Bidisperse and polydisperse suspension rheology at large solid fraction

Abstract

At the same solid volume fraction, bidisperse and polydisperse suspensions display lower viscosities, and weaker normal stress response, compared to monodisperse suspensions. The reduction of viscosity associated with size distribution can be explained by an increase of the maximum flowable, or jamming, solid fraction φ m . In this work, concentrated or "dense" suspensions are simulated under strong shearing, where thermal motion and repulsive forces are negligible, but we allow for particle contact with a mild frictional interaction with interparticle friction coefficient of µ = 0.2. Aspects of bidisperse suspension rheology are first revisited to establish that the approach reproduces established trends; the study of bidisperse suspensions at size ratios of large to small particle radii of δ = 2 to 4 shows that a minimum in the viscosity occurs for ζ slightly above 0.5, where ζ = φ l /φ is the fraction of the total solid volume occupied by the large particles. The simple shear flows of polydisperse suspensions with truncated normal and log normal size distributions, and bidisperse suspensions which are statistically equivalent with these polydisperse cases up to third moment of the size distribution, are simulated and the rheologies are extracted. Prior work shows that such distributions with equivalent low-order moments have similar φ m , and the rheological behaviors of normal, log normal and bidisperse cases are shown to be in close agreement for a wide range of standard deviation in particle size, with standard correlations which are functionally dependent on φ/φ m providing excellent agreement with the rheology found in simulation. The close agreement of both viscosity and normal stress response between bi-and polydisperse suspensions demonstrates the controlling influence of the maximum packing fraction in noncolloidal suspensions. Microstructural investigations and the stress distribution according to particle size are also presented.

Force chains and networks: wet suspensions through dry granular eyes

“…2, show a remarkably similarity in form compared to simulations of isotropically-compressed packings [19] and simple shear [40] of monodisperse granular spheres. Our φ µ J values are slightly higher than those in monodisperse systems, as expected [41]. The same is true of Z µ J even in the 0.56…”

Viewing Earth’s surface as a soft-matter landscape

“…The unifying framework of µ(I) rheology is appealing in its simplicity, and recent work has demonstrated how it may be generalized to account for: Non-Newtonian carrier fluids [226]; thermal effects [227]; and cohesion [228,229]. On the other hand, qualitative changes in flow behavior may be induced by: particle polydispersity and shape [230,231], surface roughness [124], repulsion [130] and hydrogen bonding [125], at-traction [74], and capillary forces [232]. All of these factors ultimately influence particle microstructure, and explicit accounting for these changes in bulk continnum models is a challenge.…”

Nanoparticle diffusion in sheared cellular blood flow

“…The angle bracket represents the ensemble average among independent realizations, which in the current case is through time averaging given the ergodic hypothesis. Similar techniques have recently been used in calculating PPDFs in bidisperse and polydisperse rigid particle suspensions (Wang & Brady 2016;Pednekar et al 2018). Projection of g 21 (r) to principal planes follows the integration procedure discussed in Kumar & Higdon (2011) but with a smaller integration interval, [−a 2 /4, a 2 /4], to better capture the RBC morphological change.…”

“…Figure 7 presents a matrix of g 21 (r) projections onto the velocity-velocity gradient (xy) plane, the velocity-vorticity (xz) plane and the velocity gradient-vorticity (yz) plane under two shear rates (γ=100 or 2000 s −1 ) and two haematocrits (φ=0.1 or 0.4). In general, all PPDFs feature a large-scale rhombus shape as opposed to typical circular shape commonly observed in rigid-sphere-particle suspensions (Foss & Brady 2000a;Wang & Brady 2016;Pednekar et al 2018). This can be attributed to the disk-shape of RBC that causes geometry-specific anisotropy of the microstructure.…”