Sticking Together. Steven Abbott

frying pan, the same drop will spread out far less. Oil has a low surface tension and will spread out more on any of your kitchen surfaces than a drop of water, though the difference will depend on the surface itself. The water with the detergent also has a low surface tension so it too will spread out easily on many surfaces – one of the reasons we add detergents.

      If you were to look carefully at each drop you would find that it makes a specific angle, called the contact angle, which is diagnostic of the relative surface tensions and surface energies (Figure 2.8).

      Figure 2.8 A drop of liquid forms a shape that depends on a combination of the surface tension and surface energy. The result is that the liquid meets the surface at a contact angle, θ.

      If you have a Teflon frying pan, then this is “hydrophobic” (water hating) so a water drop does not spread. Even oil is unimpressed by Teflon's surface energy and oil drops hardly spread. With some tricks it is possible to make a “superhydrophobic” surface where a water drop is so unimpressed by the surface that it will roll along at the slightest tilt. These superhydrophobic surfaces have attracted a lot of excitement as self-cleaning surfaces but, although they are marvellous as lab demos, they are generally unsuited to the real world.

      It is a common myth that surface energy is important for adhesion. As we will learn in Chapter 3, it is irrelevant for any sort of strong adhesive bond and is used only for those cases where easy breaking of the bond is a requirement – such as when a gecko needs to walk, or you need some temporary adhesion for wrapping a sandwich in a thin plastic film.

2.6 VISCOSITY

      We are familiar with the fact that some adhesives are thin and runny while others are thick and resistant to flow. A thick adhesive can be said to be “viscous” and the measure of the ease of flow is “viscosity”. If we define water as having a viscosity of 1 (the units are cP, which means centipoise) then some typical numbers for familiar materials are found in Table 2.1.

      Table 2.1 Typical viscosity measurements of familiar materials.

Liquid	Viscosity, cP
Water	1
Olive oil	100
Glycerine	1000
Honey	5000
Ketchup	50 000
Lard	100 000
Peanut butter	250 000

      Adhesives manufacturers have to worry incessantly about viscosity. Users can be equally as frustrated by an adhesive that is too viscous to flow nicely into a joint, as by one with such a low viscosity that it runs everywhere. Fortunately, there are some tricks they can play. For many viscous adhesives, if you apply a shearing or sliding force, their viscosity decreases rapidly (this is called “shear thinning”), allowing them to flow in the gap between the substrates. Others are “thixotropic” which means that they become thin when stirred or sheared (so they are also shear thinning), making them easy to apply, then, after some time, become thick again, stopping them from “slumping” out of a joint.

      The study of how things flow is called rheology and interested readers can find a friendly (but technical) eBook and set of apps on my Practical Rheology web pages, https://www.stevenabbott.co.uk/practical-rheology/.

      Even if the manufacturer has created the perfect viscosity, there is still the problem that squeezing a joint together is not as simple as it sounds.

2.7 SQUEEZING GLUE

      It may seem odd to be discussing the simple act of squeezing some glue between two surfaces. What can possibly be of interest in such a basic process? It turns out that many of our frustrations and problems arise because squeezing is far more difficult to control than we might imagine. There are times when we need a thick layer of adhesive. Other times we need as thin a layer as possible. It would be nice to put one drop or blob in the middle and squeeze it evenly to the edge – a large drop for a thick layer and a small drop for a thin one. Unfortunately in the thick case it is far too easy to over-squeeze and get an excess of glue that is messy to wipe off because, well, it's rather sticky. In the thin case it can prove too difficult to get the adhesive to reach the edge at all.

      The frustration arises thanks to Stefan's law of squeezing (Figure 2.9). There are various ways of thinking about it, and interested readers can find out more in this app, https://www.stevenabbott.co.uk/practical-adhesion/drop-squeeze.php. Stefan's law tells us a number of things about how quickly the drop spreads and the thickness decreases:

       The higher the viscosity, the slower the process. This is intuitively obvious. A “gel” superglue with 20× the viscosity will spread 20× slower than a “pure” superglue without additives. This, with perhaps some shear thinning behaviour, is under the control of the adhesive manufacturer and with things like superglue we can choose which viscosity to use.

       As the drop expands it gets super-hard to expand further. If it takes 1 s to go from, say, 1 mm diameter to 2 mm, it will take 16 s to go from 2 mm to 4 mm. For those who like equations, the rate of increase of the radius, R, is proportional to 1/R4.

       As the thickness of the drop decreases it gets super-hard to decrease it further. If it takes 1 s to go from 0.4 mm to 0.2 mm, it will take 8 s to go from 0.2 mm to 0.1 mm. In equation terms, the rate of decrease of height, H, is proportional to H3.

      Figure 2.9 Stefan's squeeze law tells us that squeezing a cylinder of glue of radius R and height H, gets considerably harder as R increases and H decreases and it becomes near-impossible to obtain a very thin layer of glue.

      https://youtu.be/M0z1Xq52-HQ The video shows this nicely – six individual drops squeeze out to almost 3× the area of one blob containing six drops.

      Because drops with a large thickness are easy to squeeze, if we start a little too thick then we can easily over-squeeze. Because thin drops are hard to squeeze, if we start with a thin drop in the middle then it becomes very difficult to get the drop to come right to the edge of the joint.

      If you are in the unfortunate position of having a thick layer of adhesive at one side of a joint and a thin layer at the other then, well, give up. It is super-difficult to get such a layer to re-adjust itself.

      If we combine the previous paragraphs with Stefan's law, especially the bit about the difficulty of expanding R, the least bad way to achieve a good overall thin coverage is to place lots of little drops across the surface (Figure 2.10). They can easily expand (because R is small) and become self-adjusting in terms of thickness (if H of one is small, a thicker H can more readily reduce its thickness). All the demos I've seen of superglue holding up some heavy truck from a crane start with a bunch of dots of glue (on a super-polished metal surface). Whether they know of Stefan or not, clearly the technique has been found to be reliable. The “dot and dab” technique for plasterboard/drywall,