and the particle/fluid interface position at each instant was obtained by solving a trans-
port equation. Roughnesses of different shapes were considered and the magnitude of the particle/pore
physicochemical interaction was monitored through the change of the ionic strength of the suspending
fluid. We first show that if pore surface is smooth no retention of the transported particle occurs whether
the particle/pore surface is attractive or repulsive. However for shape roughnesses of “peak” or “valley”,
particles may be retained inside pores or not depending on the considered ionic strength. In absence of
particle retention, the residence time (the time needed for a particle to travel a characteristic pore dis-
tance) is finite and was found to be an increasing function of ionic strength for every considered roughness
at fixed hydrodynamic conditions.
1. Introduction
Flow of reactive solutions or suspensions in saturated porous
media is of great interest in many environmentally relevant
applications such as contaminant dissemination, filtration and
remediation processes. In such processes, the determination of the
∗
Corresponding author. Tel.: +33 556 84 54 06; fax: +33 556 84 54 36.
E-mail address: h.bertin@i2m.u-bordeaux1.fr (H. Bertin).
concentration of species as a function of time and space is of major
concern [1]. It is admitted that besides porous media structure,
transport and chemical aspects are the most important phenomena
that should be considered in interpreting field and laboratory data
or in analyzing modeling results.
Considering chemical aspects, when reactive species
are charged colloid particles of finite size, the DLVO
(Derjaguin–Landau–Verwey–Overbeek) theory is often put
forward to describe particle/pore surface interaction. If such an
interaction is purely attractive the adsorption conditions are called
http://dx.doi.org/10.1016/j.colsurfa.2013.03.005
favorable with no energy barrier while unfavorable conditions are
reserved to non-monotonic interaction pr ofiles which generally
present an energy barrier, a deep primary minimum and a shallow
secondary minimum. Under physicochemical conditions such that
unfavorable conditions are expected to prevail, the calculated
energy barrier is usually high enough (several hundreds of kT)
so that colloid adsorption should be precluded. However, this
behavior was reported to be in contrast with experimental evi-
dences showing a significant adsorption. To explain such apparent
discrepancy several possible sources were examined. Among
them, the predominant role of the secondary minimum in the
adsorption process was emphasized [2–4] and it was shown that
on the basis of this, the influence of physicochemical parameters
as ionic strength and pH of the background solution were well
predicted [2]. Nevertheless despite qualitative theory/experiment
agreement, quantitative discrepancies were reported to persist. It
was therefore argued that as particle and pore wall surfaces are not
chemically and/or topographically homogenous, a more precise
calculation of interaction potentials on small scale is needed for
quantitative comparison. Chemical heterogeneity is introduced
through the existence of nano-sized chemical patches whose
composition may locally induce irreversible adsorption of particles
in the primary minimum [5,6]. In that respect, several models
containing two or more classes of adsorption sites were proposed
in the literature [7–11]. The local pore structure and surface
topography heterogeneity considered as asperities were shown to
induce a shift of the actual interaction potential. Indeed, repulsive
interaction between a colloidal particle and a solid surface is
lower on a rough surface compared to a smooth surface [12–14].
The extent of this interaction depends mainly on the asperities
characteristic height H, their form and the inter-asperities distance
relative to particle size. Moreover, these topographic hetero-
geneities play an important role in both particle retention and
its counterpart particle release phenomena through flow pattern
modification. When a porous medium is modeled as a collection of
spherical grains, non-deformable colloid particles are considered
to firstly adsorb onto grain surface and may subsequently roll on
it under hydrodynamic drag force and/or diffusion and then are
retained by accumulation in stagnation regions at grain–grain
contact zone or in the rear of the grain [15–18]. Similarly colloid
particles may be re-entrained by escaping from these retention
regions going back to the bulk flowing suspension (re-suspension
mechanism). This was introduced in the convection–dispersion
equation [19] in order to simulate experimental breakthrough
curves but too many rate dependent constants had to be
adjusted.
Basically, detachment of an adsorbed particle results from a bal-
ance between external forces exerted on it. These are adhesion
(physicochemical interactions), drag and lift forces. So, depending
on whether the particle is hard (slightly deformable) or soft (highly
deformable), an adapted continuum mechanics model is usually
used to predict the physicochemistry/hydrodynamic relationship
that governs particle detachment. For smooth surfaces, major stud-
ies predict that detachment should occur mainly by rolling [20–23].
Bergendahl and Grasso [22] have shown that incipience of particle
rolling is well correlated to a dimensionless parameter N
TFT
; the
ratio of the depth of the primary minimum to the exerted shear
force torque. The roughness of grain surface was earlier considered
by several authors [24–27]. Burdick et al. [26] studied the behavior
of colloids of given sizes in the vicinity of an obstacle. Examina-
tion of balance of forces and torques that are exerted on a retained
deformable colloid showed that its re-entrainment follows a lift
process rather than a rolling which is expected to predominate in
the removal of particles adsorbed on smooth surfaces. By the same
way, Neyland [28] examined the influence of both the height (and
the depth) of asperities and their separation distance on critical
flow rate for particle re-entrainment. However, the problem con-
sidered was only in 2 dimensions and the discussion of results was
only qualitative.
