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Abstract
Velocity profiles of Newtonian immiscible liquids undergoing laminar flow between two horizontal plates under pressure gradient are investigated using a momentum balance equation. The differential equation describing the flow has been solved and equations for the velocity profiles of a two-layer and three-layer liquid systems are presented. As examples, we show flow patterns of two-layer water-crude oil system and three-layer system involving water, tetrachloromethane, xylene, cyclopentane and hexane. A distinctive pattern is noticeable between the velocity profiles of heavy (API 19.19) and light (API 40.89) Omani crude oils.
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References
- Brennen, C.E. Fundamentals of Multiphase Flow. Cambridge University Press, Cambridge, 2005.
- Brauner, N. On the relation between two-phase flow under reduced gravity and Earth experiment. Int. Comm. Heat Mass Transfer. 1990, 17, 271.
- Kumara, W.A.S., Halvorden, B.M. and Melaaen, M.C. Particle image velocimetry for characterizing the flow structure of oil-water flow in horizontal and slightly inclined pipes, Chem. Eng. Sci. 2010, 65, 4332-4349.
- Hess, P.C. Upper and lower critical points: Thermodynamic constraints on the solution properties of silicate melts, Geochim. Cosmochim. Acta. 1996, 60, 2365-2377.
- Costa, A. and Macedonio, G. Viscous heating in fluids with temperature-dependent viscosity: Implications for magma flows. Nonlinear Processes in Geophys. 2003, 10, 545–555.
- Wylie, J., and Lister, J. The stability of straining flow with surface cooling and temperature-dependent viscosity, J. Fluid Mech. 1998, 365, 369–381.
- Castro, A., Aragon, E., Morneo-Ventas, I. and Fernandez, C. Liquid immiscibility and magma flow in calc-alkaline glassy and plutonic rocks. Implications for magma rheology and differentiation in deep magma chambers, Geophys. Res. Abs. 2007, 9, 05444.
- Veksler, I.V. Liquid immiscibility and its role at the magmatic-hydrothermal transition: a summary of experimental studies, Chem. Geol., 2004, 210, 7-31.
- Birch, F. Elasticity and Constitution of the Earth's Interior. J. Geophys. Res. 1952, 57, 227-286.
- Dasgupta, R., Buono, A., Whelan, G. and Walker, D. High pressure near-liquidus phase relations in Fe-C-S systems and implications for composition, structure, and process of formation of metallic cores in planetary bodies. 40th Lunar and planetary Science Conference, March 23-27, 2009, The Woodlands, Texas, USA.
- Helffrich, G. and Kaneshima, S. Seismological constraints on core composition from Fe-O-S liquid immiscibility. Science, 2004, 306, 2239-2242.
- Eaton, D.W. and Kendall, J.M. Improving Seismic resolution of outermost core structure by multichannel analysis and deconvolution of broadband SmKS phases. Phys. Earth and Planet. In. 2006, 155, 104-119.
- Yiantsios, S.G. and Higgins, B.G. Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids, 1988, 31, 3225.
- Yih Chia-Shun. Instability due to viscosity stratification. J. Fluid Mech., 1967, 27, pp. 337.
- Anturkar, N.R., Papanastasiou, T.C. and Wilkes, J.O. Linear stability analysis of multilayer plane Poiseuille flow. Phys. Fluids, 1990, 2, 530-541.
- Bird, R.B., Stewart, W.E. and Lightfoot, E.N. Transport Phenomena. John-Wiley Co., New York, 2002.
- Arafin, S., AL-HabsI, N. and Rahman, S.M.M. Transport properties and model- based dynamical properties of Omani crude oils, Arab J. Geosci. 2012, 5, 1085–1092.
- Arafin, S. and Rahman, S.M.M. Dynamical Properties of Omani Crude Oils for Flow Through a Vertical Annulus and a Cylindrical Pipe, SQU J. Science. 2011, 16, 102-117.
References
Brennen, C.E. Fundamentals of Multiphase Flow. Cambridge University Press, Cambridge, 2005.
Brauner, N. On the relation between two-phase flow under reduced gravity and Earth experiment. Int. Comm. Heat Mass Transfer. 1990, 17, 271.
Kumara, W.A.S., Halvorden, B.M. and Melaaen, M.C. Particle image velocimetry for characterizing the flow structure of oil-water flow in horizontal and slightly inclined pipes, Chem. Eng. Sci. 2010, 65, 4332-4349.
Hess, P.C. Upper and lower critical points: Thermodynamic constraints on the solution properties of silicate melts, Geochim. Cosmochim. Acta. 1996, 60, 2365-2377.
Costa, A. and Macedonio, G. Viscous heating in fluids with temperature-dependent viscosity: Implications for magma flows. Nonlinear Processes in Geophys. 2003, 10, 545–555.
Wylie, J., and Lister, J. The stability of straining flow with surface cooling and temperature-dependent viscosity, J. Fluid Mech. 1998, 365, 369–381.
Castro, A., Aragon, E., Morneo-Ventas, I. and Fernandez, C. Liquid immiscibility and magma flow in calc-alkaline glassy and plutonic rocks. Implications for magma rheology and differentiation in deep magma chambers, Geophys. Res. Abs. 2007, 9, 05444.
Veksler, I.V. Liquid immiscibility and its role at the magmatic-hydrothermal transition: a summary of experimental studies, Chem. Geol., 2004, 210, 7-31.
Birch, F. Elasticity and Constitution of the Earth's Interior. J. Geophys. Res. 1952, 57, 227-286.
Dasgupta, R., Buono, A., Whelan, G. and Walker, D. High pressure near-liquidus phase relations in Fe-C-S systems and implications for composition, structure, and process of formation of metallic cores in planetary bodies. 40th Lunar and planetary Science Conference, March 23-27, 2009, The Woodlands, Texas, USA.
Helffrich, G. and Kaneshima, S. Seismological constraints on core composition from Fe-O-S liquid immiscibility. Science, 2004, 306, 2239-2242.
Eaton, D.W. and Kendall, J.M. Improving Seismic resolution of outermost core structure by multichannel analysis and deconvolution of broadband SmKS phases. Phys. Earth and Planet. In. 2006, 155, 104-119.
Yiantsios, S.G. and Higgins, B.G. Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids, 1988, 31, 3225.
Yih Chia-Shun. Instability due to viscosity stratification. J. Fluid Mech., 1967, 27, pp. 337.
Anturkar, N.R., Papanastasiou, T.C. and Wilkes, J.O. Linear stability analysis of multilayer plane Poiseuille flow. Phys. Fluids, 1990, 2, 530-541.
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. Transport Phenomena. John-Wiley Co., New York, 2002.
Arafin, S., AL-HabsI, N. and Rahman, S.M.M. Transport properties and model- based dynamical properties of Omani crude oils, Arab J. Geosci. 2012, 5, 1085–1092.
Arafin, S. and Rahman, S.M.M. Dynamical Properties of Omani Crude Oils for Flow Through a Vertical Annulus and a Cylindrical Pipe, SQU J. Science. 2011, 16, 102-117.