Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: Definition sketch of two cylinders and the coordinate system. The clockwise direction of θ is defined as positive. The radii of the inner and outer cylinders are R1 and R2, respectively; δ is the shear layer thickness, ur and uθ are radial and angular velocities, respectively. The inner cylinder rotates counterclockwise at a constant speed Ω, and the outer cylinder is stationary.

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: Schematic sketch of flow conditions and normalized BCs: (a) flow with plug layer and (b) flow without plug layer. B is Bingham number; α is radius ratio; β is normalized shear layer thickness and Δ=1+β is the normalized location of the interface between the plug and shear layers.

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: The normalized shear layer thickness β: (a) as a function of Bingham number B and (b) as a function of rotational speed Ω for different Bingham material (different values of τ0/μ).

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: The critical Bingham number Bcr = τ0/μΩcr, where Ωcr is the critical rotational speed, as a function of radius ratio α. The upper and lower zones represent the flow conditions with and without plug layer, respectively.

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: The absolute value of the ratio of inner cylinder wall shear stress Γ to yield stress τ0 as a function of radius ratio α and different values of Bingham number B

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: The absolute value of the ratio of inner cylinder wall shear stress Γ to yield stress τ0: (a) as a function of rotational speed Ω for a given Bingham material (fixed τ0/μ) in the gaps with different values of radius ratio α = R2/R1 and (b) as a function of Ω for different material (different τ0/μ) in the gap with fixed α = 1.5

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer J. Fluids Eng. 2015;137(4):041202-041202-11. doi:10.1115/1.4028813 Figure Legend: Diagram of ln(η)/η as a function of η, which η = Γi/τ0 represents the ratio of measured value of shear stress Γi to yield stress τ0, and η must be greater than unity