Analytical Model of Capillary Suction Velocity of a Pipe with Multiple Sizes

Abstract:

Absorption of water in concrete is often described by simple linear water uptake vs. square-root-of-time law. This model based on the classical capillary model derived from the Hagen-Poiseuille’ flow which travel on a single pipe dimension. However, in cement-like material concrete, the pore structure is complex, including for example, variable pore radius and complicated topological changes. In this work, an analytical velocity model of Hagen Poiseuille’s flow on a pipe with multiply sizes is constructed. This model takes the pipe geometry as described by two sets of parameters α_i and β_i;i=1,2…,N into account. In addition, a numerical study of other flow models using Navier Stokes and Stokes models has been conducted. The analytical model is in good agreement with the numerical models at a series of different pipe geometry sizes.

• Periodical: Advanced Materials Research (Volumes 652-654)
• Pages: 1201-1208
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.652-654.1201
• Online since: January 2013
• Authors: Hung Thanh Nguyen, Bjørn R Sørensen
• Keywords: Analytical Capillary Velocity Model, Capillary Absorption, Concrete, Numerical Modeling

References

[1] Edvind N. Lighfoot, R. Byron and Warren E. Steward , (2002): Transport phenomena, Second edition, John Wiley&-son, Inc.

[2] Sellevold, E. J; Punkki, J (1994): Capillary suction in concrete: Effects of drying procedure. Nordic Concrete Research, 15, pp.59-74.

[3] Karolou, M.; Moropoulou, A.; Giakoumaki, A.; Krokida, M.K. (2005): Capillary rise kinetics of some building materials. Colloids and Interface Science, 284, p.260—264.

DOI: 10.1016/j.jcis.2004.09.065

[4] Nikhil Barbare, Arun Shukla, Arijit Bose (2003): Uptake and loss of water in a chemosphere-concrete composite media. Colloid and Interface Science, vol. 33, pp.1681-1689.

DOI: 10.1016/s0008-8846(03)00148-0

[5] Fagerlund, G. (1982): On the capillary of concrete. Nordic Concrete reseach. 1, 20pp.

[6] Nicos, S. Martys; and Chiara, F. Ferraris (1997): Capillary transport in mortars and concrete. Cement and Concrete Research 27, p.747—760.

DOI: 10.1016/s0008-8846(97)00052-5

[7] Dullien, F.A.; El-Sayed, M.S.; Batra V.K. (1976): Rate of Capillary Rise in Porous Media with Nonuniform Pores. Journal of Colloid and Interface Science. 60, p.497—506.

DOI: 10.1016/0021-9797(77)90314-9

[8] Wen-Bin Young (2004): Analysis of capillary flow in non-uniform cross-sectional capillaries. Colloids and Surfaces A: Physicochem. Eng. 234, p.123—128.

DOI: 10.1016/j.colsurfa.2003.12.007

[9] Chatterje, S. (2002): An explanation for the unsaturated state of water stored concrete. Cement and Concrete Composites. 26, p.75—79.

DOI: 10.1016/s0958-9465(02)00124-5

[10] Merle, C. Potter; and David, C. Wiggert (1991): Mechanics of Fluid. Prentice Hall, Inc.

[11] Hung, T. Nguyen; Frank Melandsoe and Stefan Jacobsen (2010): Capillary suction in concrete with analytical pipe model-part 1: Numerical study of flow conditions. Nordic Concrete Research 42, p.71—87.

[12] (2005): Comsol Multiphyscis 3. 2. COMSOL AB.