Adding Weight to the Scanty Bookshelf on the Study of Granular Materials

The study of granular materials was totally absent from the physics literature until little more than a decade ago. In the late 1980s, Per Bak, Chao Taug, and Kurt Wiesenfeld published a now famous paper in Physical Review Letters, volume 59, page 381, 1987, proposing the theory of self-organized criticality, in which they used sand piles as a paradigm for a large class of complex systems: earthquakes, avalanches, forest fires, epidemics--systems that might be expected to show self-similar behavior. In the next year or so, three additional papers appeared in the same journal: one on granular convection, one on sand-pile avalanches, and one--on wave phenomena in a simple granular flow--with a title very similar to that of Gerald H. Ristow's new book Pattern Formation in Granular Materials. I was coauthor of the last of these, and I remember well one referee's very serious comment that studies of granular materials were appropriate for engineering journals, not for Physical Review Letters.

In the intervening years, a deep fascination has developed within the physics community for the rich and complex phenomena that occur in all aspects of granular materials, from static systems to the rapid flow that occurs in real-life avalanches. Accompanying this growing interest has been a dramatic increase in contributions to the literature from authors within the physics community. The phenomena that have drawn this interest include complex spatiotemporal fluctuations that occur in static or nearly static systems (so-called stress chains); complex waves and flows that occur when granular materials are shaken; segregation, or separation, of differing types of materials that seems to defy our concepts of entropy; and instabilities in dilute, gaslike systems, leading to the formation of clusters that make granular "gases" distinct from their classical elastic-hard-sphere gas cousins. The list of unanswered questions is long. We have at best fledgling theories or models of a fundamental first-principle nature. Arguably, we are at the same stage with our models of granular materials as scientists were with Newtonian fluids one to two centuries ago.

Although there has been a flood of papers dealing with recent developments concerning granular materials, few monographs have been published on the topic--an exception being the book by Jacques Duran, (Sables, Poudres et Grains, Eyrolles, Paris, 1997) newly translated by Axel Reisinger and published as Sands, Powders, and Grains. Thus, Ristow's work is a welcome addition.

Ristow has chosen to review recent work in several sub-areas of granular materials, including flows induced by various types of shaking; stratification, mixing, and segregation; flows in hoppers; flows in rotating drums; and an appendix on numerical methods. There are also introductory and concluding chapters. For instance, in an early chapter, the author covers basic concepts such as dilatancy and angle of repose. He also provides a brief discussion of fluctuations and a useful table of some material properties. In two chapters on shaking, he discusses many of the recent experiments and molecular dynamics simulations for both vertical and horizontal shaking. Included are studies that describe compaction, surface patterns, and flows for vertically shaken systems, and that explore the fluid-solid transition (related to Mohr-Coulomb failure) in horizontally shaken systems. In a chapter on stratification, Ristow reviews experiments on avalanching, drum and hopper flows, and continuum and discrete models. He presents a brief section on fluctuations and flow properties for hoppers, and, in the most extensive chapter, he presents results on flow regimes and segregation phenomena in rotating drums. It is perhaps this last area that most represents the author's own area of research.

The style of these presentations is a straightforward review of results, which is particularly valuable to a reader who would like a broad description of much of the field. However, the descriptive approach does not always give insight into the relative importance of the topics that are discussed. Furthermore, some areas are left uncovered. For instance, the author does not describe recent work on granular gases or on microscopic models, such as the q model of Susan Coppersmith and colleagues, or the three-leg model of Jean-Philippe Bouchaud, Michael Cates, Philippe Claudin, and Joachim Wittmer. Similarly, he has not considered recent work on constitutive modeling that was stimulated by this microscopic modeling. Nor does he treat jamming and connections to jammed systems such as foams or colloids, or granular gases (including clustering). Nevertheless, there is a wealth of information in this work. In particular, the author provides an extensive bibliography that should be very useful to those with a relatively sophisticated interest in the field. The style of this work is actually much like that of a review article. Specifically, it provides brief summaries of various areas relevant to the subjects covered. The writing is clear and the organization sensible.

It is also interesting to compare this monograph to the comparably sized work by Duran. Ristow's work is written much more with the idea of providing a review of recent work. In contrast, Duran's book is didactic in style and provides an excellent starting point for an advanced student to enter the field. In Duran's work, there is considerable discussion of the physical principles involved and of simple models such as the Janssen model for stresses in a silo. There is a greater emphasis on models and mechanisms than in Ristow, but there is probably less of an attempt to be inclusive of all the recent work in this area. As with Ristow, the prose is clear. Both these volumes would be valuable additions for those with interest in the field.

Robert P. Behringer is chairman of the physics department at Duke University. He has been working, principally experimentally, in the field of granular flow for a dozen years.