progress

2 files changed, 13 insertions, 4 deletions

diff --git a/typst/main.typ b/typst/main.typ
index eb9f708..4de29dc 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -174,9 +174,10 @@ fluid which then in turn dominate the interaction.
 
 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.
+The least interesting phenomenon compared to the other two is sieving which results purely from a single particle having
+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 in the fluid and surface boundaries at micrometer scales. In Laurez study@laurez2025bridging this
 effect is disregarded due to the scale of the problem and accumulation of particles occuring gradually.
 
@@ -185,11 +186,19 @@ image("narrow_channel.png"),
 caption: [One example geometry from Laurez@laurez2025bridging describing]
 )
 
+With the narrow throat diameter $D$ and the pore radius $d_p$ the clogging probability starts to occur spuriously around
+$2.43 < D/d_p < 5.26$
+while higher ratios allow for the unobstructed passage of particles, lower ratio begin to form stable arches
+and ratios below $D/d_p < 1$ cause immediate sieving.
+
 #figure(
   image("bridging.png"),
   caption: [Particles forming an arch visualized by Laurez@laurez2025bridging]
 )
-
+#figure(
+  image("prob_bridge.png"),
+  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]
+)
 
 
 == Discusion
diff --git a/typst/prob_bridge.png b/typst/prob_bridge.png
new file mode 100644
index 0000000..ada91ee
--- /dev/null
+++ b/typst/prob_bridge.png