A new model to describe the response of a class of seemingly viscoplastic materials. (English) Zbl 07511499

Summary: A new model is proposed to mimic the response of a class of seemingly viscoplastic materials. Using the proposed model, the steady, fully developed flow of the fluid is studied in a cylindrical pipe. The semi-inverse approach is applied to obtain an analytical solution for the velocity profile. The model is used to fit the shear-stress data of several supposedly viscoplastic materials reported in the literature. A numerical procedure is developed to solve the governing ODE and the procedure is validated by comparison with the analytical solution.


34B60 Applications of boundary value problems involving ordinary differential equations
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[1] Bingham, E. C., Fluidity and Plasticity, McGraw-Hill, New York (1922)
[2] Bird, R. B.; Dai, G. C.; Yarusso, B. J., The rheology and flow of viscoplastic materials, Rev. Chem. Eng. 1 (1983), 1-70
[3] Blechta, J.; Málek, J.; Rajagopal, K. R., On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion, SIAM J. Math. Anal. 52 (2020), 1232-1289 · Zbl 1432.76075
[4] Casson, N., A flow equation for pigment-oil suspensions of the printing ink type, Rheology of Disperse Systems Pergamon Press, Oxford (1959), 84-104 · Zbl 0119.19901
[5] Edgeworth, R.; Dalton, B. J.; Parnell, U. T., The pitch drop experiment, Eur. J. Phys. 5 (1984), 198-200
[6] Herschel, W. H.; Bulkley, R., Konsistenzmessungen von Gummi-Benzollösungen, Kolloid-Z. 39 (1926), 291-300 German
[7] Huilgol, R. R., Fluid Mechanics of Viscoplasticity, Springer, Berlin (2015) · Zbl 1328.76001
[8] Mitsoulis, E., Flows of viscoplastic materials: Models and computations, Rheology Rev. 2007 (2007), 135-178
[9] Rajagopal, K. R., Conspectus of concepts of elasticity, Math. Mech. Solids 16 (2011), 536-562 · Zbl 1269.74014
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