Contact Angle Hysteresis (CAH) & Waterspot

Everyone knows about contact angle and the tilt angle. But one almost unknown but very important phenomenon is the contact angle hysteresis. It is in fact a very common occurrence in nature and are very crucial in various industrial processes.

Contact angle hysteresis (CAH) is one of the most important and classic elements of wetting of liquid droplets in systems from centimeter to micrometer scales. One of the easiest method to understand CAH is by looking at a droplet resting on a horizontal substrate.

A drop on a vertical surface, stuck at the critical advancing angle θa and the critical receding angle θr




Just like a rain drop on a window, gravity will pull the droplet to move it down, while CAH in return will keep the droplet in place. This results in the droplet not moving and become asymmetric. This can be seen in the figure above where the top of the droplet becomes thin, with a low contact angle, while the bottom becomes thick, with a high contact angle.

Once the droplet reaches a certain size, it will slide down in an asymmetric shape, and the difference between its front, θa and back, θr contact angles is called the contact angle hysteresis.

Other occurrences are seen in coating processes, digital microfluidics and evaporation of droplets (coffee stain issue). CAH also plays a role in industrial applications which includes immersion lithography, fiber coatings, and ink-jet printing. It is clear that in some cases, hysteresis is a problem (immersion lithography) while in others it is essential (dipcoating).



Contact angle hysteresis appears in various aspects that directly influence our daily life.

Sliding droplet

Droplets stick to surfaces in many applications, due to contact angle hysteresis. A classic example is a droplet on an airplane or car window obscuring vision, or the sticking of pesticides to leaves. Simply having droplets roll off a car window, rather than needing a wiper system, could then be possible. This is possible through hydrophobic coatings for glass such as IGL Ecocoat Window.


Coffee stain phenomenon

Coffee stain phenomenon is a  specific example of the influence of the contact angle hysteresis on pattern formation in process. A droplet that contains nonvolatile component will leave behind heterogeneous solid residue while evaporating. How does this relate to the auto detailing industry? Water staining. Water that has high amount of calcium will leave deposits of calcium on the surface similar to how coffee will leave stain. But here, I will explain in more detail exactly HOW the stain occurs using CAH.


Everyone had seen this effect but only a few keen eye are able to realise the common feature of these solid residue named after the most common example : coffee stains. Various nonvolatile materials such as solid particles with sizes ranging from hundreds of microns to a few nanometers, polymers, even various biomolecules such as DNA or proteins form similar patterns upon evaporation on a flat substrate.  The formation of a coffee stain occurs through two factors :

(i) the contact angle hysteresis and

(ii) the evaporation driven capillary flow pulling the contents of the droplet towards contact line.

A wedge-like shape is formed when the contact line pins. This create the scenario where the droplet is thinnest the evaporation rate becomes dramatically higher. This locally high evaporation rate sucks particles to the contact line with a capillary flow. And this capillary flow towards to contact line is the cause of coffee stains. As a drop evaporates with the contact line pinned, the particles accumulate and jam near the contact line, further strengthening the pinning.

As mentioned above, contact angle hysteresis can be visualised easily by thinking of a rain drop sliding on a tilted window. A droplet will slide down gradually on a very smooth window surface. If the surface is rougher i.e. full of scratches and cracks, the droplet will stick. In other words the contact line will pin and not move. As expected the rougher the surface, the easier the droplet will pin.

When a droplet on a horizontal surface evaporates the contact line tends to move inwards over the aforementioned cracks and dents. If finally the contact line pins due to this roughness, the shape of the drop at the rim becomes wedge-like. It is also important to realise that contact line pinning is not only due to roughness but also the particles confined at the three-phase contact line contributes to the pinning.

Due to the wedge shape of the evaporating droplet, the local evaporation rate (J) increases towards the edge. This is because at the rim an evaporating molecule has a larger free space available than in the central region of the drop where it has to compete with more evaporating molecules for that free space. In other words,

From our daily experience we know that evaporation can be enhanced by increasing the available area. The evaporation of water over a flat surface will always be faster than the evaporation in a glass of water. As the evaporation is higher at the edge of the drop than in the bulk, both liquid and particles are sucked towards the contact line. Due to this outward flow the nonvolatile particles accumulate near the rim and that is why we observe the coffee stain or water staining.


In this article, we hope to provide a brief introduction to the understanding of contact angle hysteresis in the simplest method. The occursnce of contact angle hysteresis are everywhere in our daily lives.

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