This Website is not fully compatible with Internet Explorer.
For a more complete and secure browsing experience please consider using Microsoft Edge, Firefox, or Chrome

CμFD: Simulation of Microfluidic Systems

NAFEMS International Journal of CFD Case Studies

Volume 5, January 2006

ISSN 1462-236X


CµFD: Simulation of Microfluidic Systems

Friedhelm Schönfeld1, Klaus S. Drese1 and Steffen Hardt2
1Fluidics and Simulation Department, Institut für Mikrotechnik Mainz GmbH - IMM
2Chair of Technical Thermodynamics, Darmstadt University of Technology, Germany

https://doi.org/10.59972/5f1ncmu3

Keywords: Micro Fluidics, Free-Surface Flows, Micro Mixers and Dynamic Contact Angle

 


Abstract

We discuss the applicability of standard CFD techniques in µ-fluidics, highlight challenges and introduce methods which allow for corresponding extensions. The focus is especially on problems of major practical importance, namely liquid mixing in micro mixers and free-surface micro flows. With respect to the former two approaches are presented allowing eliminating the problems due to numerical discretisation errors for specific cases of miscible liquids. In the case of emulsion formation of immiscible liquids the RayleighPlateau decay is identified to be the driving mechanism for droplet formation under certain process conditions. Furthermore we investigate capillary filling of a narrow slit, where a special focus is put on the effects induced by a dynamic variation of the contact angle. The test case shows that on practically manageable grids the dynamic behaviour of the contact angle cannot be sufficiently reproduced. A result of the studies performed is the possibility to incorporate the correct contact-angle dynamics even on comparatively coarse grids by introducing a macroscopic slip range at the 3-phase contact line. By virtue of such an “artificial slip method”, correct results for free-surface micro flows can be obtained on grids with a moderate number of computational cells, without the need to resolve the contact line very accurately. Finally, a micro fluidic application involving both mixing of miscible liquids and free-surface flows is exemplarily outlined as one of the future challenges.

References

[1] Baier T., and Drese K.; CFD- und analytische Modellierung von Mikrowärmetauschern, present issue.

[2] Karniadakis, G. E., Beskok, A.; Micro Flows - Fundamentals and Simulation, Springer-Verlag, New York, (2002).

[3] Hessel, V., Hardt S. and Löwe, H.; Chemical Micro Process Engineering: Fundamentals, Modelling and Reactions, Wiley-VCH, (2004).

[4] Sharipov, F., Kalempa, D.; Gaseous mixture flow through a long tube at arbitrary Knudsen numbers, J. Vac. Sci. Technol. A 20, (2002) 814-822.

[5] Kaviany, M.; Principles of Heat Transfer in Porous Media, Springer Verlag, New York, (1995).

[6] Probstein, R. F.; Physicochemical Hydrodynamics, Wiley and Sons Inc., New York, (1994).

[7] Rice, C., Whitehead, R.; Electro kinetic flow in a narrow cylindrical capillary, J. Phys. Chem. 69, (1965) 4017-4023.

[8] Adamson, A. W., Gast, A. P.; Physical Chemistry of Surfaces, 6th Ed.; John Wiley & Sons, New York, (1997).

[9] Hardt, S., Drese, K.S., Hessel V. and Schönfeld, F.; Passive micro mixers for applications in the micro reactor and µTAS field, Microfluidics Nanofluidics 1 (2005) 2, 108-118.

[10] Boris, J.P. and Book, D.L.; Flux-corrected transport. I. SHASTA a fluid transport algorithm that works, J. Comput. Phys., 11, (1973) 38-69.

[11] Pope, S.B.; Turbulent Flows, Cambridge University Press, (2000).

[12] Aubin, J., Fletcher, D.F., Bertrand J. and Xuereb, C.; Characterization of the mixing quality in micromixers, Chem. Eng. Technol., 26, (2003) 1262-1270.

[13] Ottino J.M., The Kinematics of Mixing: Stretching, Chaos and Transport, Cambridge University Press, (1989).

[14] Ottino, J.M., Muzzio, F.J., Tjahjadi, M., Franjione, J.G., Jana, S.C. and Kusch, H.A.; Chaos, symmetry, and self-similarity: exploiting order and disorder in mixing processes, Science, 257, (1992) 754-760.

[15] Jiang, F., Drese, K.S., Hardt, S., Küpper M. and Schönfeld, F.; Helical flows and chaotic mixing in curved microchannels, AIChE J., 50 (2004) 9, 2297.

[16] Discretization errors dominate numerical solutions of convection-diffusion equations for low diffusive scalars. Since typical kinematic viscosities of liquids are orders of magnitude above corresponding diffusion coefficients such errors are well controlled for numerical solutions of the Navier-Stokes equations.

[17] Schönfeld, F., Hessel V. and Hofmann, C.; An optimised split-and-recombine micro-mixer with uniform `chaotic’ mixing, Lab Chip, 4, (2004) 65-69.

