Start-up of channel-flow of a Bingham fluid initially at rest
Daprà, Irene ; Scarpi, Giambattista
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004), p. 125-135 / Harvested from Biblioteca Digitale Italiana di Matematica
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We present an analytical solution of plane motion for a Bingham fluid initially at rest subjected to a suddenly applied constant pressure gradient. Using the Laplace transform we obtain expressions which allow a direct easy calculation of the velocity, of the plug thickness and of the rate of flow as function of time.

In questa Nota viene presentata una soluzione analitica per il moto piano laminare di un fluido di Bingham inizialmente in quiete sottoposto ad un gradiente di pressione costante. Si ottengono espressioni per il calcolo della velocità e dell’ampiezza del nucleo solido centrale in funzione del tempo.

Publié le : 2004-06-01
@article{RLIN_2004_9_15_2_125_0,
     author = {Irene Dapr\`a and Giambattista Scarpi},
     title = {Start-up of channel-flow of a Bingham fluid initially at rest},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {15},
     year = {2004},
     pages = {125-135},
     zbl = {1104.76031},
     mrnumber = {2148540},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_2_125_0}
}

Daprà, Irene; Scarpi, Giambattista. Start-up of channel-flow of a Bingham fluid initially at rest. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 125-135. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_2_125_0/

[1] Duggins, R.K., The commencement of flow of a Bingham Plastic fluid. Chem. Eng. Sci., 27, 1972, 1991-1996.

[2] Mitra, A.K., Impulsively started flow of a Bingham Plastic in a tube. ASME FED, 15, 1984, 23-25.

[3] Hammad, K.J., Unsteady pipe flows of a viscoplastic non-Newtonian fluid: effects of pressure gradient waveform. ASME FED, 247, 1998, 197-204.

[4] Ly, D.P. - Bellet, D., The study of time-dependent pipe flows of inelastic non-newtonian fluids using a multiviscous approximation. J. Non-Newtonian Fluid Mech., 1, 1976, 287-304. | Zbl 0345.76001

[5] Al Katib, M.A.M. - Wilson, S.D.R., The development of Poiseuille flow of a yield-stress fluid. J. Non-Newtonian Fluid Mech., 100, 2001, 1-8. | Zbl 1018.76003

[6] Makarov, A.M. - Zhdanova, L.A. - Polozova, O.N., Non steady-state flow of a viscoplastic medium in a plane channel. J. Eng. Phys., 22, 1972, 51-55.

[7] Safronchik, A.I., Non-steady Flow of a visco-plastic Material between parallel Walls. PMM, 23, 1959, 5, 925-935 (J. Appl. Math. Mech., 23, 1959, 1314-1327). | Zbl 0098.39305

[8] Glowinski, R., Sur l’écoulement d’un fluide de Bingham dans une conduite cylindrique. J. de Méc., 13, 1974, 601-621. | MR 371245 | Zbl 0324.76004

[9] Huilgol, R.R. - Mena, B., On the time estimate for start-up of pipe flows in a Bingham fluid – a proof of the result due to Glowinski, Lions and Trèmoliéres. J. Non-Newtonian Fluid Mech., 94, 2000, 113-118. | Zbl 0995.76005

[10] Atabek, H.B., Start-up Flow of a Bingham Plastic in a Circular Tube. ZAMM, 44, 1964, 332-333. | MR 168234 | Zbl 0127.40403

[11] Amadei, B. - Savage, W.Z., An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures. Int. J. Rock Mech., 38, 2001, 285-296.

[12] Bird, R.B. - Dai, G.C. - Yarusso, B.J., The Rheology and Flow of viscoplastic Materials. Review in Chemical Engineering, 1, 1983, 1-70.

[13] Brown, R.G. - Nilsson, J.W., Introduction to Linear System Analysis. Wiley, New York 1962. | MR 169743 | Zbl 0124.17103