Abstract
Fluid mechanics and rheology involve many unsolved challenges related to the transport mechanisms of mass, momentum and energy – especially when it comes to realistic, industrially relevant materials. Very interesting are suspensions or granular fluids with solid, particulate ingredients that feature contact mechanics on the micro-scale, which affect the transport properties on the continuum- or macro-scale. Their unique ability to behave as either fluid, or solid or both, can be quantified by non-Newtonian rheological rules, and results in interesting mechanisms such as super-diffusion, shear thickening, fluid–solid transitions (jamming) or relaxation/creep. Focusing on the steady state flow of a granular fluid, one can attempt to answer a long-standing question: how do realistic material properties such as dissipation, stiffness, friction or cohesion influence the rheology of a granular fluid? In a recent paper Macaulay & Rognon (J. Fluid Mech., vol. 858, 2019, R2) shed new light on the effect cohesion can have on mass transport in sheared, sticky granular fluids. On top of the usual diffusive, stochastic modes of transport, cohesion can create and stabilise clusters of particles into bigger agglomerates that carry particles over large distances – either ballistically in the dilute regime, or by their rotation in the dense regime. Importantly, these clusters must not only be larger than the particles (defining the intermediate, meso-scale), but they must also have a finite lifetime, in order to be able to exchange mass with each other, which can seriously enhance transport in sticky granular fluids by rotection, i.e. a combination of rotation and convection.
Highlights
The macroscopic Navier–Stokes equations allow one to describe Newtonian fluids with constant transport coefficients
For simple fluids (Hansen & McDonald 1986), it is possible to bridge between the hydrodynamic and the atomistic scales; as an example, the diffusion coefficient quantifies mass transport mediated by microscopic fluctuations, see figure 1(a)
The Enskog equation gives a good description of dense gases of hard atoms (Hansen & McDonald 1986) or of particles including the effects of dissipation (Pöschel & Luding 2001), reaching out towards realistic systems (Luding 2009)
Summary
The macroscopic Navier–Stokes equations allow one to describe Newtonian fluids with constant transport coefficients (e.g. viscosity). For simple fluids (Hansen & McDonald 1986), it is possible to bridge between the (macroscopic) hydrodynamic and the (microscopic) atomistic scales; as an example, the diffusion coefficient quantifies mass transport mediated by microscopic fluctuations, see figure 1(a). The Enskog equation gives a good description of dense gases (or fluids) of hard atoms (Hansen & McDonald 1986) or of particles including the effects of dissipation (Pöschel & Luding 2001), reaching out (empirically) towards realistic systems (Luding 2009). Charges or cohesion are other practically relevant material properties: repulsive forces, with potential energy scale φ > 0, suppress structure formation since collisions become less probable, so that dissipation is reduced. Attractive forces, with cohesive (surface) energy φ < 0, can enhance structure formation by favouring collisions, enhancing dissipation and keeping particles together. Since cluster-mediated mass transport requires some free space, one remaining question is: how is cohesion influencing the transport properties in very dense systems?
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