Microstructure and thickening of bi-disperse granular suspensions in simple shear flow

Most granular suspensions in nature and industrial applications comprise multimodal particles in a broad size range. Despite numerous studies attempting to establish a unified viscosity model for polydisperse suspensions with different particle size distributions (PSDs), the microstructure exhibits a strong PSD dependence, such as the peculiar shear-induced particle ordering in bidisperse suspensions. However, understanding of the stability of such ordered structures remains limited. In this study, we aim to reveal the role of microstructural transformation in the flow of shear thickening bidisperse suspensions with large particle size ratio. Discrete-particle simulations accounting for short-range hydrodynamic and contact forces were performed to simulate the simple shear flow of granular suspensions, with three PSDs at the small particle fraction: zeta 1 equals 0.10 comma 0.26 comma 0.50 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.10</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0.26</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0.50</mml:mn> </mml:math> $\zeta _1=0.10, 0.26, 0.50$ . We found that an order-to-disorder transition that occurs in the suspension with the theoretical optimal PSD ( zeta 1 equals 0.26 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.26</mml:mn> </mml:math> $\zeta _1=0.26$ ) causes unusual discontinuous shear thickening in inertial flows. The contact force network, accompanied by particle rearrangement, switches from sparse to nearly percolated, with decreased stress anisotropy. Compared with monodisperse and bidisperse suspensions that do not exhibit significant structural transformation during thickening, the layered structure in the zeta 1 equals 0.26 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.26</mml:mn> </mml:math> $\zeta _1=0.26$ suspension reduces the effective friction of the system. These findings demonstrate the possibility of achieving stronger shear thickening of inertial flows by adopting an optimised PSD, which can help to achieve active rheology control by compositional tuning.