The Probability of Clogging

Much higher if you're in Holland ...


General Probabilistic Approach to the Filtration Process

N. Roussel, T.L.H. Nguyen, and P. Coussot

PRL 98, 114502 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e114502

The authors start with a somewhat surprising experimental observation. Imagine taking a mesh grid and using it to filter particles of a characteristic size. You would probably expect one of the two following outcomes:
• If the particles are smaller than the holes in the mesh, all the particles pass through.
• If the particles are larger than the holes, none of them pass through.
Interpolating between these two, you might expect some linear crossover as the particles get larger. The surprising results of the authors is that perfect clogging takes place before the particle size exceeds the mesh size, and the crossover is rapid.

To explain this observation, they develop a probabilistic model. In the model, a pore will become clogged if the right number of particles arrive at the right location within a certain period of time. Their model reproduces experimental observations quite well, with perfect clogging for particles smaller than the holes as long as the volume fraction is large enough. It contains only a single free parameter that depends on properties of the fluid flow.

The authors extend their model to a porous medium by considering the medium as a stack of meshes with some characteristic spacing. Their model of a single sieve determines the outflow as a fraction of the inflow, so the extension to many layers leads to a geometric series.

The model and its predictions don't run contrary to my intuition, but I would not say the results are "intuitively obvious to even the most casual of observers." This is a very nice example of model building. The authors captured the essential features of clogging in a simple coincidence model, and collected all the complications of fluid dynamics into a single parameter. It's easy to add terms to the model to make it more realistic, but the authors have isolated the features that lead to the general "all or nothing" behavior observed in experiments.