What is a contact angle?

The contact angle gives us an indication of how well (or poorly) a liquid spreads over a surface. When formulating inks, the contact angle provides a useful indicator of how modifications to the ink will affect its spreading.

The contact angle can be large or small, depending on the physical properties of the material under study. The image below shows three different droplets on a surface. The droplet on the left has a larger contact angle because it does not spread on the solid surface. The droplet on the right has a low contact angle because it spreads out so well. This spreading is called "wetting," and the droplets "wet" or "wet" as they deposit on the surface.

The figure below shows a 2D cross-section of a droplet on a solid surface. Find the point where the droplet profile intersects the solid surface. The angle between the droplet profile and the solid surface is the contact angle.

If we wanted a solution that was easier to spread on the substrate, we could change the solvents used in the formulation and test if they increased its wetting ability. In this case, a low contact angle would be a good result.

Or, we might be developing a waterproof coating for a piece of clothing. In this case, a high contact angle is required. We will vary the coating formulation and use water droplets to determine which coating is more resistant to wetting.

Surface Tension

The surface tension of a droplet is determined by the interactions between its constituent molecules. The molecules in a drop of liquid are shown in the figure below. In the bulk of the droplet, intermolecular forces act on the molecules equally from all sides. However, on the surface of the droplet, there are no liquid molecules on the outside.

Molecules on the surface are held together more tightly than those in the bulk because they are not pulled from all sides. This means that it is more difficult for an object to penetrate a surface than it is for an object to move through the body after being submerged.

balance of power

When a droplet comes into contact with a solid surface, three boundaries need to be considered: the solid, the liquid, and the vapor (usually air) surrounding them.

Each force pulls away from the equilibrium point, so if the droplet is in equilibrium, the forces are balanced, which can be described by the following equation:

where cos θ gives the x component of the liquid-gas surface tension. This can be rearranged to give:

This equation provides some useful information:

If γ sv > γ ls, then cos θ is positive and θ < 90o (and the droplet is wet). This can happen in high surface energy solids (such as metals) or low surface tension liquids.

If γ sv < γ ls, the cos θ will be negative, so θ > 90o (and the droplet dewetting). This can occur in low surface energy solids or high surface tension liquids such as water.

This may raise the question of how we equate surface energy density (in J/m2) with surface tension (in N/m).

Therefore, the surface energy density and surface tension can be equal.