Surface tension

Contact angle measurements

Measuring the contact angle between a liquid and a solid is the domain of our optical Drop Shape Analysis intruments (DSA). Nevertheless, contact angles can also be measured using tensiometrical measurements.

Contact angles of solid bodies

The theoretical principles of the plate method also apply to the determination of the contact angle between a liquid and a solid surface. In this method liquids with a known surface tension are used and a plate made of the material to be investigated is used instead of the platinum plate. The wetted length of the plate must be measured; it is obtained from the following equation:

L = 2 × length + 2 × thickness

The height of the plate does not matter.
The plate is suspended from the balance by using a sample holder. The liquid is moved upwards. As soon as a contact is registered the measurement of the force is started. By using the equation for the plate method the contact angle θ can be calculated from the surface tension of the liquid, the wetted length and the measured force:

$\cos \theta = \frac {F}{L \cdot \sigma}$

From the contact angle data the surface energy of a solid can be calculated. In the contact angle add-in of the LabDeskTM tensiometer software various methods for calculating the surface energy have been included, the program also includes a database containing the physical data of numerous liquids which is required for this.

Contact angles of powders: Sorption measurements using the Washburn method

Sorption measurements are used for determining the surface energy of a powder-form solid. The powder to be measured is filled into a glass tube with a filter base and this is suspended from the balance. After the vessel has contacted the liquid the speed at which the liquid rises though the bulk powder is measured by recording the increase in weight as a function of time.

: Scheme of a Sorption measurement

Bulk powder through which a liquid flows can be regarded as being a bundle of capillaries. This means that for the calculation of the advancing angle, which corresponds to the contact angle between the solid and the liquid, the Washburn equation which applies to capillaries can be used:

$\frac {l^2}{t} = \frac {\sigma_l \cdot r \cdot \cos \theta}{2\eta}$

( $l$ = flow front; $t$ = flow time; $\sigma_l$ = surface tension of liquid; $r$ = capillary radius; $\theta$ = advancing angle; $\eta$ = viscosity of the liquid)

The capillary radius r for bulk powder must be replaced by a quantity which describes the orientation of the microcapillaries c and the mean radius. As a result r is replaced by the constant (c • r), this applies to a particular powder.

$\frac {l^2}{t} = \frac {(c \cdot \rho) \cdot \sigma_l \cdot \cos \theta}{2\eta}$

This assumes that the bulk density of the powder is uniform.
As the flow front cannot be determined directly, it must be calculated from the measured increase in weight, the liquid density and the tube diameter. The viscosity and surface tension of the liquid are known, only two unknown quantities remain: the required advancing angle (contact angle) and the material constant (c • r).

This is why a measurement with an optimally wetting liquid (e.g. hexane, whose advancing angle is virtually 0° , is carried out first; this gives a value for cos $\theta$ of approximately 1.

When the term $2 \eta  \frac {l^2}{\sigma_l}$

is plotted against t a linear section is obtained whose slope is (c • r) i.e. the required constant.

For measurements with other liquids this constant can be inserted into the Washburn equation, so that the advancing angle $\theta$ can be determined for other liquids.