**3. Wetting**

The displacement of a solid-air interface with a solid-liquid contact is commonly referred to as 'wetting'. Two separate equilibrium regimes may be identified when a small liquid droplet comes into contact with a flat solid surface. Complete wetting with a zero-contact angle or partial wetness with a finite contact angle is shown in **Figure 1**. The equilibrium at a solid-liquid boundary is commonly described by the Young's equation:

$$
\gamma\_{\rm SV} - \gamma\_{\rm SL} - \gamma\_{\rm LV} \cdot \cos \,\theta = 0 \tag{9}
$$

where, γSV, γSL and γLV denote interfacial tensions between solid/vapour, solid/ liquid and liquid/vapour, respectively, and θ is the equilibrium contact angle.

The parameter that distinguishes partial wetting and complete wetting is the socalled spreading parameter S, which measures the difference between the surface energy (per unit area) of the substrate when dry and wet:

$$\mathbf{S} = [\mathbf{E}\_{\text{substrate}}]\_{dry} - [\mathbf{E}\_{\text{substrate}}]\_{wet} \tag{10}$$

Or,

$$\mathcal{S} = \chi\_{\rm SV} - (\chi\_{\rm SL} + \chi\_{\rm LV}) \tag{11}$$

The liquid spreads entirely to lower its surface energy (θ = 0) if the parameter S is positive. The end result is a layer with a nano-scopic thickness that results from molecular and capillary forces competing. If S is negative, the drop does not spread out and instead forms an equilibrium spherical cap resting on the substrate with a contact angle of. When θ ≤ π/2, a liquid is said to be 'mainly wetting', while when θ > π/2, it is said to be 'primarily non-wetting'. When a surface is connected with water, it is referred to as 'hydrophilic' when it is θ ≤ π/2 and 'hydrophobic' when it is θ > π/2 [6].

#### **3.1 Wicking**

Wicking is the capillary-driven spontaneous flow of a liquid in a porous medium. Wetting causes capillary forces; hence, wicking is the result of spontaneous wetting in a capillary system. A meniscus is created in the simplest case of wicking in a single capillary tube as shown in **Figure 2**. A pressure difference across the curved liquid/ vapour contact is caused by the surface tension of the liquid. The value for the pressure difference of a spherical surface was deduced in 1805 independently by Thomas Young and Pierre Simon de Laplace and is represented with the so-called Young-Laplace equation [6]:

ΔP ¼ γLV 1 *R*1 � 1 *R*2 (12)

**Figure 1.**

*A small liquid droplet in equilibrium over a horizontal surface: (a) partial wetting, mostly non-wetting; (b) partial wetting, mostly wetting; (c) complete wetting.*

*Absorbency and Wicking Behaviour of Natural Fibre-Based Yarn and Fabric DOI: http://dx.doi.org/10.5772/intechopen.102584*

For a capillary with a circular cross section, the radii of the curved interface *R*1 and. *R*2 are equal. Thus:

$$
\Delta \mathbf{P} = 2\gamma\_{\rm LV}/\mathbf{R} \tag{13}
$$

where,

$$R = r/\cos\Theta \tag{14}$$

and *r* is the capillary radius. Since the capillary spaces in a fibrous assembly are not uniform, the effective capillary radius *re* is utilised instead, which is usually an indirectly determined parameter.

#### **3.2 Capillary theory**

Capillary action is governed by the properties of the liquid, the fibre surface wetting characteristics and the geometric configurations of the porous medium. In a capillary, liquid rises due to the net positive force (ΔP) across the liquid-solid interface.

$$
\Delta \mathbf{P} = \mathbf{P} \text{--} \delta \mathbf{g} \mathbf{h},
\tag{15}
$$

where δ = liquid density in g/cc, g = gravitational acceleration of 980.7 cm/s2, height of liquid rise in cm = h, the capillary pressure (p) is described by the initial wetting force (Fwi) in the capillary area (πri<sup>2</sup> ):

$$\mathbf{P} = \mathbf{F}\mathbf{w}\mathbf{i}/\pi\mathbf{r}\mathbf{i}^2 = 2\,\pi\,\mathbf{r}\mathbf{i}\chi\cos\theta/\pi\mathbf{r}\mathbf{i}^2 = 2\,\chi\cos\theta\tag{16}$$

where, γ = liquid surface tension in dyne/cm.

ri = radius inside the capillary in cm and.

θ = liquid-solid contact angle.

Where capillary pressure (P) is greater than the weight of the liquid (δgh), the positive forces drive the liquid upward. Upon reaching equilibrium where P – δgh, the net driving force ΔP becomes zero. The liquid stops rising at the equilibrium height (h).
