Contact Angles

Less Traditional Definition

Capillarity is the ability of a substance to draw another substance into it and It occurs when the adhesive intermolecular forces between the liquid and a substance are stronger than the cohesive intermolecular forces inside the liquid. The effect causes a concave meniscus to form where the substance is touching a vertical surface (Figure \(\PageIndex{3}\)​). The same effect is what causes porous materials to soak up liquids. Capillary forces pull a wetting liquid has a low contact angle with the surface, it wets the surface. Assuming that there are no other factors involved (e.g. roughness), a low contact angle with water means that the surface is hydrophilic. A completely wetting liquid forms a zero contact angle into a capillary by creating a curved meniscus at the rising liquid front. This phenomenon can be described with the Young-Laplace equation and the Laplace pressure inside a capillary.

The Sessile Drop Method

The most frequently used is the goniometer-telescope measurement of sessile-drop contact angles. Commercial contact angle goniometers employ a microscope objective to view the angle directly. In the static method a drop is deposited on a surface and the contact angle can be measured by looking at the drop through a goniometer (an instrument that measures contact angles). The dynamic method is similar to the static one but the drop of liquid which is deposited on a surface is modified. The droplet is being deposited via a syringe and the droplet’s volume is changed dynamically without increasing its solid-liquid interface area and this maximum angle is the advancing angle. Volume is then removed to produce the smallest possible angle, which is called the receding angle. The difference between those two measured angles is called contact angle hysteresis.

Wilhelmy Plate Method

The capillary rise on a Wilhelmy plate is a good way to obtain the contact angle by measuring the height of the meniscus created on a partially immersed plate. The contact angle is obtained directly form the height trough:

\[ \sin ( \theta) = 1 - \rho g h^2 / 2 \gamma \label{3} \]

where:

• h – height of the meniscus created
• γ - surface tension of the tested liquid (N/m)
• ρ - density of the tested liquid (kg/m³)
• θ - contact angle of the liquid on the solid (º)
• g – gravitational acceleration = 9.8 m/s²

Capillary Rise

The common direct measurement of contact angles of a liquid drop on a flat and smooth solid is not applicable to powders and dry porous foods. The common method of measuring the contact angle in capillary rise in porous media is by using the Lucas-Washburn’s equation which is derived from Poiseulle's law of liquid flow in capillary rise:

\[ h^2 = r c(\gamma \cos \theta / 2 \eta) t \label{4}\]

\[ w^2 = c (\rho^2 \gamma \cos \theta / \eta) t \label{5}\]

Where:

• h – height of the rising liquid
• w – weight gain of the sample (caused by the water absorbed into it)
• γ - surface tension of the tested liquid (N/m)
• ρ - density of the tested liquid (kg/m³)
• θ - contact angle of the liquid on the solid (º)
• r - mean static radius of the pores (m)
• η - liquid viscosity (Pa s)
• c - geometric factor (m⁵)

The common method to measure the contact angles in this case is to conduct capillary rise experiments where your sample is hang bellow a balance and you dip it in the tested liquid. The main deficiency of this approach (using Washburn’s equation) is its inability to separate between those two variables (r and cos θ or c and cos θ). The common method to overcome the problem of the unknown term r•cos(θ) is by using a reference liquid that completely wets the sample (θ=0, cos(θ)=1). It was discovered however that dynamic advancing contact angle is generally larger than the static one, even for a total wetting liquid and as a result this method can be erroneous.

Seibold et al, (2000) suggested a way to overcome this problem. It was observed that this constant term varies as a function of the liquid used, in contradiction with the Washburn approach which uses Hexane as a completely wetting liquid in order to find the radius of the pores. In this study, it was proposed to get the actual constant term r in Washburn equation by plotting the measured value r cos θ versus the rate of rise of the alkanes (the slope in Equations \ref{4} and \ref{5}). The intercept at zero velocity gives the value of r. Siebold el al. (2000) carried out capillary rise experiments with different n-alkanes, which are all considered completely wetting, due to their low surface tension. In each case, a linear relationship was obtained between squared height of the rising liquid and time, their results of the term r•cos(θ) were calculated from the slopes of those curves. This finding was transformed into a method to calculate or measure the contact angle at zero velocity. Siebold et al. (2000) suggested that for porous media the term r•cos(θ) for each alkane (the term was calculated from Washburn equation) can be ploted against the initial front rate of each liquid. The curve that was created can be extrapolated to velocity zero (and therefore, cos(θ)=1) and this enables the determination of the representative radius r. After finding r, which is a property of the solid sample and doesn’t change as a function of the liquids used, we can conduct capillary rise experiment with our test liquid and calculate the contact angles this liquid creates with the solid porous sample.