| Title:
|
A new model to describe the response of a class of seemingly viscoplastic materials (English) |
| Author:
|
Garimella, Sai Manikiran |
| Author:
|
Anand, Mohan |
| Author:
|
Rajagopal, Kumbakonam R. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2022 |
| Pages:
|
153-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
viscoplastic fluid |
| Keyword:
|
constitutive model |
| Keyword:
|
pipe flow |
| Keyword:
|
semi-inverse method |
| Keyword:
|
exact solution |
| MSC:
|
34B60 |
| MSC:
|
74C10 |
| MSC:
|
76A10 |
| idZBL:
|
Zbl 07511499 |
| idMR:
|
MR4396682 |
| DOI:
|
10.21136/AM.2021.0163-20 |
| . |
| Date available:
|
2022-03-25T08:21:42Z |
| Last updated:
|
2024-05-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149564 |
| . |
| Reference:
|
[1] Bingham, E. C.: Fluidity and Plasticity.McGraw-Hill, New York (1922). |
| Reference:
|
[2] Bird, R. B., Dai, G. C., Yarusso, B. J.: The rheology and flow of viscoplastic materials.Rev. Chem. Eng. 1 (1983), 1-70. 10.1515/revce-1983-0102 |
| Reference:
|
[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, MR 4076814, 10.1137/19M1244895 |
| Reference:
|
[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 |
| Reference:
|
[5] Edgeworth, R., Dalton, B. J., Parnell, U. T.: The pitch drop experiment.Eur. J. Phys. 5 (1984), 198-200. 10.1088/0143-0807/5/4/003 |
| Reference:
|
[6] Herschel, W. H., Bulkley, R.: Konsistenzmessungen von Gummi-Benzollösungen.Kolloid-Z. 39 (1926), 291-300 German. 10.1007/BF01432034 |
| Reference:
|
[7] Huilgol, R. R.: Fluid Mechanics of Viscoplasticity.Springer, Berlin (2015). Zbl 1328.76001, 10.1007/978-3-662-45617-0 |
| Reference:
|
[8] Mitsoulis, E.: Flows of viscoplastic materials: Models and computations.Rheology Rev. 2007 (2007), 135-178. |
| Reference:
|
[9] Rajagopal, K. R.: Conspectus of concepts of elasticity.Math. Mech. Solids 16 (2011), 536-562. Zbl 1269.74014, MR 2857911, 10.1177/1081286510387856 |
| . |
