[M-IS21] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS21-03] Effective viscosity of particle suspensions in unsteady shear flow

*Hiroshi Chin¹, Akihide Takano¹, Kohei Ohie¹, Yasufumi Horimoto¹, Hyun Jin Park¹, Yuji Tasaka¹, Yuichi Murai¹ (1.Hokkaido University)

Keywords:Suspension, Effective viscosity, Particle shape

We investigated the effective viscosity of fine particle suspensions under unsteady shear utilizing ultrasonic spinning rheometry (USR), which evaluates rheological properties via the equation of motion and velocity profile an oscillating cylindrical container measured by ultrasonic velocity profiler (UVP). Since USR evaluates spatially local rheological properties, it is suitable for complex fluids such as particle suspensions. Two kinds of particles, one of them is Opalin particles, anisotropic particles whose characteristic size and density are O(10) μm and 2.7×10³ kg/m³ and the another is spherical glass beads with the similar specifications to the Opalin, were examined to highlight influence of anisotropy of the particles. The particles were dispersed into 500 cSt silicon oil (0.97×10³ kg/m³ in density) as a Newtonian dispersant with 5 vol%. Radial distributions of the effective viscosities for both suspensions in the container obtained via USR showed similar manner despite the anisotropy of the particles. They were almost constant in a wide region except for quite large value near the wall. The constant effective viscosity was evaluated much larger than the value evaluated from the constitutive equation given by Guth and Gold [Phys. Rev., 53, 322 (1932)] describing the effective viscosity of particle suspensions as a function of the volume fraction. Furthermore, using this equation for the high viscosity near the wall, the corresponding volume fraction should be assumed more than 30%, which is much larger than the set value 5 vol%. By calculating local effective shear rate from the velocity profile, the spatial distribution of the viscosity is converted into a viscosity curve. Above a critical shear rate, the curve folded back to the low shear rate regime with a rapid increase of the viscosity. It seemed that shear banding occurred in the near-wall region because on reminding that, in USR, the shear rate was not predetermined but was determined by the local viscosity, the high viscosity near the wall probably resulted in the low shear rate. The same trend was observed in both of the examined particles, and this indicates that the particle shape is not a dominant factor to give the trend. In response of this fact, we considered the following factors to explain the two remarkable characteristics mentioned above. The deviation of the viscosity from one predicted by the equation of Guth and Gold (1932) is attributed to the oscillatory shear flow applied in USR. It was already found by Llewellin et al. [Proc. R. Soc. A, 458, 987 (2001)] that the effective viscosity under unsteady shear takes larger value than that under steady shear. Second factors are the particles size and density for the rapid increase in the viscosity curve. A previous USR study by Yoshida et al. [Phys. Fluids, 31, 103304 (2019)] indicated that the increase of viscosity by adding neutrally buoyant spherical particles with diameters of O(100) μm can be estimated by the Einstein’s equation [Ann. Physik, 19, 289 (1906)]. It is deduced that phase difference of rotation of the particles to flow with considerable density difference in the oscillatory shear flow modifies momentum propagation from the oscillating wall resulting in rapid increase of the local viscosity.