We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ( $0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$ ) and particle Reynolds numbers ( $0.1\leqslant Re_{p}\leqslant 10$ ). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$ . This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. ( J. Rheol. , vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$ . The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$ .
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The effect of medium viscosity and particle volume fraction on ultrasound directed self-assembly of spherical microparticles
Ultrasound directed self-assembly (DSA) allows organizing particles dispersed in a fluid medium into user-specified patterns, driven by the acoustic radiation force associated with a standing ultrasound wave. Accurate control of the spatial organization of the particles in the fluid medium requires accounting for medium viscosity and particle volume fraction. However, existing theories consider an inviscid medium or only determine the effect of viscosity on the magnitude of the acoustic radiation force rather than the locations where particles assemble, which is crucial information to use ultrasound DSA as a fabrication method. We experimentally measure the deviation between locations where spherical microparticles assemble during ultrasound DSA as a function of medium viscosity and particle volume fraction. Additionally, we simulate the experiments using coupled-phase theory and the time-averaged acoustic radiation potential, and we derive best-fit equations that predict the deviation between locations where particles assemble during ultrasound DSA when using viscous and inviscid theory. We show that the deviation between locations where particles assemble in viscous and inviscid media first increases and then decreases with increasing particle volume fraction and medium viscosity, which we explain by means of the sound propagation velocity of the mixture. This work has implications for using ultrasound DSA to fabricate, e.g., engineered polymer composite materials that derive their function from accurately organizing a pattern of particles embedded in the polymer matrix.
more » « less- Award ID(s):
- 2017588
- NSF-PAR ID:
- 10364566
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 131
- Issue:
- 13
- ISSN:
- 0021-8979
- Page Range / eLocation ID:
- Article No. 134901
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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