Disorder characterizes most of the materials that surround us in nature. Despite their great technological importance, materials with ordered crystalline structures are relatively rare. Examples of disordered materials, however, abound, and their forms can be as varied as their number. The paper on which these words are printed has a disordered structure composed of a highly interconnected network of fibers. It has also been coated with particulate materials to improve its properties and the visibility of the ink. The reading glasses you may require to focus on these words are composed of a glass or polymer material that is disordered on a molecular level. Even the structure of your hand holding this magazine is disordered. These and virtually all other disordered materials are typically parameterized by a characteristic length scale. Above this length scale, the material is homogeneous and the effects of the disorder are not directly manifest; below this characteristic length the disorder of the structure dominates, directly affecting the properties.

The range of characteristic length scales for the disordered materials around us is immense. For the glass or polymer of your reading glasses, it is microscopic; the disorder is apparent only at the molecular level, while above this level the material is homogeneous. For the paper on which this magazine is printed, the scale is larger; the paper is white partly because the disordered fiber network has within it structures that are comparable in size to the wavelength of light, resulting in strong scattering of the light.

Colloidal aggregation is a very old field of research. The basic mechanism that controls the stability of colloidal solutions has been described in the celebrated papers of Derjaguin, Landau, Verwey, and Overbeek (DLVO), and indeed the prevention of undesired aggregation is one of the primary concerns in many industrial processes involving colloids. In the last 10 years a resurgence of interest in aggregation rather than in stability has been spurred by a number of fortuitous coincidences. Both through simulations and experiments, it was realized that colloidal aggregates exhibit a fractal nature. More importantly, it was found that there are two universal modes of aggregation, irrespective of the type of colloidal system. The aggregates grown according to these modes have different fractal dimensions, different reaction kinetics, and different mass distributions. The two modes are called diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA), according to whether the probability that a bond formed as a consequence of an encounter is equal to, or much smaller than one, respectively. The study of these limiting cases has been the object of extensive studies in the late 1980s, and many of the features of these modes are by now well understood.

This article describes some recent results in the area of colloidal aggregation. Although we present mostly static light-scattering data from our laboratory, connections to similar work from other groups are also discussed. For the convenience of the reader, we start by recalling some of the relevant features of both DLCA and RLCA.

The behavior of fluids confined in porous materials has been of interest to engineers and scientists for many decades. Among the applications driving this research are the use of porous membranes to achieve liquid-liquid separations and to deionize water, the use of porous materials as beds for catalysis, and the need to extract liquids (especially oil and water) from such media. Many of these applications depend on transport, which is governed by flow or diffusion in the imbibed fluids. Both the flow and diffusion of multiphase fluids in porous media, however, strongly depend on the morphology of phase-separated domains, and on the kinetics of domain growth. Thus, it is worthwhile to study the behavior of multiphase fluids in porous media in the absence of flow. Recently, much attention has focused on even simpler systems that still capture these essential features, namely, near-critical binary liquid mixtures and vapor-liquid systems in model porous media, such as Vycor and dilute silica gels. Although near-critical fluids may seem rather artificial as models for multiphase liquids, there are several advantages associated with them. In general, domain morphology and growth kinetics are governed primarily by competition between interfacial tension and the preferential attraction of one phase to the surface of the medium. In near-critical fluids, the relative strength of these two energy scales is sensitive to temperature, and can therefore be altered in a controlled fashion. In addition, the kinetics of domain growth are sensitive to the temperature quench depth, and can be controlled.

In 1831, Faraday reported to the Royal Society of London that granular material inside a container, when vibrated, would spontaneously begin to exhibit convection rolls, similar to what is observed in normal fluids when heated from below. This observation indicated that not only can a granular material act like a fluid, but also that vibrations can affect the properties of these materials in important ways. Such phenomena are of immediate practical importance because granular materials exist all around us. We use sand and gravel to build the roads we drive on; we process grain to provide our food supply; we mine ore to provide coal, minerals, and precious commodities; we take powders and pills to cure what ails us. Many of the phenomena observed in granular media are prototypical examples of complex, nonequilibrium behavior that is also found in an increasing number of other systems. As a result, sandpiles have served as a macroscopic and visually appealing metaphor for thinking about a number of microscopic systems that are not directly accessible to our senses. Despite the common occurrence of these materials, their properties are not at all well understood and most of our knowledge centers on the subset of static, equilibrium properties of granular matter. Only over the last few years have physicists and engineers begun to unravel some of the exceptional time-dependent, nonequilibrium properties that these seemingly simple materials exhibit. This review focuses on recent developments in the newly emerging field of granular dynamics and, in particular, addresses the role of vibration in determining the phenomena observed in such media.

Porous media represent a broad class of mesoscopically disordered materials that are important in many industrial processes, mostly involving the transport of fluids. For examples, the flow of oil and water in sedimentary rock determines the producibility of oil reservoirs; diffusion and dispersion of molecules in soil govern the spreading of both fertilizers and contaminants; chemical reactors use porous catalysts to enhance the mixing of reagents; the containment of chemical and nuclear wastes depends on the low permeability of concrete barriers. These are just a few problems familiar to our everyday lives. The study of porous media has traditionally been under the disciplines of chemical, mechanical, and petroleum engineering. Only in recent years has the field begun to attract the interest of physicists. The displacement of one fluid by another in a porous medium is now recognized as one of the archetypal systems for studying the physics of pattern formation and interface growth. Fluids transport is known to involve effects due to the microgeometry of the pores, the connectivity of the pore network, and the wetting properties of the pore surfaces. These are all fundamental scientific issues that require the understanding of the physics and chemistry associated with the porous materials. Tackling these problems requires the collaboration of scientists from many different disciplines. Although much work has been done and a great deal has been learned, many interesting and important issues remain. In an article written five years ago, I gave a pedagogical overview of some of the problems in porous media that captivated my own interest.

A large class of materials of great technological importance and scientific interest are highly disordered on length scales comparable to, or larger than, the wavelength of light. As a consequence of this disorder, these materials are often composed of a large number of regions with different indices of refraction, separated by interfaces that are abrupt on the scale of the wavelength of light. Each of these interfaces refracts or scatters light, making these materials quite opaque optically. Even in the absence of absorption, the strong scattering precludes the direct transmission of light rays through the material. This greatly complicates the study of these materials.

Examples of these disordered materials abound. Many are complex fluids; colloidal suspensions and other dispersions such as foams and emulsions often consist of particles or droplets whose diameters are comparable to the wavelength of light. Unless they are very dilute, these dispersions are typically highly opaque. Other materials consist of solid grains of similar sizes without the surrounding fluid. For example, most ceramics are composed of oxide grains sintered together; the voids between the grains lead to the large number of interfaces, and hence to the strong scattering and opaque appearance commonly associated with these materials. Similarly, many porous materials also possess a high density of voids that scatter light; filters, oxide catalyst supports, and even rocks are all optically opaque because of the strong scattering. Sand and other unconsolidated granular materials are also opaque in part because of the large number of interfaces that scatter light.