Preface: Physics of dense suspensions

Abstract

The research reported in this issue of the Journal of Rheology devoted to the "Physics of Dense Suspensions" captures several aspects emerging from discussions in recent years within the rheology community. Two brief workshops-at the University of Edinburgh (June 2015) and at Georgetown University (June 2016)-followed by a conference and an extended workshop at the Kavli Institute for Theoretical Physics (KITP) at UCSB in January-April 2018 brought together researchers using different methods of study and having different perspectives on the rheology of liquid-solid dispersions. Several themes and research questions , and a number of investigations represented in this issue, grew out of the intensive discussions at these gatherings. When rheology became a distinct area of mechanics in the 1920s, suspensions were immediately a topic of interest, with the recognition that forces of numerous origins acting between the particles result in the range of observed behaviors. Mechanistic study requires probing the detailed interaction forces and applying statistical physics arguments to deduce the bulk behavior, and this arose from the fluid mechanics community. Building on Einstein's insight into how the disturbance flow caused by a rigid sphere increases effective viscosity in the dilute limit [1], the generalization of this result to the full rheological response by Batchelor in 1970 [2] established suspension mechanics as a well-defined discipline, providing a foundation for rigorous simulation methods [3] focused on mechanistic understanding of the roles of the fluid mechanical, thermal, and interparticle forces [4,5]. In the recent discussions, "dense" means not simply concentrated , but highly concentrated in particles. The implication is that a dense suspension has volume fraction, f, approaching the maximum flowable value, f max. For suspensions of spheres that are relatively monodisperse, i.e., composed of particles all about the same size, this is given by random close packing or f max 0:65, and one could say a concentrated suspension has f. 0:4, while the typical understanding of the dense regime is that f. 0:5. A number of the papers in this issue use the terminology of a "jamming fraction" coming from the study of granular systems [6], f J , in place of f max. The conditions for shear jamming depend on a number of factors-particle surface characteristics such as roughness, surface forces, and the imposed stress level. Jamming under shear is a topic that bridges between granular and suspension flows and was one of many to which the late Robert (Bob) Behringer contributed [7]; the echoes of Bob's thoughts and probing questions live on in contributions in this issue, which developed out of the KITP workshop in 2018. The relationship of suspension rheology to that of granular materials [8] is not new, as in 1938 Freundlich and Röder [9] showed that quartz powder (crushed silica) in water exhibited a strong shear thickening with an increase of shear rate, and called this a "dilatant" behavior, occurring for solid concentrations of about 80% of the value of 55% found in a settled bed of the same particles. Dilatancy was discussed by these authors in connection with its description by Reynolds [10] for wet gran-ular beds that expand on shearing, and was used interchangeably with shear thickening in this and much of the earlier literature, but is now usually reserved for conditions in which the material exerts a thrust that would push plates apart in a torsional rheometer, implying roughly that the first normal stress difference is positive, N 1. 0. It is now known that N 1 may transition from negative to positive with an increase of shear rate and/or solid fraction [11-14]. Suspension normal stresses and their consequences in terms of particle migration have provided a major impetus to the development of understanding of the suspension microstructure, beginning in the 1980s and extending until recently [15-19], but these results in dense suspensions have brought novel insights and new challenges [20-24]. The concepts of particle contact, force chains, or force networks have come together in the study of suspension rheology and have become, as seen in many papers of this special issue, the tools to analyze and discuss stress transmission, relaxation, and flow. Shear thickening is one of the principal manifestations of the non-Newtonian rheology of suspensions, but it should be noted that it occurs in different forms. In simplest terms, these have been described as continuous and discontinuous shear thickening, the latter implying an abrupt and apparently discontinuous stress response at some shear rate. A weak continuous shear thickening seen in near hard-sphere dispersions at solid fractions up to about f ¼ 0:48, e.g., by D'Haene et al. [25] is reproduced by simulations of Brownian hard spheres [26], and is explainable through hydrodynamic interactions alone, as illustrated in pair theory [27]. Note: This paper is part of the special issue on Physics of Dense Suspensions.