Fixing the CO2 reference and also rewriting the creeping flow since I

kinda was thinking in weird reference frames

1 files changed, 12 insertions, 11 deletions

diff --git a/typst/main.typ b/typst/main.typ
index 78978de..1274795 100644
--- a/typst/main.typ
+++ b/typst/main.typ
@@ -30,7 +30,7 @@
 Flow in porous subsurface structures often is dominated by extremely low velocity and high viscous fluids with low Reynolds numbers $"Re" << 1$.
 In such a condition, the flow enters a state called the Stokes Flow or creeping flow, where inertial forces can be assumed to be zero and viscous
 forces dominate the whole connected set.
-This kind of flow is found in geological processes, in carbohydrate recovery, filtration systems and CO_2 storage where the pore-scale motion
+This kind of flow is found in geological processes, in carbohydrate recovery, filtration systems and $CO_2$ storage where the pore-scale motion
 of particles and their interaction with the surrounding porous medium strongly influence macroscopic properties such as the permeability of
 rock layers.
 Undestanding particle transport, bridging and in general clogging phenomena is critical for the effective use and management of subsurface
@@ -43,7 +43,7 @@ The study of the Stokes Flow has a long history, beginning with Stokes' study of
 Subsequent work expanded his work to include a multitude of shapes and the interaction of multiple particles, different geometries and
 boundary other conditions.
 More recently, research was performed in the understanding of creeping flow, the particle transport and the clogging associated with it, and how those microscopic properties impact the macroscopic development. These carry implications which are essential in water treatment, medicine,
-carbohydrate recovery and CO2 storage. // CITE
+carbohydrate recovery and $CO_2$ storage. // CITE
 
 This report delves into the central aspects governing the known behaviour of Stokes Flow and the key extension results towards past single and multiple spheres.
 Explores the effect of it in porous media and examines the more recent particle bridging behaviour found in porous structures.
@@ -95,8 +95,8 @@ The original study for simplicity also included the boundary conditions
 
 #math.equation(
 block: true,
-$ v = U "at particles boundary",\
-v arrow 0 "as" |x| arrow infinity
+$ v_n = 0 "at particles boundary",\
+v arrow U "as" |x| arrow infinity
 $
 )
 
@@ -117,8 +117,8 @@ with our boundary conditions specified as
 
 #math.equation(
 block: true,
-$ u = v "at" a = r,\
-u arrow 0 "as" a arrow infinity
+$ v_n = 0 "at" a = r,\
+v arrow U "as" a arrow infinity
 $
 )
 
@@ -270,13 +270,14 @@ While the potential again contains a singularity with zero distance these can be
 
 The particles forming arches are often inherently unstable. Slight fluctuations in flow rate, local velocity gradients or the particle shape
 can impact the particle arch formation and restore partial flow.
-But with the progression of aggregation arrive at less unstable states.
-Which in turn makes a stochastic analysis of particles in different conditions@laurez2025bridging based on different widths feasible.
+As aggregation progresses, the particle bridge arrive at less unstable states.
+Which in turn makes a stochastic analysis of particles in different conditions@laurez2025bridging based on different width to gap ratios interesting.
 
-Laurez@laurez2025bridging goes into detail how probable clogging mechanisms are, while these are quite in depth, opportunities
+Laurez@laurez2025bridging explores in detail how probable clogging mechanisms are. While these are quite in depth, opportunities
 in relation to multiphase fluid interaction with the solid structures arise as well since his work focuses on a single phase fluid.
-Another interesting question is a variation in the inbound boundary pressure condition as Laurez looks into a constant inbound pressure
-while also mentioning that pressure changes are naturally introduced into pores within complex geometries which makes the observation of a single pore throat with only a constant pressure unsatisfying.
+
+Another point of interest is a variation in the inbound boundary pressure condition as Laurez looks into a constant inbound pressure.
+Laurez mentions that pressure changes are naturally introduced into pores within complex geometries which makes the observation of a single pore throat with only a constant pressure unsatisfying.
 Similar gaps can be seen in the other clogging mechanisms which might provide additional research targets analogous to the gaps in regard to the bridging phenomena.
 A comparison with a Lattice-Boltzmann-Method modell is promising.
 The required forces within the particles are accounted for now.