progress

1 files changed, 11 insertions, 1 deletions

diff --git a/typst/main.typ b/typst/main.typ
index 32fbad0..fe545be 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -195,7 +195,7 @@ $
 partial (epsilon rho_f) / (partial t) + nabla ( epsilon rho_f v^f) = 0
 $
 )
-with a fluid momentum balance equation
+with a fluid momentum balance equation of the form
 
 #math.equation(
 block:true,
@@ -204,6 +204,9 @@ partial(epsilon rho_f v^f) / (partial t) + nabla (epsilon rho_f v^f v^f ) = - ep
 (mu_f (nabla v^f + (nabla v^f)^T) - epsilon^2 mu_f ( v^f - #overline[v]^p) / K). $
 )
 
+where $p$ is the pressure, $mu_f$ is the fluid dynamic viscosity, $g$ is the gravitational acceleration, and $#overline[v]^p$ is the averaged
+particle velocity on the grid with K being the cell-permeability with distinctions in unresolved and resolved particles@MAYA2024.
+
 
 == Clogging of porous structures
 
@@ -235,6 +238,13 @@ and ratios below $D/d_p < 1$ cause immediate sieving.
   caption: [Probability 𝑃 (𝑠) of clogging after s escape events for (a) 5, (b) 50, (c) 500, (d) 5000 particles in round constriction pore geometry. @laurez2025bridging]
 )
 
+For the aggregational aspects other forces are significant. Derjaguin-Landau-Verwey-Overbeek (DLVO) theory is one which unifies
+Van-Der-Waal forces and electromagnetic repulsion where the final particle-particle force reads as
+
+#math.equation(
+block:true,
+F_ij^DLVO_pp
+)
 
 == Discusion