diff options
| -rw-r--r-- | typst/main.typ | 25 |
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 |