progress

2 files changed, 42 insertions, 2 deletions

diff --git a/typst/main.typ b/typst/main.typ
index 4de29dc..f389c9c 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -170,6 +170,30 @@ These forces diverge the smaller $h$ becomes.
 This is due to the viscous stress increasing on small films of
 fluid which then in turn dominate the interaction.
 
+== Volume Averaged Navier-Stokes(VANS)
+
+For the suspension of multiple particles Laurez et al suggests the use of a volume averaged Navier-Stokes equation where
+the a porostiy field $epsilon$ is introduced and defined as
+
+#math.equation(
+  block:true,
+$ epsilon = 
+{
+  cases(
+    1", if the cell is occupied by fluids only",
+    (0,1)", if the cell is occupied by a fluid-solid aggregate or interface",
+    0", if the cell is occupied by solids only."
+  )
+ $
+)
+
+The mass balance equation for the fluid phase then reads
+
+#math.equation(
+block:true
+
+)
+
 == Clogging of porous structures
 
 Modifying a poiseulle channel flow by narrowing the channel we can observe mainly three different ways how the porosity is reduced.
@@ -183,7 +207,7 @@ effect is disregarded due to the scale of the problem and accumulation of partic
 
 #figure(
 image("narrow_channel.png"),
-caption: [One example geometry from Laurez@laurez2025bridging describing]
+caption: [One example geometry from Laurez@laurez2025bridging describing the general narrow setup]
 )
 
 With the narrow throat diameter $D$ and the pore radius $d_p$ the clogging probability starts to occur spuriously around
@@ -241,4 +265,6 @@ To couple a particle dynamics system two major approaches exist within Lattice B
 The Immersed Boundary Method(IBM)@Peskin_2002 and the Homogenized Lattice-Boltzmann-Method(HLBM)@KRAUSE2017HLBM.
 The IBM approach is managed by calculating the coupling based on Lagrangian nodes from the point of view of the particles,
 requiring the recovery of the macroscopic variables and also distributing the force back.
-While the approach by HLBM incorporates most the of the 
+While the approach by HLBM incorporates most the of the coupling into the collision modell.
+The key difference between those two being that the coupling in IBM happens from the point of view of the cell while
+the exchange in HLBM happens from the cell grids. There are key similarities to VANS due to the identical model of fluid averaging.
diff --git a/typst/refs.bib b/typst/refs.bib
index ec46a23..130de47 100644
--- a/typst/refs.bib
+++ b/typst/refs.bib
@@ -158,3 +158,17 @@ despite omitting an explicit particle collision model.}
 @article{Peskin_2002, title={The immersed boundary method}, volume={11},
 DOI={10.1017/S0962492902000077}, journal={Acta Numerica}, author={Peskin, Charles
 S.}, year={2002}, pages={479–517}}
+
+@article{MAYA2024,
+title = {Particulate transport in porous media at pore-scale. Part 2: CFD-DEM and colloidal forces},
+journal = {Journal of Computational Physics},
+volume = {519},
+pages = {113439},
+year = {2024},
+issn = {0021-9991},
+doi = {https://doi.org/10.1016/j.jcp.2024.113439},
+url = {https://www.sciencedirect.com/science/article/pii/S0021999124006879},
+author = {Laurez {Maya Fogouang} and Laurent André and Philippe Leroy and Cyprien Soulaine},
+keywords = {DLVO theory, JKR theory, Colloid deposition, Pore-scale modeling, CFD-DEM model, Pore-clogging},
+abstract = {Pore-clogging by aggregation of fine particles is one of the key mechanisms in particulate transport in porous media. In this work, the unresolved-resolved four-way coupling CFD-DEM (Computational Fluid Dynamics - Discrete Element Method) proposed in Part 1 is coupled with colloidal forces (long-range interactions) to model the transport of charged particles and retention by aggregation at the pore-scale. The model includes hydro-mechanical interactions (e.g. collision, drag, buoyancy, gravity) and electrochemical interactions (e.g. Van der Waals attraction, electrostatic double layer repulsion) between the particles, the fluid, and the porous formation. An adhesive contact force based on the Johnson-Kendall-Roberts theory allows for realistic particle adhesion on the walls. The model robustness is verified using reference semi-analytical solutions of the particle dynamics including long-range interactions. Finally, our CFD-DEM for particulate transport including DLVO and JKR adhesive contact forces is used to investigate the effect of fluid salinity on pore-clogging and permeability reduction. Importantly and unlike other approaches, our CFD-DEM model is not constrained by the size of the particle relative to the cell size. Our pore-scale model offers new possibilities to explore the impact of various parameters including particle size distribution, particle concentration, flow rates, and pore geometry structure on the particulate transport and retention in porous media.}
+}