Focus: Filter Physics

Published March 22, 2007  |  Phys. Rev. Focus 19, 9 (2007)  |  DOI: 10.1103/PhysRevFocus.19.9

General Probabilistic Approach to the Filtration Process

N. Roussel, Thi Lien Huong Nguyen, and P. Coussot

Published March 15, 2007
+Enlarge image Figure 1
Phys. Rev. Lett. 98, 114502 (2007)

Blocked beads. A 5 millimeter metal mesh retains some 3-millimeter-wide beads. A new theory predicts the conditions that will lead to filtering of particles from a solution even when the particles are smaller than the holes.

A colander is supposed to trap any objects larger than its holes, but for some sieves, even objects smaller than the holes get caught. The phenomenon is common, from swimming pool filters to the soil and rocks that filter underground oil. In the 16 March Physical Review Letters, a team describes a theory that predicts the conditions for the “clogged filter” effect and verifies it with experiments. They believe that extensions of the theory could apply to a wide variety of natural and artificial filters.

The filter physics project began when Nicolas Roussel and Thi Lien Huong Nguyen of the French national civil engineering laboratory (LCPC) in Paris were studying concrete, which is often injected into networks of steel bars for reinforcement. The sand and gravel can get caught in the network, disrupting the flow, even though the spaces are larger than the particles. The researchers were struck by the fact that clogging happens in a similar way in a wide variety of other situations, both natural and man-made. Examples include swimming pool filters that fill with debris; lake beds, where gravel accumulates much finer sediments; and standard biochemistry techniques that filter one kind of molecule from a mixture of many.

The physicists teamed up with Philippe Coussot of the Navier Institute in Paris to develop a theory of filtering. Most of the past work on filtration and clogging applied only to the set-up worked on by a specific research team–such as a cylinder with a single hole that could clog–whereas the French team wanted a more general theory for filtering in a variety of situations. They focused on the dome-like clusters of several particles that cover individual holes in a sieve when it clogs. The team calculated the probability for those particles to arrive simultaneously and jam together based on the number of particles in the flow and their size relative to the holes. Although the concept for these clusters isn’t new, no one has worked out a general theory before.

The team tested their model with two kinds of experiments. First, they let gravity draw an imitation concrete mixture through a metal sieve. The concrete stand-in was a gel containing different amounts of glass beads–up to 40 percent of the mixture in some tests–with diameters ranging from 0.5 to 7 millimeters. Then they performed similar experiments with dry beads, vibrating the sieve to start the particles falling through. In both cases, the number of beads left behind in the sieve was directly related to the bead size and total number as predicted by the model. As bead size increased from one test to the next, there was a fairly sudden change from no trapping to trapping of all beads. This minimum, or “critical,” bead size could be as small as one-third the size of the mesh holes, and it agreed with the theory. “We inferred that we likely captured the basic physics of the problem,” Coussot says.

J. Carlos Santamarina of the Georgia Institute of Technology in Atlanta calls the work “elegant.” He says it “provides insightful guidelines for filter design” and adds that many fascinating questions remain in this line of research, such as the role of interparticle forces.

Coussot and his colleagues hope that others will refine the model and adapt it for various applications. They are exploring such an application with partners in the oil industry, who want to model the flow of petroleum through soils. In the meantime, they are using magnetic resonance imaging to see inside porous materials, such as soil and concrete, as they filter out particles from a fluid. The MRI allows the team to watch the clusters as they form.

–Pam Frost Gorder

Pam Frost Gorder is a freelance science writer in Columbus, OH.