progress

1 files changed, 22 insertions, 3 deletions

diff --git a/typst/main.typ b/typst/main.typ
index b7d00fe..1162980 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -71,8 +71,8 @@ an infinite space with a set solid boundary interface.
 
 #math.equation(
 block: true,
-$ v = U "at" a = r,\
-v arrow 0 "as" a arrow infinity
+$ v = U "at particles boundary",\
+v arrow 0 "as" |x| arrow infinity
 $
 )
 
@@ -86,6 +86,15 @@ block: true,
 $ F_S = 6 pi mu r v $
 )
 
+with our boundary conditions specified as
+
+#math.equation(
+block: true,
+$ u = v "at" a = r,\
+u arrow 0 "as" a arrow infinity
+$
+)
+
 where according to Proudman and Pearson@proudman_pearson_1957 at a Reynolds number of 0.05 the predicted drag is two percent lower
 than the possibly more correct value by Proudman and Pearson@proudman_pearson_1957.
 
@@ -124,8 +133,18 @@ These forces diverge the smaller $h$ becomes.
 This resistance becomes crucial to modell bridging behaviour
 
 
-== Clogging and Bridging
+== 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.
+By sieving, bridging and aggregation of surface deposition.
+The least interesting phenomenon is sieving which results purely from a single particle having a too large of a volume to fit into the
+pore. While bridiging occurs when multiple particles arrive at a passage at the exact time, forming a stable arch which blocks the flow.  
+Aggregation involves the deposition of particles gradually  narrowing the channel.
+And while sieving and bridging results from purely mechanical forces aggregation results from electrostatic interactions between particles, the fluid and surface boundaries at micrometer scales@laurez2025bridging.
+
+The arches resulting from clogging are often inherently unstable, but with the progression of aggregation arrive at more less unstable states.
 
+// Insert png
 
 == Lattice-Boltzmann-Method