#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. Be it either for carbohydrate resource recovery or storage of CO2. Understanding the behaviour of particles in Stokes flow
is key to analyzing more complex phenomena emerging over time such as permeability reduction over periods of time.

The study of Stokes flow has a rich history, beginning with Stokes solution analyzing flow along a sphere.// CITE
Subsequent work analyzed a multitude of shapes and the interaction of multiple particles.
More recently, research was performed in the understanding of creeping flow which are essential in water treatment, carbohydrate recovery
and CO2 storage. // CITE

This report delves into the central aspects governing the known behaviour 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.


== 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