From what is briefly exposed here, it may be seen that represen-
tative simulations of retention and removal of colloidal particles of
given size in presence of a rough surface is still lacking. So, the
goal of this paper is to propose a numerical modeling of retention
and re-entrainment of micron sized colloids in presence of rough-
ness on a grain surface. In this work, a direct numerical simulation
method was adopted including both hydrodynamic and physico-
chemical interactions in the vicinity of asperities of various shapes
and characteristic sizes. In the next section the adopted method
is described before presentation in section 3 of primary results
showing successively the influence of physicochemical conditions
through the ionic strength variations and hydrodynamic conditions
all in presence of a rough or a smooth surface.
2. Numerical model
2.1. Configuration
The geometrical configuration and physical parameters chosen
for this study are based on recent experiments [29,30]. In those
works, deposition and release of negatively charged colloidal latex
particles of a radius, a
p
, of 400 nm in an artificial sintered silicate
porous medium were investigated.
Hydrodynamic parameters are also based on laboratory experi-
ments [29,30]. The inlet velocity used in the simulations is equal to
4 × 10
−5
ms
−1
leading to the following values of the Péclet number
and the Particulate Reynolds number respectively:
P
e
=
V
p
a
p
D
b
= 9.8 (1)
,
Re
p
=
p
a
p
¯
u
= 1.66 × 10
−5
(2)
where V
p
is the particle velocity corresponding to the fluid veloc-
ity evaluated at a distance of 3a
p
from the grain surface, D
b
is the
bulk particle diffusion coefficient.
p
,
¯
u and are respectively the
particle density, the interstitial velocity and the dynamic viscosity
of the fluid.
For given P
e
and Re
p
and for each roughness, three different val-
ues of salinity (0.5, 1.2 and 2 or 3 g/L of NaCl) are considered leading
to three levels of ionic strength, I, designated by weak (I = 3 mM),
medium (I = 7.8 mM) and strong (I = 12 or 18 mM). These values of
I correspond to DLVO forces of significantly different intensities
(Fig. 1).
The domain chosen for this study is a rectangular prism
(5 m × 4 m × 3.8 m), in contact with the grain surface (Fig. 2).
The topographic heterogeneities considered here are surface
asperities on the grain surface. The roughness geometries are sim-
ple and have acute angles, which for a class of porous media such
as sands can be closer to reality than hemispherical plots or asperi-
ties that are mostly used in the literature [12,25,31–33]. Therefore,
besides the smooth surface, right triangular prisms of the form of
peaks and valleys with two different sizes are considered. (Fig. 3)
The heights, H, correspond to one or two times the particle radius,
a
p
and therefore vary from −2a
p
to 2a
p
. Despite the 2D nature of the
asperities, particles are spherical and all simulations are performed
in 3 dimensions. The colloid is placed on the symmetry plane of the
domain in the thickness and the results will be presented in this
plane.
The particle transport is solved by Direct Numerical Simulation
(DNS) with fixed Cartesian grids. The size of the grid blocks are cho-
sen so that the particle diameter contains 16 blocks. Previous works
Fig. 1. DLVO Interaction forces for different ionic strength values as a function of surface-to-surface separation distance, h.
Fig. 2. Schematic view of the simulation domain (case of peak geometry).
have shown that, with the numerical choices made here which will
be presented in the next section, a number of grid blocks between
8 and 16 ensure numerical results in agreement with the physics
of particle transport for a large range of Reynolds numbers [34,35].
2.2. Model
2.2.1. Governing equations
Simulations are performed using the numerical code Thetis
®
,
developed in our lab, in which additional modules have been added
in order to take into account particle/particle and particle/grain sur-
face physicochemical interactions. A generalized one-fluid model
has been used for the transport of particles [35]. The entire domain
is considered as fluid and the solid is a particular fluid with special
properties, the two phases being distinguished through a phase
indicator function, F
c
. The evolution of the particle is described by
an advection equation on F
c
. The flow of the incompressible New-
tonian fluid is governed by the Navier–Stokes and the mass balance
equations. The final set of partial differential equations is given by
the one-fluid model given below:
∇
.u = 0 (3)
Fig. 3. Roughness geometries with respect to particle dimension H ∈ [[−2a
p
; 2a
p
]].
![Fig. 3. Roughness geometries with respect to particle dimension H ∈ [[−2ap; 2ap]].](/figures/fig-3-roughness-geometries-with-respect-to-particle-sctfbbum.webp)
