Finite depth Stokes' first problem of thixotropic fluid

doi:10.1007/s10483-016-2016-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (1): 59-74.doi: https://doi.org/10.1007/s10483-016-2016-9

Finite depth Stokes' first problem of thixotropic fluid

Wenwen LIU, Jie PENG, Keqin ZHU

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

收稿日期:2015-03-12 修回日期:2015-06-15 出版日期:2016-01-01 发布日期:2016-01-01
通讯作者: Jie PENG E-mail:peng-jie@mail.tsinghua.edu.cn

Finite depth Stokes' first problem of thixotropic fluid

Wenwen LIU, Jie PENG, Keqin ZHU

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Received:2015-03-12 Revised:2015-06-15 Online:2016-01-01 Published:2016-01-01
Contact: Jie PENG E-mail:peng-jie@mail.tsinghua.edu.cn

摘要/Abstract

摘要：

This paper presents a study of the finite depth Stokes' first problem for a thixotropic layer. The yield behavior of the thixotropic fluid in this problem is investigated for the first time. The main physical features of this problem are discussed, including the flow field, the wall stress, and the depth of the yield region. It is shown that the yield region appears near the wall, and the yield surface moves from the wall into the flow region and moves back to the wall finally. In contrast to the solution of the Newtonian fluid, the velocity of the thixotropic layer generally does not increase with time monotonously during the start-up process. The classical solution of the Newtonian fluid can be recovered from our results in extreme cases.

关键词: Stokes' first problem, yield, thixotropy

Abstract:

Key words: thixotropy, yield, Stokes' first problem

中图分类号:

76A05

Wenwen LIU, Jie PENG, Keqin ZHU. Finite depth Stokes' first problem of thixotropic fluid[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(1): 59-74.

参考文献

[1] Barnes, H. A. Thixotropy-a review. Journal of Non-Newtonian Fluid Mechanics, 70, 1-33(1997)
[2] Coussot, P., Nguyen, Q. D., Huynh, H. T., and Bonn, D. Avalanche behavior in yield stress fluids. Physical Review Letters, 88, 175501(2002)
[3] Balmforth, N. J., Frigaard, I. A., and Ovarlez, G. Yielding to stress:recent developments in viscoplastic fluid mechanics. Annual Review of Fluid Mechanics, 46, 121-146(2014)
[4] De Vicente, J. and Berli, C. Aging, rejuvenation, and thixotropy in yielding magneto-rheological fluids. Rheologica Acta, 52, 467-483(2013)
[5] Mewis, J. and Wagner, N. J. Thixotropy. Advance in Colloid and Interface Science, 147, 214-227(2009)
[6] Cheremisinoof, N. P. Encyclopedia of fluid mechanics. Rheology and Non-Newtonian Flows, 7, Gulf Publishing Company, Houston (1988)
[7] Coussot, P. Rheophysics of pastes:a review of microscopic modeling approaches. Soft Matter, 3, 528-540(2007)
[8] Moore, F. The rheology of ceramic slips and bodies. Transactions and Journal of the British Ceramic Society, 58, 470-494(1959)
[9] Houska, M. Inzenyrske Aspekty Reologie Tixotropnich Kapalin, Ph. D. dissertation, Czech Techanical University (1980)
[10] Worrall, W. E. and Tuliani, S. Viscosity changes during the ageing of clay-water suspensions. Transactions and Journal of the British Ceramic Society, 63, 167-185(1964)
[11] Dullaert, K. and Mewis, J. A structural kinetics model for thixotropy. Journal of Non-Newtonian Fluid Mechanics, 139, 21-30(2006)
[12] Huynh, H. T., Roussel, N., and Coussot, P. Aging and free surface flow of a thixotropic fluid. Physics of Fluids, 17, 033101(2005)
[13] Liu, W. W. and Zhu, K. Q. A study of start-up flow of thixotropic fluids including inertia effects on an inclined plane. Physics of Fluids, 23, 013103(2011)
[14] Chanson, H., Jarny, S., and Coussot, P. Dam break wave of thixotropic fluid. Journal of Hydraulic Engineering, 132, 280-292(2006)
[15] Roussel, N., Le Roy, R., and Coussot, P. Thixotropy modelling at local and macroscopic scales. Journal of Non-Newtonian Fluid Mechanics, 117, 85-95(2004)
[16] Coussot, P., Tocquer, L., Lanos, C., and Ovarlez, G. Macroscopic vs. local rheology of yield stress fluids. Journal of Non-Newtonian Fluid Mechanics, 158, 85-90(2009)
[17] Billingham, J. and Ferguson, J. W. J. Laminar, unidirectional flow of a thixotropic fluid in a circular pipe. Journal of Non-Newtonian Fluid Mechanics, 47, 21-55(1993)
[18] Corvisier, P., Nouar, C., Devienne, R., and Lebouché, M. Development of a thixotropic fluid flow in a pipe. Experiments in Fluids, 31, 579-587(2001)
[19] McArdle, C. R., Pritchard, D., and Wilson, S. K. The Stokes boundary layer for a thixotropic or antithixotropic fluid. Journal of Non-Newtonian Fluid Mechanics, 185, 18-38(2012)
[20] Stokes, G. G. On the effect of the internal friction of fluids on the motion of pendulums. Transaction of the Cambridge Philosophical Society, 9, 8-106(1851)
[21] Liu, C. M. Complete solutions to extended Stokes' problems. Mathematical Problems in Engineering, 2008, 754262(2008)
[22] Jordan, P. M., Puri, A., and Boros, G. On a new exact solution to Stokes' first problem for Maxwell fluids. International Journal of Non-Linear Mechanics, 39, 1371-1377(2004)
[23] Fetecau, C. and Fetecau, C. A new exact solution for the flow of a Maxwell fluid past an infinite plate. International Journal of Non-Linear Mechanics, 38, 423-427(2003)
[24] Tan, W. C. and Masuoka, T. Stokes' first problem for an Oldroyd-B fluid in a porous half space. Physics of Fluids, 17, 023101(2005)
[25] Tan, W. C. and Masuoka, T. Stokes' first problem for a second grade fluid in a porous half-space with heated boundary. International Journal of Non-Linear Mechanics, 40, 515-522(2005)
[26] Qi, H. T. and Xu, M. Y. Stokes' first problem for a viscoelastic fluid with the generalized OldroydB model. Acta Mechanica Sinica, 23, 463-469(2007)
[27] Moller, P. C. F., Rodts, S., Michels, M. A. J., and Bonn, D. Shear banding and yield stress in soft glassy materials. Physical Review E, 77, 041507(2008)
[28] Cheng, D. C. H. Yield stress:a time-dependent property and how to measure it. Rheologica Acta, 25, 542-554(1986)
[29] Roussel, N., Le Roya, R., and Coussot, P. Thixotropy modelling at local and macroscopic scales. Journal of Non-Newtonian Fluid Mechanics, 117, 85-95(2004)

Finite depth Stokes' first problem of thixotropic fluid

Finite depth Stokes' first problem of thixotropic fluid

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