Darcy’s law: equation that describes the flow of a fluid through a porous medium. La vitesse de l’eau entre deux points est proportionnelle au gradient de la pression entre ces deux points.
$Q=\frac{KA ∆P}{L}$
K= conductivité hydraulique
A= surface de la section étudiée
L= longueur traversée par l’eau (dans notre cas, l’épaisseur de la ficelle)
∆P= différence de pression
Hydraulic conductivity: represented as K, is a property of a medium that describes the ease with which a fluid (usually water) can move through pore spaces or fractures. It depends on
• the properties of the material: size and disposal of grains and pores
• the properties of the fluid: viscosity and density (=masse volumique)
• the degree of saturation
By definition, hydraulic conductivity is the ratio of velocity to hydraulic gradient indicating permeability of porous media.
$K=\frac{κρg}{μ}$
κ= la perméabilité intrinsèque du milieu poreux ($m^2$)
ρ = la masse volumique du fluide (kg/$m^3$)
g= gravitation (m/$s^2$)
μ= viscosité (Pa s= kg/m/s)
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La porosité d'un substrat poreux et sa conductivité hydraulique K sont
notamment déterminés par la taille des grains et la taille des interstices
entre ces grains, ainsi que par la communication entre ces interstices. Ici, un même fluide incompressible cheminera plus facilement et plus rapidement
dans la situation 1 que dans la situation 2.
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Liquid transport in porous media: When a dry porous medium, such as a brick or a wick, is brought into contact with a liquid, it will start absorbing the liquid at a rate which decreases over time. Liquid penetration will reach a limit dependant on parameters of temperature humidity and permeability. For a bar of material with cross-sectional area A that is wetted on one end, the cumulative volume V of absorbed liquid after a time t is
$V=AS\sqrt{t}=AI$
where S is the sorptivity of the medium, in units of $m s^{−\frac{1}{2}}$ or $mm min^{−\frac{1}{2}}$
and $I=S\sqrt{t}$ is the cumulative infiltration (see “sorptivity” below)
Permeability: measure of the ability of a porous material (often, a rock or an unconsolidated material) to allow fluids to pass through it. The permeability of a medium is related to the porosity, but also to the shapes of the pores in the medium and their level of connectedness. High permeability will allow fluids to move rapidly through the medium. Knowing the height of the soil sample column L, the sample cross section A, and the constant pressure difference Δh, the volume of passing water Q, and the time interval ΔT, one can calculate the permeability of the sample as
$κ=\frac{QL}{A∆h∆t}=\frac{Kμ}{ρg}$
Porosity: The wetted length of the bar, that is the distance between the wetted end of the bar and the so-called wet front, is dependent on the fraction f of the volume occupied by voids. This number f is the porosity of the medium. It is calculated as follows
$f=\frac{V_{voids}}{V_{total}}$
Sorptivity: measure of the capacity of the medium to absorb or desorb liquid by capillarity. It expresses the tendency of a material to absorb and transmit water and other liquids by capillarity. The sorptivity is widely used in characterizing soils and porous construction materials such as brick, stone and concrete. Sorptivity can be determined from horizontal infiltration where water flow is mostly controlled by capillary absorption
$I=\frac{S}{\sqrt{t}}$
For vertical infiltration, the solution is adapted using a parameter $A_1$. This results in the following equation, which is valid for short times:
$I=S\sqrt{t}+A_1 t$
The two properties normally used to predict wicking performance in a fabric are capillary pressure and permeability. Capillary pressure is the main force responsible for the movement of moisture along or through a fabric, where the force of the surface tension between the liquid and the walls of a narrow gap or pore overcome the forces between the molecules of the liquid, moving it into empty gaps until the forces even out. Permeability is the measure of a fabric’s ability to transport moisture through itself, and is determined by a combination of sizes of spaces within it and the connections between the spaces.
Other properties that certainly do effect the wicking properties of a fabric include yarn twist (how threads in the fabric turn around each other), contact angle (between the fibre and the liquid), knit (tricoté) or weave (tissé) (the larger scale construction of the fabric), yarn roughness and a whole lot more.
Conclusion:
- We need a material which allows capillary action
- Suited for this are porous materials, with many small pores, like sponges or wicking fabric
- We want our material to hold a large amount of water
- According to Darcy’s law, at given Q, we want to maximise the area
- We want a large cumulative volume V of absorbed liquid
- Thus, we need a material with large area and sorptivity
- This means that we need a large cumulative infiltration I
- We need low permeability, thus a large area and a low hydraulic conductivity coefficient
Small: K, κ
Pour prochain blog, on va commencer à chercher des matériaux qui répondent à ces critères.
