Contact angle

2.9 Predicting the wetting behavior: the "wetting envelope"

The “wetting envelope” is not an independent calculation method for the polar and disperse fractions of the surface energy of a solid, but only a special type of presentation. It can be used for all surface energy calculation methods which provide a polar fraction and a disperse fraction in the result.

With the help of the wetting envelope and a knowledge of the polar and disperse fractions of the surface energy of a solid it is possible to predict whether a particular liquid, whose surface tension components are also known, will wet the solid completely. The following relationships make this possible:

A liquid will wet a solid surface completely when the work of adhesion $W_{sl}$ between the solid surface and the liquid is greater than work of cohesion $W_{ll}$ within the liquid. The difference between these two quantities is known as the spreading pressure $S_{l\ /\ s}  $ :

$S_{l\ /\ s} = W_{sl} - W_{ll}$ (Equation 57)

this means that a liquid will wet a solid when the spreading pressure is positive.

The work of adhesion can also be described with the help of the contact angle between the liquid and the solid and surface tension of the liquid:

$W_{sl} = \sigma_l (\cos\theta + 1)$ (Equation 58)

As according to DUPRÉ $W_{ll}$ is defined as $2 \cdot \sigma _l$ ; this means that for a contact angle of 0° ( $(\cos\theta = 1)$ ) the spreading pressure $S_{l\ /\ s}$ is 0 and the liquid will wet the solid completely.

: Fig.8: Contact angle and wettability

In order to represent the wetting envelope the methods described for the determination of the disperse and polar fractions of the surface energy (FOWKES; OWENS, WENDT, RABEL and KAELBLE; WU) are reversed: disperse and polar fractions of the solid are known (from a measurement or from the literature); the corresponding equations are used instead to calculate the polar and disperse fractions of the liquid which have a value of $\cos\theta = 1$ for the solid under investigation. By plotting the polar fraction against the disperse fraction a curve is produced for $\cos\theta = 1$ which starts at the origin (0/0), attains a maximum value and then returns to the X-axis. The area enclosed within this curve is the wetting envelope or wetting range; all liquids whose data lie within this enclosed area will wet the corresponding solid.

The procedure is demonstrated below using two liquids as an example:

: Fig.9: Predicting the wetting behavior by using the wetting envelope

The following Table shows the data used for Fig.9, this was taken from the DSA1 liquid database. The values for ethanol lie within the wetting envelope; this means that we can expect that ethanol will wet the solid. In contrast, cyclopentanol lies outside the envelope and should therefore not wet the solid.

Liquid	Disperse fraction	Polar fraction	Wetting behavior
Ethanol	17.5 mN/m	4.6 mN/m	wetted completely
Cyclopentanol	27.2 mN/m	5.5 mN/m	not wetted completely

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