For my experiment I have to obtain a water surface (1 m$^2$) seeded with floating particles. I found particles of the right size, density (and very acceptable price): expanded glass granulate. However, as other particles, the particles form clusters and stick to the walls of my aquarium.

How do I stop the particles from forming clusters (probably has to do with surface tension/hydrophobicity)? I tried to spray paint the particles using car paint which did Improve their behaviour but still they form clusters.

Does painting/coating the particles provide a solution, and if yes what kind of paint/coating should I use?

Something more about the experiment: The target of the experiment is to perform surface PIV (Particle image velocimetry). So as long as the hydrodynamics aren't affected (too much) adding chemicals/paint is no problem.

  • $\begingroup$ if doable: charge them with electrons, add a paint with an isolating coating, idem to the tank surface. They will end away one from the others. $\endgroup$ Jun 17, 2015 at 12:59
  • 3
    $\begingroup$ "Wetting agents" of various sorts may help. Depending on what the experiment is (details may help) a very thin surface layer of some other substance may help (or be wholly unnacceptable) . $\endgroup$ Jun 17, 2015 at 13:02
  • $\begingroup$ more elastic the collisions are, less clusters you get $\endgroup$
    – user46925
    Jun 17, 2015 at 14:05
  • $\begingroup$ How about using one particle at a time? $\endgroup$ Jun 17, 2015 at 14:42
  • $\begingroup$ I have found that silicon paste used for filling up holes is hydrophobic ( have used it so that the water does not drip down the side when pouring from the water heating pot) $\endgroup$
    – anna v
    Jun 17, 2015 at 15:04

1 Answer 1


This is sometimes called the "Cheerios effect". It basically occurs because each floating object forms a meniscus, and other floating objects want to "move downhill" in this meniscus. The meniscus forms (roughly speaking) because the interfaces between the spheres, the water, and the air form a preferred angle, known as the wetting angle.

If one could tweak things so that this meniscus didn't form, there would be no attraction. You probably don't have much control over the buoyant force or the density of the spheres, but by applying a coating to the spheres you might be able to change the wetting angle to avoid the formation of meniscuses. (Menisci?) Here's a rough calculation of what you should be aiming for.

In classic physics fashion, I'm going to assume that the particles are spheres. The "depth" of the meniscus is determined by a force balance between the buoyancy of the particle (upwards), the surface tension from the water (parallel to the water surface, at the point of contact), and the weight of the particle, subject to the constraint that the angle between the particle surface and the water surface is at the wetting angle $\theta$. (See Figure 7 in the above linked paper.) In particular, if it is the case that the buoyant force on the sphere balances out its weight exactly, and that the resulting geometry implies that the water surface meets the sphere at the wetting angle, then the surface tension forces will be purely horizontal, no meniscus will form, and the objects will not cluster:

enter image description here

To get this to be the case, we have to have the weight of the sphere equal the weight of the displaced fluid (in the shaded region above.) The volume of the sphere is $\frac{4}{3} \pi R^3$, and the volume of the displaced fluid is $$ V = \frac{\pi R^3}{3} (2 - 3 \cos \theta + \cos^3 \theta). $$ So the ratio of the densities must be equal to the ratio of these volumes: $$ \frac{\rho_s}{\rho_w} = \frac{1}{4} (2 - 3 \cos \theta + \cos^3 \theta) $$

This means that for a given ratio of the densities, there is a given wetting angle that will work to avoid the formation of a meniscus. Since the density of the spheres and the density of the water are pretty much fixed, you'll need to coat them in such a way as to change the wetting angle closer to this special value. How to go about this is not my area of expertise (I'm just a theorist), but hopefully this will give you an idea of what you should be aiming for.


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