1, The Saffman-Taylor definition for capillary number describes the ratio of (vμ)/σ with v as the fluid velocity, μ as the fluid viscosity, and σ as surface tension between the two immiscible liquids or gas and liquid. σ n Bengaluru - India #36/5, 2 nd Floor, Somasandra Palya, Adjacent 27 th Main Road, Sector 2, HSR Layout, Bengaluru - 560102 . For example, as shown in Figure 1.3.6, if the material of a capillary is not wet with liquid specimen, the diameter of a bubble is expanded to the outer edge of the capillary, which means that we adjust the value of r for Equations (1.3.6) or (1.3.7). Based on the forces and capillary number affecting the fluid, determines the potential of overcoming the forces of the capillary valve.13, 1. 75 016601. https://dx.doi.org/10.1088/0034-4885/75/1/016601, http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/multi-phase-saturated-rock-properties/dominance-capillary-forces-viscous-forces/capillary-number/, https://dx.doi.org/10.1098/rspa.2014.0557, https://dx.doi.org/10.1016/j.jcis.2004.08.108, https://dx.doi.org/10.1016/j.memsci.2008.01.023, https://dx.doi.org/10.1016/j.jnnfm.2013.09.011, https://dx.doi.org/10.1103/revmodphys.77.977, https://dx.doi.org/10.1016/j.aca.2003.11.024, https://dx.doi.org/10.1146/annurev.bioeng.8.061505.095758, https://dx.doi.org/10.1088/0034-4885/75/1/016601, https://openwetware.org/mediawiki/index.php?title=Capillary_Number_-_Christopher_Sparages&oldid=1057154. The droplets travel as small drips. Please read our, 1. When Ca<<1, surface forces dominate the viscous forces. is a characteristic velocity and The capillary number is defined as:[1][2]. {\displaystyle \mathrm {Ca} } [3], The capillary number plays a role in the dynamics of capillary flow; in particular, it governs the dynamic contact angle of a flowing droplet at an interface.[5]. It was found through experimentation by isolating wetting as the independent variable that at low capillary numbers capillary end effects had high influence. [3], For low capillary numbers (a rule of thumb says less than 10−5), flow in porous media is dominated by capillary forces,[4] whereas for high capillary numbers the capillary forces are negligible compared to the viscous forces. Comparing the bubble viscosity to the capillary number, results can be seen that with an increase in capillary number there is a sigmoidal response in the bubble viscosity (Figure 3).3, The capillary number theory is also used as a basic theory for chemical flooding. (2017). d In the case of dripping mode, viscous shear stress and interfacial tension compete as the capillary number increases with flow rate and the droplet fluid is broken up along its pathway through the channel. The pressure resulting from the rotation of the CD device increases the forces and capillary number in the channel. The Relative Permeability Function for Two-Phase Flow in Porous Media: Effect of Capillary Number. instead of Multiphase flows forms when two of more partially or immiscible fluids are brought in contact. 9. , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2173), 20140557-20140557. https://dx.doi.org/10.1098/rspa.2014.0557, 4. A large reason for studies conducted with bubble suspension is to learn more about to develop models, characterize, and control the flow of the respective gas. Capillary tubes are the simplest of all refrigerant flow controls, with no moving parts. Journal of Non-Newtonian Fluid Mechanics, 202, 112-119. https://dx.doi.org/10.1016/j.jnnfm.2013.09.011, 10. Effects of viscosity on droplet formation and mixing in microfluidic channels. c The capillary number is influential for chemical flooding because it is crucial in determining oil saturation. }, Ratio of viscous drag forces to surface tension in fluids, Ding, M., Kantzas, A.: Capillary number correlations for gas-liquid systems, SEP 2004-062 (2004), http://myweb.clemson.edu/~jsaylor/paperPdfs/aichej.2012.SaylorBounds.pdf, "What is Capillary Number? μ = fluid viscosity where μ As a result, the capillary valve can be overcome and droplets can form and progress into the larger expanded portion of the microfluidic channel. https://dx.doi.org/10.2523/12693-ms, 5. σ Gerbis, M., Gunter, W. D., & Harwood, J. When Ca>>1, surface forces are dominated by the viscous forces. All rights reserved. σ Lastly, by increasing the capillary number and forces farther jetting occurs, resulting in droplets traveling as either spheres or plugs ( Droplet Microfluidics: T-Junction).14, Capillary valves have been implemented frequently on CD fluidic platforms. Syllabus = The capillary number represents the ratio of viscosity to interfacial tension and with an increase in capillary number, there is a decrease in droplet diameter. Truby, J. M., Mueller, S. P., Llewellin, E. W., & Mader, H. M. (2014). They droplets travel as plugs. Analytica Chimica Acta, 507(1), 73-77. https://dx.doi.org/10.1016/j.aca.2003.11.024, 13. Over the years, the capillary number has been represented by a series of different forms across literature with one of the most common one being the formalism by Saffman and Taylor (Figure 1, No. Journal of Colloid and Interface Science, 282(1), 182-187. https://dx.doi.org/10.1016/j.jcis.2004.08.108, 6. ^ U = fluid velocity Zheng, B., Tice, J. D., & Ismagilov, R. F. (2004). Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods. making the viscous forces negligible. 6). . Being a dimensionless quantity, the capillary number's value does not depend on the system of units. Capillary numbers are usually large for high-speed flows and low for low-speed flows; thus, typically for flow through pores in the reservoir NC is ~10−6, and for flow in production tubulars NC is ~1. Counter-intuitively the higher the capillary number is the lower the effect of capillary pressure is in the flow behavior. The Annual Review of Biomedical Engineering. {\displaystyle N_{c}} μ Phys. Li, Y. However, to produce a corresponding CDC to a data set one must first test the wettability effect of the solids involved which has an effect on the overall saturation(Figure 3). In the example provided here, uses a PDMS fabricated microfluidic device that was based on the geometry of sandstone. is the dynamic viscosity of the liquid, Schedule The capillary number is used to determine which forces dominate in a specific scenario. μ The CDC shows the pore arrangement within the media and fluid distribution within the pores. (2004). {\displaystyle \sigma } Canadian International Petroleum Conference, 46(2), 27-32. https://dx.doi.org/10.2118/2004-062. Journal of Membrane Science, 314(1-2), 76-89. https://dx.doi.org/10.1016/j.memsci.2008.01.023, 7. a The capillary number (Ca) is a dimensionless number and it represents the relation between viscous forces and capillary forces, which occur between two immiscible liquids. {\displaystyle \mathrm {Ca} ={\frac {\mu V}{\sigma }}~{and}~{\frac {\mu }{\hat {\mu }}}. This website uses tracking cookies to analyze how you use our website in order to allow us to improve our website and its features. Wiki Textbook, The capillary number (Ca) is a dimensionless number and it represents the relation between viscous forces and capillary forces, which occur between two immiscible liquids. μ V Microfluidics: Fluid physics at the nanoliter scale. Effect of fluid rheology on enhanced oil recovery in a microfluidic sandstone device. Journal of Chemistry, 2017, 1-11. https://dx.doi.org/10.1155/2017/4307368, 3. ^ μ {\displaystyle V} Mobilization or trapping of fluids in porous media, fundamentally, is a result of a force competition. To be more specific, spherical droplets form at low capillary values and long liquid plugs at high capillary values ( Droplet Microfluidics: T-Junction).Liu, Squeezing, dripping, and jetting are other events that occur in droplet microfluidics. Retrieved February 23, 2018. V Use of the capillary number for the prediction of droplet size in membrane emulsification. Ding, M., & Kantzas, A. By continuing using our website, you consent to this usage. In the petroleum industry, capillary number is denoted Reviews of Modern Physics, 77(3), 977-1026. https://dx.doi.org/10.1103/revmodphys.77.977, 11. Introduction CO2 capture and geological storage in energy and climate policy. The capillary number is defined as the ratio of viscous to capillary forces. - Definition from Petropedia", https://en.wikipedia.org/w/index.php?title=Capillary_number&oldid=981929218, Creative Commons Attribution-ShareAlike License, This page was last edited on 5 October 2020, at 06:43. {\displaystyle {\hat {\mu }}} a With Capillary, we build your branded mobile app, and Capillary Number Correlations for Gas-Liquid Systems. are the viscosity of the continuous and the dispersed phases respectively. and Tice, J. D., Lyon, A. D., & Ismagilov, R. F. (2004). Ralf Seemann et al 2012 Rep. Prog. Retrieved February 23, 2018, from http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/multi-phase-saturated-rock-properties/dominance-capillary-forces-viscous-forces/capillary-number/, 2.Guo, H., Dou, M., Hanqing, W., Wang, F., Yuanyuan, G., Yu, Z., . We derive the new definition from a force balance on a nonwetting ganglion trapped by capillarity. a Capillary numbers are usually large for high-speed flows and low for low-speed flows; thus, typically for flow through pores in the reservoir N C is ~10 −6, and for flow in production tubulars N C is ~1. A capillary is a small blood vessel from 5 to 10 micrometres (μm) in diameter, and having a wall one endothelial cell thick. Nilsson, M. A., Kulkarni, R., Gerberich, L., Hammond, R., Singh, R., Baumhoff, E., & Rothstein, J. P. (2013). Specifically, a series of steady-state relative permeability measurements were carried out to determine whether the capillary number causes changes in the two-phase permeabilities or whether one of its constituents, such as flow velocity, fluid viscosity, or interfacial tension (IFT), is the controlling variable.

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