In this article series, we will explore one of the most complicated subjects of cosmetic chemistry: rheology. In the first part, we will see the basic concepts of rheology. In the second part, we will see the main rheology modifiers (“thickeners”) used in cosmetics.

- What is Rheology
- The pillars of rheology: Viscosity, shear rate and shear stress
- Newtonian and non-newtonian fluids
- Impact of viscosity on the final cosmetic product
- References

**What is Rheology**

**Rheology **is the study of the flow properties of fluids. It is a very complex subject and it’s much more physics than chemistry. We will try to keep it simple here and understand the basics that we need when formulating our cosmetic products. For more detailed information about the topic, I suggest to watch Sam Morell’s video series (1) and check References (2) and (3). The discussion that follows is mostly based on these three sources.

Why are we interested in such a complicated physics subject? Because when we talk about emulsions, like our creams, or hydro- and lipogels for personal care, the flow properties of such products are among their fundamental characteristics. They have substantial impact on two main aspects of the cosmetic products:

- Their stability: the stability of an emulsion is strongly affected by the rheology of the system, and especially by the viscosity of the external and the internal phases;
- The final behaviour of the product on our skin, its appearance, its body, and its sensory properties. Basically: everything!

**Viscous and viscoelastic fluids**

When we think about the physical state of materials, we are used to distinguish them into gases, liquids and solids. If we think about cosmetic products, we would generally say that we can have liquids and solids. However, not all liquids and solids are the same. There’s a big difference in the aspect and behaviour of a liquid toner, a fluid lotion and a body butter. We would not say that they are solid, but neither are they the same kind of liquid.

Most materials are defined as *viscoelastic* materials. Materials that are prevalently *viscous* are liquids and always have the same viscosity. Examples are water and oils. These are called *Newtonian fluids* by rheologists.

Materials like lotions, creams and jellies are *viscoelastic*: they have properties of viscous liquids, but also something more. They do not behave in the same way as pure water.

**The pillars of rheology: Viscosity, shear rate and shear stress**

**Viscosity** is the fluid resistance to flow by shear stresses. We all have a general feeling of what viscosity is: if I ask you to compare the viscosity of a syrup and of pure water, you will tell me that the syrup is more viscous than water. The viscosity is a very complicated parameter, and intuitively we can say that it depends on the internal friction between the particles of the fluid. When water flows, there is low internal friction between its molecules, therefore it flows very easily. This does not happen with syrup or honey or glycerin.

But viscosity can be defined more precisely if we take into account the two other “pillars” of rheology: shear rate and shear stress.

**Fluid deformation: shear**

There are different ways through which a fluid can be deformed: it can be compressed, bended, pulled, etc. The deformation force we are most interested into in rheology is *shear*. We have *shear* when we apply a force on the fluid that is parallel to its surface and we make the fluid particles “slide” on top of each other.

To explain this concept and how fluids react to it, we can consider what happens if we have water flowing through a pipe. The water “layers” do not flow with the same velocity in the whole pipe.

- The layers close to the pipe wall are slower, because of the frictional forces with the wall
- The layers will flow with higher velocity as they are more distant from the walls
- The “fastest” layers will be the central ones

So we have different flow velocities in different points of the bulk water. For example, we have a difference in velocity between the flow in the center of the pipe and the flow at the wall. This difference of velocity, ∆v, divided by the distance between the two points we are considering, ∆d (the center and the wall), is the **shear rate γ̇**. The shear rate is therefore a velocity gradient, and it is measured in 1/s.

The **shear stress** τ is the force applied over a unit area.

Shear stress is directionally proportional to shear rate: if I apply a higher force on the pipe, water will flow with a higher velocity.

**The role of viscosity**

However, if we compare two different fluids in identical pipes, for example glycerin versus water, applying the same shear stress does not result in the same shear rate. Glycerin will flow with a lower shear rate. There is a factor between shear stress and shear rate: that’s **viscosity η**. Glycerin has higher viscosity than water, therefore with same shear stress it will flow with lower shear rate.

So in the end, **viscosity **is given by the shear stress divided by the shear rate. A higher viscosity requires a higher shear stress to reach a certain shear rate.

Let’s see briefly the **unit of measurement of viscosity**: viscosity is the ratio between a *stress* (force per unit of area, N/m^{2}) and a *velocity/distance* ratio (velocity = distance per second, m/s; distance = m). The resulting viscosity is measured in N ⋅ s/m^{2}, commonly Pa ⋅ s or Poise.

**Viscosity vs. density**

Viscosity is often confused with density, but as you can see, they are two different parameters. Viscosity, measured in Pa ⋅ s, is the resistance to shear stress or to flow when a force is applied. Density is the mass of substance per volume, measured in g/ml (we already encountered it when we spoke about units of measurement).

