Interfacial Rheology: Dynamic Interfacial Tension Changes

Figure 1: In the food industry, the viscoelastic properties of interfaces are crucial factors for the stability, texture, and shelf life of products such as mayonnaise, ice cream, or whipped cream.

Interfacial rheology is a field that describes dynamic changes at interfaces. It is of particular interest when surfactants that change the interfacial tension are added to a liquid. The quantitative analysis of the changes at such complex interfaces is carried out using the measurement parameter of the viscoelastic modulus.

Interfacial rheology describes how the properties at the interface change when the interface becomes smaller or larger. This is also referred to as the "viscoelastic behavior" or "stress relaxation" of an interface.

For simple systems such as water against air, the behavior is relatively easy to describe. Here, the surface tension (i.e., the interfacial tension between the liquid water and the gas air) remains constant, even if the surface area changes.

The situation is different if surface-active agents, also known as surfactants, are present in one of the phases. Surfactants prefer to accumulate at the interface and thus change the interfacial tension. The surface tension is usually reduced by the addition of such substances.

In systems with surfactants, it is not only of interest how strongly the interfacial tension is changed by the addition of surfactants, but also how quickly they react to an area change of the interface. Quantifying the reaction time is the aim of the following measurements.

Effects of interface area changes

There must be enough surface-active particles or molecules in the system for the following considerations to apply. In other words: the critical micelle concentration must be reached. The following section does not apply to systems with concentrations below the critical micelle concentration, as in this case there are too few surface-active particles or molecules to saturate the interface.

Surface-active particles or molecules adsorb preferentially at the interface, i.e., they attach themselves to the interface and form a layer there. In the equilibrium state, these molecules or particles occupy a certain space at the interface and have an average distance from each other. The resulting equilibrium interfacial concentration c₀ with its specific interfacial tension σ₀ is characteristic of the system.

If the size of the available interface changes, e.g., by changing the volume of a droplet or by shifting barriers along the interface, surfactants react to this shift. In detail, the concentration of the surface-active particles or molecules at the interface changes temporarily. Accordingly, there is also a temporary change in the interfacial tension between the phases before the characteristic concentration c₀ and interfacial tension σ₀ are restored.

What happens in detail when the interface is changed? If the interface is reduced in size, the concentration of the active particles at the interface increases; they are squeezed together. In response, the system now restores the concentration equilibrium c₀ by desorption. During desorption, the excess of surface-active molecules or particles at the interface is released into the phase. As long as the molecules are "crowded" at the interface, the interfacial tension decreases. During desorption, the interfacial tension increases until it finally reaches the system-specific equilibrium σ₀ again.

If the interface is enlarged, the interfacial concentration decreases - the individual surfactant particles or molecules now have more space. The state of equilibrium is restored by adsorption, i.e., the attachment of further surface-active molecules or particles to the interface. If the interface is enlarged, the interfacial tension initially increases. As new molecules or particles are adsorbed onto the interface, the interfacial tension decreases until it finally reaches the system-specific equilibrium σ₀ again (see Figure 2).

The reaction of the surface-active components to the altered interface can occur at different speeds. The speed at which the change takes place depends on factors such as the mobility and concentration of the surfactants within the phases and the interfacial tension between the phases.

Figure 2: If the interface is reduced in size, surface-active molecules or particles desorb from the interface. If the interface is enlarged, additional surface-active molecules or particles adsorb at the interface.

Using the viscoelastic modulus describes dynamic changes at the interfaceThe dynamic behavior of the interface can be described by the complex viscoelastic modulus E*. It consists of an elastic component E′ and a viscous component E″:

In measuring practice, the complex viscoelastic modulus can be measured by a uniform, oscillatory enlargement and reduction of the interface. If the interface is changed sinusoidally, the interfacial tension also changes sinusoidally. The two sinusoidal curves are shifted by the phase 𝜑. The phase shift depends on the reaction rate of surfactant (see Figure 3). The elastic modulus E′ and the viscous modulus E″ can be calculated from the sinusoidal change in interfacial area and interfacial tension:

The following symbols have been used:
E*: complex viscoelastic modulus
E′: elastic component of the viscoelastic modulus 
E″: viscous component of the viscoelastic modulus
i: imaginary unit
Δσ: peak-to-peak amplitude of the interfacial tension
ΔA: peak-to-peak amplitude of the interfacial area
A0: mean interfacial area
𝜑: phase shift
Applications for measuring the viscoelastic modulusMeasuring the viscoelastic modulus can advance product development in many industries. Two examples of practical applications are given below.
In the food industry, the viscoelastic interfacial properties of proteins and surfactants at the oil-water or air-water interface are crucial for the stability, texture, and shelf life of products such as mayonnaise, ice cream, or whipped cream.
In the pharmaceutical industry, the release of drugs in emulsions or foams is also influenced by interfacial rheology. Understanding the viscoelastic modulus helps in the development of effective and stable formulations.

Figure 3: Sinusoidal oscillation of a pendant drop with interface A and interfacial tension σ as a function of time. The phase shift 𝜑 provides information about the interfacial elasticity and the interfacial viscosity.
Measurement of the viscoelastic modulusVarious methods are suitable for measuring the viscoelastic modulus, depending on the application.
An optical contour analysis of a hanging, oscillating drop in the ambient air or a second liquid is possible with contact angle meters of the OCA series from DataPhysics Instruments and corresponding accessories (see Figure 3).
An optical contour analysis of a rotating drop in a surrounding liquid is possible with a SVT 25 spinning drop tensiometer from DataPhysics Instruments.
Force-based measurements on a surface can be realized with tensiometers of the DCAT series from DataPhysics Instruments together with a Langmuir trough.
After optimizing the viscoelastic behavior, the influence on the stability of a dispersion can be investigated using an MS 20 MultiScan from DataPhysics Instruments.

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