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Study Guide - Practical 4
Interfaces, Bubbles, and Foams
Introduction - Interfaces
Cohesion and Adhesion
Cohesion and adhesion are important phenomena that occur at the interface between two distinct materials and play a key role in the formulation of a diversity of products.
In a liquid, cohesion is a measure of the attraction between similar molecules, whereas adhesion is a measure of the attraction between two dissimilar molecules.
Let’s consider a cylinder of liquid A, whose surface tension is γA, with a cross-sectional area S = 1 cm^2. The work needed to divide such a cylinder into two halves so that two new surfaces are created is the work of cohesion, which can be expressed as:
Wc = 2γA
On the other hand, the work of adhesion, which is necessary to overcome the attraction between two dissimilar molecules A and B in a liquid, is equal to the newly generated surface tensions γA + γB minus the the interfacial tension γAB lost in the separation. Thus, the adhesion work can be calculated as: Wa = γA + γB − γAB
In the case of a solid/liquid interface, the adhesion work is:
WSL = γS + γL − γSL
This equation is often referred to as the "Duprè Equation".
Spreading
If a drop of a water-insoluble substance, such as oleic acid, is layered onto the surface of water, it may behave in one of three ways:
- It may remain in the form of a lens;
- It may spread into a thin film until the entire surface is covered with a "duplex film";
- It may spread into a monolayer in equilibrium with lenses of excess oil.
If the affinity of the oil molecules for one another is greater than the affinity of the oil for water, then no spreading occurs. Otherwise, the oil spreads out over the surface of the water. In other words, spreading occurs when the adhesion work is greater than the cohesion work Wa − Wc > 0. This difference is known as the spreading coefficient S, defined as:
S = Wa − Wc = (γA + γB − γAB ) − 2 γA = γB − γA − γAB
Spreading occurs when S > 0 ; that is, a substance spreads out if the sum of the free surface energy of the new surface and of the new interface is smaller than the free energy of the old surface. If a liquid L spreads ofer a solid S, the equation becomes:
S = γS − γL − γSL
Some values of spreading coefficients on water are reported in the Table below:
Substance Spreading Coefficient S [mN/m]
Ethanol 50.
Propionic Acid 45. Diethyl Ether 45.
Acetic Acid 45.
Acetone 42. Oleic Acid 24.
Undecylenic Acid 32
Chloroform 13 Benzene 8.
Hexane 3.
Octane 0. Dibromoethene -3.
Liquid Paraffin -13.
Table 1: Initial spreading coefficients on water at 20°C
Contact Angle – Solid/Liquid Interface
When a drop of liquid is placed on a solid surface, it can either spread completely over the surface or remain a droplet on the surface with a distinct contact angle θ.
Figure 1: Contact angle between a droplet of liquid and a solid surface
Introduction - Bubbles and Foams
Foams
Foams are coarse dispersions in which a gas phase is dispersed within a continuous liquid phase. Structurally, they consist of gas bubbles separated by thin liquid films known as lamellae. In typical aqueous foams, gas occupies the majority of the volume, up to 95%, while the liquid phase accounts for only about 5%. This liquid fraction is primarily water, with a small percentage of surfactants and other stabilizing additives that contribute to foam formation and stability. Foams are inherently thermodynamically unstable, as the system tends to evolve toward a state of lower free energy. The thin liquid films between bubbles possess significant surface area, which translates into a high interfacial energy. As the foam ages, gravitational drainage, bubble coalescence, and gas diffusion (Ostwald ripening) reduce the surface area by collapsing lamellae and forming larger bubbles or liquid drops. The collapse of a lamella leads to a configuration with a smaller total interfacial area, thus lowering the system’s free energy. Consequently, foams are only kinetically stable; their persistence is determined by the time required for destabilizing processes to occur.
Foaming Agents
Surfactants that promote and stabilize foam formation are called foaming agents. Their effec- tiveness depends largely on their molecular structure and surface activity. In general, surfac- tants with low critical micelle concentrations tend to be more efficient at foam formation, as they more readily saturate the interface and reduce surface tension. A strong foaming agent must form a robust, elastic interfacial film that can resist mechanical stress and thermal fluc- tuations. Molecular features that enhance foam stability include long, linear hydrophobic chains that pack tightly at the gas-liquid interface, forming a cohesive barrier. However, excessively long chains may reduce the surfactant’s mobility and surface activity. For optimal performance, foaming surfactants typically possess medium-length alkyl chains, usually comprising 12 to 14 carbon atoms, which provide a balance between interfacial packing strength and dynamic sur- face activity. The behavior of foaming agents is also influenced by the surrounding medium. In ionic en- vironments, such as saline solutions, non-ionic surfactants generally produce less foam, and the foam tends to be less stable. This is due to their lower surface elasticity and weaker elec- trostatic stabilization compared to ionic surfactants, which benefit from charge repulsion and more rigid interfacial structures. As a result, ionic surfactants are often preferred in applica- tions where persistent and resilient foams are required, such as in cleaning agents or personal care formulations.
Pressure Inside Bubbles
The pressure inside a bubble is always higher than the pressure outside. This pressure difference arises due to surface tension, which tends to minimize the surface area of the interface and, in doing so, exerts a contracting force on the bubble. The pressure difference across the curved interface is directly related to the curvature of the bubble and the interfacial tension of the liquid phase. In general, the smaller the bubble, the higher the internal pressure, as curvature increases with decreasing radius. For a spherical gas bubble in a liquid, the pressure difference between the inside (gas phase) and the outside (liquid phase) can be derived in two ways:
- Mechanical Approach: By considering the balance of forces acting on a hemispherical cap of the bubble due to surface tension and pressure, it is possible to write:
FIN = PIN · A = PIN · 4 πr^2
FOU T = POU T · A + Fsurf = POU T · 4 πr^2 + γL · 8 πr
At equilibrium, FIN = FOU T and, after some rearranging, it is possible to obtain:
∆P = PIN − POU T =
2 γL r
- Surface Energy Approach: By evaluating the change in Gibbs free energy due to a virtual increase in the bubble’s surface area and equating it to the mechanical work done by the pressure difference, the same expression is obtained:
dWIN = PIN dV = PIN · 4 πr^2 dr
dWOU T = POU T dV + γLdA = POU T · 4 πr^2 dr + γL · 8 πrdr
Similarly as before, at equilibrium dW (^) IN = dW (^) OU T and, then it is possible to obtain:
∆P = PIN − POU T =
2 γL r
Both methods lead to the same result, which is known as the Young–Laplace equation, where γL is the surface tension of the liquid film, and r is the internal radius of the droplet. This fundamental relation describes how the pressure inside a curved interface depends on the mean curvature of the surface and the surface tension.
In the case of a gas bubble enclosed by a thin liquid film in air, as in the case of soap bubbles, there are two gas-liquid interfaces (an inner and an outer surface of the film). When the film thickness is considered, the generalized form of the Young-Laplace equation becomes:
∆P = γL
rIN
rOU T
= 2γLH
Where rIN and rOU T are the inner and outer radii of the bubble respectively, and H = 1 2
1 rIN +^
1 rOU T
is the mean curvature of the bubble.
If the film is sufficiently thin, such that the two radii of curvature can be approximated as equal, the Young-Laplace Equation for a bubble in air can be approximated as:
∆P =
4 γL r
The factor of 4 instead of 2 arises because both interfaces contribute equally to the net force resisting internal gas pressure. This approximation is often valid for soap bubbles, so the simplified form above remains accurate.