I found these two parameters often mixed, especially when speaking about the *cascade of emollients* in creams. It is often said that one must choose the emollients with different *densities* to design the spreadability and sensory properties of the final cream. Actually, the property that has influence on how an emollient will spread on the skin is not the density, but viscosity, because the spreadability has to do with the flow properties of the fluid and not to its mass per volume.

It is true that *in most cases*, low viscosity fluids also have a low density and vice versa.

For example, dicaprylyl ether has a density of 0,807 g/ml and a viscosity of 3,7 mPa ⋅ s at 20°C (4, 5), whereas olive oil has a density of 0,908 g/ml and viscosity between 70 and 80 mPa ⋅ s (20°C), and castor oil has a density of 0,961 g/ml and reported viscosity range between 1000 and 1500 mPa ⋅ s (20°C) (6). So yes, liquids with higher density often have higher viscosity.

But if you take caprylic/capric triglycerides, for example, their density is in the range of 0,930 and 0,960 g/ml (higher than olive oil), while the viscosity at 20°C is only around 30 mPa ⋅ s (7), so even less than that of olive oil (while the density is greater than the one of olive oil).

**Newtonian and non-newtonian fluids**

I have to mention that this direct proportionality between shear rate and shear stress is working only in case of the so-called *Newtonian fluids*, that have a **constant viscosity**. Examples of Newtonian fluids are water, oil, glycerin, and alcohol. If you shake a bottle containing water, the water will not change its viscosity and its velocity of deformation will depend on how strong you shake it.

In case of non-Newtonian fluids, like colloids, things are much more complicated and their behaviour in response to shear stress cannot be predicted in the same way. You know those videos with the corn starch ball dancing on a speaker? That’s the level of weirdness you can get with non-Newtonian fluids.

**Flow profiles of newtonian and non-newtonian fluids**

When we observe the behaviour of a Newtonian fluid, for example water, its viscosity will not change with the shear rate (or with shear stress).

We can shake that bottle as much as we want, but water will not become more or less viscous.

With non-Newtonian fluids, we can observe different behaviours.

**Pseudo-plastic fluids** like emulsions are **shear-thinning** materials. This means that their viscosity **decreases** with the shear stress. If you mix vigorously a lotion, it will become less viscous compared to when it is resting. When you stop mixing, the cream will go back to its high “resting” viscosity.

**Dilatent fluids** like the corn starch dancing ball increase their viscosity when subject to shear stress. That’s why the corn starch ball starts to dance when the music is on: it is subject to shear stress because of the sound waves and its viscosity increases, giving it a firm paste-like structure.

**Thixotropic fluids** like wall paints and ketchup have similar behaviour as pseudo-plastic fluids, meaning that their viscosity decreases upon shear stress. But when you stop *stressing*, it takes a while before it goes back to the prior resting viscosity. This gives time to the wall paints to continue flowing and becoming uniform (without brush marks), before they dry.

So where do we place our cosmetics in all this? Emulsions and gels typically show pseudo-plastic behaviour unless they are very diluted. In very diluted conditions, they behave more like a Newtonian fluid.

**Impact of viscosity on the final cosmetic product**

As mentioned at the beginning, controlling the rheology – namely, the viscosity – of the cosmetic product is very important both in terms of stability and of final performance of the product.

This is true for both monophase products (hydrogels and oleogels) and multiphase products (emulsions, that is, lotions and creams). In a hydrogel or oleogel, the viscosity of the gel will obviously play an important role in the final flow characteristics of the gel.

In emulsions, what we can control in our formulation is mainly the **viscosity of the continuous phase (water in o/w emulsions, oil in w/o emulsions). **Luckily for us, the viscosity of the continuous phase has substantial impact in determining the overall viscosity of the final product.

**Impact on stability**: increasing the viscosity of the outer phase will make the emulsified droplets remain suspended in the continuous medium, avoiding sedimentation and creaming. In this sense, increasing the viscosity of the continuous phase increases the stability of the emulsion.**Impact on the final texture and characteristics:**the use of rheology modifiers in the outer phase will give the emulsion more body, improve its appearance, modulate its spreadability and how the emulsion flows onto the skin, and improve moisture retention.

## References

(1) Rheology video series by Sam Morell on Youtube

(2) Barnes (2004), The rheology of emulsions. In Emulsions: structure stability and interactions (ed. Petsev)

(3) Lochhead (2017), The use of polymers in cosmetic products. In Cosmetic science and technology: Theoretical principles and Applications (eds Sakamoto, Lochhead, Maibach, Yamashita)

(4) Dicaprylyl ether: ECHA, European chemical agency, Dioctyl ether Registration Dossier ;

(5) Sasol Chemicals, Safety data sheet for NACOL Ether 8

(6) Castor oil e olive oil: de Vries (2017), The effect of oil type on network formation by protein aggregates into oleogels, RSC Advances, 7, 11803

(7) Caprylic/Capric Triglycerides: Wilmar International Ltd, Technical sheet for Caprylic/capric Triglycerides