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#import "@preview/charged-ieee:0.1.3": ieee
#show: ieee.with(
title: [Stokes flow - Particle interaction in low Reynolds Number environments],
abstract: [
],
authors: (
(
name: "Claudius Holeksa",
department: [CSSR],
organization: [NORCE Research AS],
location: [Bergen, Norway],
email: "clho@norceresearch.no"
),
),
index-terms: ("Scientific writing", "Typesetting", "Document creation", "Syntax"),
bibliography: bibliography("refs.bib"),
figure-supplement: [Fig.],
)
= Introduction
Flow in porous subsurface structures often is dominated by low velocity and high viscous fluids with low Reynolds numbers,
often referred to as Stokes flow or creeping flow.
It occurs when the viscous forces are significantly larger compared to inertial forces.
For the understanding of porous media, where particle transport, bridging and clogging phenomena are critical to the use of subsurface
reservoirs. Understanding the behaviour of particles in Stokes flow is key to analyzing these phenomena emerging over time.
For the understanding of near-well injections multiple elements such as multiphase behaviour, particle-solid interaction and
the geometry of the porous structure is required.
While at heart most numerical modelling approaches such as the Lattice-Boltzmann-Method are based on the Navier-Stokes Equations,
here we will take a glance on a more special case.
Since we are interested in low velocity and high viscous cases the Reynolds number (Re \< \< 1) of our base equation reduces itself to
the Stokes Equations due to the relation $Re=U*v/L$,
which are well understand in terms of the description by Stokes [dummy, I mean the old paper from 1851].
So starting from the incompressible Navier-Stokes equations we will assume a mostly laminar flow such that the inertial effects
are not considered, but are dominated by the viscous forces.
Viscous flows are often
== Navier
// Write about Navier
The incompressible Navier Stokes equations are a set of equations
#math.equation(
block: true,
$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\
∇ · u = 0 $
)
// Introduction
== Stokes flow
While we are often interested in Navier-Stokes flows, on higher viscous fluid such as in the earth's mantle the inertial term is negligable.
Since we
// Stokes
#math.equation(
block: true,
$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\
∇ · u = 0 $
)
== Solid-Fluid interaction with Stokes flow
Since
// Boundary
//
// Different boundary examples ?
// References
== References
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