#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

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 very viscous cases with our Reynolds number (Re \< \< 1) our base equation reduces itself to the Stokes Equations,
which are well understand in terms of the description by Stokes [dummy, I mean the old paper from 1851].
So the Navier-Stokes equations

todo insert NS eqs here

are reduced to

todo insert S eqs here
// Rather move this to the lower chapters and use book citations I guess. Well, maybe also Stokes paper. The initial rant is quite fun


== Navier

The Navier Stokes equations are governed as follows

// we don't really need the external force here? do we?

#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 fluids the viscosity dominates.


== Solid-Fluid interaction with Stokes flow

So while

// References
== References