# Contact angle associated with thin liquid films in emulsions

## Introduction

The surface tension of liquid film can be very different from the surface tension of the liquid in bulk, because of contributions from the disjoining pressure. The authors described a method to measure the surface tension of a liquid film easily by measuring the contact angle formed between the film and the plateau border. The authors showed how the contact angle is related to the disjoining pressure and demonstrated how temperature and different salt concentrations changes the surface tension of liquid film.

## Results

The tension of the film, γ_{f} is related to the bulk interfacial tension γ by

where h is the film thickness, h_{e} is the equilibrium thickness and π is the disjoining pressure. Whenever ΔF < 0, the two bulk surfaces will, on macroscopic scale, intersect an angle 2θ (see figure 1), such that

and therefore

ΔF essentially determines whether the oil droplets will repel or spontaneously flocculate as in figure 2. For ΔF < 0, we can precisely determine the value of ΔF just by measuring the macroscopic contact angle by equation (3).

The authors proceeded to study concentrated oil in water emulsions and found that ΔF is affected by both temperature and different salt concentration. For example, with alkyl sulphates in the presence of LiCl, NaCl or KCl, the contact angle angle reached at a given concentration increases in the order of Li^{+} << Na^{+} < K^{+}. The order reversed when alkyl sulphates were replaced with alkyl carbonates.

Figure 3 shows the huge effect temperature has on the contact angles of dodecane droplets in water. At high temperature > 65 ^{0}, contact angle 0 ^{0} and the oil droplets behave as discrete spheres. At a temperature of 25 ^{0} on the other hand,

## Personal Thoughts

## References

1. Contact angles associated with thin liquid films in emulsions, Aronson and Princen, Nature 1980