Testing, Testing.

Recently I wrote about some watercolours I've made. Since then I've found some scientific literature on the subject, after discovering that the 'coffee ring effect' is the scientific name of a ring shaped deposit found after a drop of liquid has dried. It's a relatively new field of study, with major research only being done since the late 1990's. This literature does confirm my basic assumption of the movement of the paint particles, which is explained by capillary flow. The literature also shows that there are many competing phenomena and variables at play, which are difficult to measure and analyse. Many of the papers I found focus on variables like temperature, relative humidity and electromagnetic influences, most of which effect the rate of evaporation.

I've done some experiments to test the influence of some of these parameters on the appearance of my own drops of watercolour, with some notable results.

First I tried to measure the influence of temperature. The results of this were mostly inconclusive. To test the influence of temperature, I uniformly applied the droplets at three different temperatures, to see if their appearance would differ after drying. The expected result from some of the literature would be that a higher temperature creates a more even distribution throughout the drying droplet. Various mechanisms have been suggested on how this works, including a greater evaporation at the contact surface with the air, which causes greater flow inside the droplet, as well as a 'surface capture' effect of particles at the contact surface.
In the rudimentary testing I have done I however didn't notice any significant effects of temperature on how uniformly the paint spread through the drying droplet:

Three drops dried at different temperatures

In this image there are three droplets of about 2 mm in diameter, made with Winsor and Newton's Payne's grey watercolour paint. The first was made on a substrate that's cooled below 0ºC, the middle was made at room temperature and the last one was heated after application in an oven to about 70ºC. It's clear that there is little significant variation between these three droplets, thereby giving indication that temperature, at least on this scale and with these materials, is not a significant contributing factor for the distribution of the pigments in the drying droplet.
However, the influence of temperature might be dependent on the exact chemical composition of the pigments, in combination with corresponding changes in the binders used. The following image consists of the results of the same experiment, showing Daniel Smith's Hematite Genuine watercolour paint, in duplicate, at <0ºC, room temperature and ~70ºC, respectively.

Two sets of three drops dried at different temperatures

What one can observe here is greater ring formation with a cooled substrate and more concentration at the center at elevated temperatures. So much so that the ring where the pigment is deposited is not even found at the outer edge of the droplet, which is something I have not observed in other situations. This behaviour is also the exact opposite of what the literature would have us expect.

When examining the literature, it must also be noted that most of the literature on the coffee ring effect seeks to eliminate it, because in an analytical or manufacturing context its existence is commonly detrimental to achieving uniform depositions or measurements. Relatively little literature thus exists on controlling the formation of the ring itself, and as far as I can tell, all research is done on colloids that are mixed prior to droplet formation. Little to no research has been done on the effects of introducing a colloid to an existing droplet. Yet I've found indications that for our purposes this provides a lot of control on the exact formation of the coffee ring, as can be seen in the following image:

Four different ways of introducing the paint

From left to right, this is a simple droplet of a diluted suspension of Winsor and Newton Payne's grey watercolour, a water droplet to which a diluted suspension was added at the centre point of the droplet after droplet formation, a water droplet to which a diluted suspension was added at the right edge of the droplet after droplet formation and a water droplet to which a near-saturated suspension was added at the right edge of the droplet after droplet formation.
As you can see, the two leftmost droplets dried nearly identical, even if their method of application was very different. For the third droplet from the left, paint was added later at an angle on the right edge with the paper, and this saw most of the pigment end up around the full perimeter of the droplet. This process was repeated with a higher concentration of pigment in the last droplet and while this contained far more pigment than the other three droplets, still most of it stayed at the perimeter of the droplet, with even more seemingly remaining at the initial point of introduction.

My explanation for this is that a similar outward pushing effect is at work here, inhibiting the possibility for pigments to enter the centre of the droplet through gravity or other forces.
It must however be also noted that in some degree this is dependent on the exact shape of the droplet and again the composition of the paint.

Three different ways of introducing the paint

In this image we have a droplet with a homogenous solution of Daniel Smith's Venetian Red water colour paint, followed by a saturated solution of the same paint added at the right edge of a droplet of water and ultimately a heavily diluted solution added at the right edge of a droplet of water. They each have their distinctive appearances, which differ subtly from the previous experiment with Payne's grey, most notably with the later introduction of a saturated solution. This produced a light centre with a thick edge in the previous experiment, while it created a mostly even spread with a thin edge in the latter example.

Even though it's difficult to observe this behaviour in real time and at actual scale, I believe the observations from the previous two figures is related to the behaviour of the pigment at the droplet's contact surface with air. I did a test where I placed a small saturated spot of Payne's grey watercolour on a piece of paper, let it dry, and then added a water droplet, without physically disturbing the spot of paint. What I found after this droplet had dried is that the paint had spread uniformly throughout the droplet, with a clear coffee ring effect present. There thus is a tendency for the paint to be distributed inside the droplet if it gets far enough inside. 

Adding water to a dried spot of paint

Generally speaking, predicting the exact behaviour of the interaction of a fluid and a colloid is complex and very difficult, as can be seen in the following example:

Introducing two paints into a single droplet

In this image two different watercolour paints are added to a single droplet. The droplet at the top was a diluted solution of Daniel Smith's Quinacridone Gold water colour paint, to which a saturated solution of Daniel Smith's Quinacridone Red was added on the right side at an angle. The droplet at the bottom was pure water, to which Quinacridone Gold was first added at the top and then Quinacridone Red was added on the right side at an angle. As is clearly visible, the latter process resulted in a nearly homogenous mixture, while the first gave a degree of separation between in the colours in the dried droplet.
However, I then repeated this experiment using Daniel Smith's Quinacridone Gold and Winsor & Newton's Payne's grey.

Introducing two paints into a single droplet

Here the same procedure was followed, with the Payne's Gray being added first, followed by Quincridone Gold on the right side at an angle. The way the paints mixed was the opposite of what I observed in the previous experiment. On this occasion the Quinacridone Gold mixed better with the droplet of diluted water colour, while the two paints stayed separated when added in sequence to a droplet of pure water. At the present time I have no simple explanation for this seeming contradiction in behaviour.

Lastly I want to note another characteristic I hadn't considered up until this point, which is the influence of magnetic effects on the droplets. Naturally electromagnetic effects are strong if there are ferromagnetic pigments present in the paint. Especially in the case of paints that contain a mixture of magnetic and non-magnetic pigments, introducing a magnetic field during the drying process produces interesting effects that can be easily controlled with the presence of any magnetic field. 

In conclusion, about a month has past since the previous post and I have still made some new observations about the behaviour of the watercolour paint inside a droplet. Some of these observations seemingly contradict the explanations found in current scientific literature, while others provide a possibility for new methods that are hitherto unexplored.