A New Model for Predicting the Marsh Funnel Test
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
This paper presents a new model for predicting the fluid flow through a Marsh funnel. Based on the Herschel-Bulkley fluid model, the model considers both the friction force and the dynamic force. Pressure drop due to the yield stress in the conical section is accounted in the model. In addition, an improved testing system is proposed for the validation of this new model. Experiments were conducted with several Newtonian fluids as well as some non-Newtonian fluids. Experiments and model results on dynamic forces show good agreement. Although the model slightly underpredicts the Marsh funnel time, the overall match is good. The general agreement suggests that the new model can be used for a fast estimation of the rheology parameters of a liquid using Marsh funnel test results and can be used in field applications.
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Acknowledgments
The first author acknowledges the financial support from the China Scholarship Council. We would like to thank Dr. Britta Schoesser for the thought-provoking discussions.
Notation
The following symbols are used in this paper:
- C
- consistency index;
- F (τ0, α, z)
- function representing the upward pressure induced by the sidewall in the conical section;
- g
- acceleration of gravity;
- HF
- maximum filling height of the conical section of the funnel;
- L
- length of the capillary tube;
- n
- flow index;
- pd
- pressure drop due to the dynamic force;
- Q
- discharge;
- R
- radius of the tube;
- RF
- maximum radius of the fluid in the conical section of the funnel;
- r
- local radius of the fluid in the conical section of the funnel;
- v
- mean velocity of the fluid;
- z
- height from the top of the capillary tube to the liquid surface;
- α
- angle between the funnel wall and the vertical direction;
- β
- underrelaxation factor;
- γ
- shear rate;
- ΔPcone
- pressure loss due to yield stress in the conical section of the funnel;
- ΔPtot
- hydrostatic pressure minus the pressure loss due in the conical section of the funnel;
- ρ
- density of fluid;
- ρ0
- density of water;
- τ
- shear stress;
- τ0
- yield stress;
- τw new
- new value in calculation;
- τw old
- previous value in calculation; and
- τw
- wall shear stress.
References
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© 2020 American Society of Civil Engineers.
History
Received: Jan 21, 2020
Accepted: Sep 10, 2020
Published online: Dec 9, 2020
Published in print: Feb 1, 2021
Discussion open until: May 9, 2021
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