[18] Hessel, V., Hardt, S., Löwe H. and Schönfeld, F.; Laminar mixing in different interdigital micromixers: I. Experimental characterization. AIChE J., 49, (2003) 566-577.

[19] Hardt, S., Pennemann, H. and Schönfeld, F., Theoretical and Experimental Characterization of a Low-Reynolds-Number Split-and-Recombine Mixer, Microfluidics Nanofluidics (2005), in press

[20] Hardt, S., Schönfeld, F., Weise, F., Hofmann, C., Ehrfeld, W.; Simulation of droplet formation in micromixers, in Proceedings of the “International Conference on Modeling and Simulations of Microsystems”, (19 - 21 March 2001); Hilton Head Island, SC.

[21] Hardt, S., Schönfeld, F.; Simulation of hydrodynamics in multi-phase microreactors, in Proceedings of the “5th World Congress on Computional Mechanics, WCCM”, p. http://wccm.tuwien.ac.at; (7-12 July 2002); Vienna, Austria.

[22] Hirt, C. W. and Nichols, B. D.; Volume of fluid (VOF) method for dynamics of free boundaries, J. Comput. Phys. 39, (1981) 201-221.

[23] Brackbill, J. U., Kothe, D. B. and Zemach, C.; A continuum method for modelling surface tension, J. Comput. Phys. 100, (1992) 335-354.

[24] CFX4 Solver Documentation “Surface sharpening in free surface flows”, CFX/ANSYS.

[25] CFX5-6. Solver and Theory Documentation, CFX/ANSYS.

[26] Eggers, J., Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys., 69, (1997) 865-930.

[27] Huh, C. and Scriven, L.E.; Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci., 35, (1971) 85-101.

[28] Hocking, L.M; A moving fluid interface. Part 2. The removal of the force singularity by a slip flow J. Fluid Mech., 79, (1977) 209-214.

[29] Huh, C. and Mason, S.G.; The steady movement of a liquid meniscus in a capillary tube, J. Colloid Interface Sci., 81, (1977) 401-419.

[30] Kistler, S. in: Wettability, J.C. Berg (Ed.), Dekker, (1993).

[31] De Gennes, P.G.; Wetting: Statics and Dynamics, Rev. Mod. Phys., 57, (1985) 827-862.

[32] Cox, R.G.; The dynamics of spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech., 168, (1986) 169-194.

[33] Quinte, A., Halstenberg, S., Eggert, H., Peters, R.-P. and Schön, C., Mikrosystemtechnische Realisierung von medizinischen Teststreifen, Proceedings 8. Workshop “Methoden und Werkzeuge zum Entwurf von Mikrosystemen”, Berlin, Dec 2-3, (1999), 13-22.

[34] Bracke, M., de Voeght, F. and Joos, P.; The kinetics of wetting: the dynamic contact angle, Progr. Colloid Polym. Sci. 79, (1989) 142-149.

[35] Van Doormal, J.P. and Raithby, G.D.; Enhancements of the SIMPLE method for predicting incompressible fluid flows, Numerical Heat Transfer, 7, (1984), 147-163.

[36] Somalinga S. and Bose A.; Numerical investigation of boundary conditions for moving contact line problems. Phys. Fluids 12 (2000) 499-510.

[37] Hoffmann, R.L.; A study of the advancing interface, J. Coll. Inter. Sci., 50, (1975) 228-241.

[38] Tanner, L.H.; The spreading of silicone oil drops on horizontal surfaces, J. Phy. D: Appl. Phys., 12, (1979) 1473-1484.

[39] Donnet, M., Jongen, N., Lemaître, J., Bowen, P. and Hofmann, H.; Better control of nucleation and phase purity using a new segmented flow tubular reactor; Model system : Precipitation of calcium oxalate, 14th International Symposium on Industrial Crystallization, Cambdridge, UK, 1999, IChemE (1999), 1-13.

[40] Jongen, N., Lemaître, J., Bowen, P. and Hofmann, H.; Oxalate precipitation using a new tubular plug flow reactor, Proc. 5th World Congress of Chemical Engineering, San Diego, 1996, AIChE (1996), 2109-2111.

[41] Schenk, R., Donnet, M., Hessel, V., Hofmann, C., Jongen, N., Löwe, H.; Suitability of Various Types of Micromixers for the Forced Precipitation of Calcium Carbonate, Proc. of 5th Int. Conf. on Micorreaction Technology, Strasbourg, (2001) 489- 498.

[42] Werner, B., Donnet, M., Hessel, V., Hofmann, C., Jongen, N., Löwe, H., Schenk, R. and Ziogas, A.; Specially Suited Micromixers for Process Involving Strong Fouling, IMRET 6 : 6th International Conference on Microreaction Technology : Conference Proceedings, AIChe Spring Meeting, March 10-14, 2002, New Orleans, LA. - New York: AIChE, (2002) 168-183.

[43] Schenk, R., Hessel, V., Werner, B., Schönfeld, F., Hofmann, C., Donnet, M. and Jongen, N.; Micromixers as tool for powder production, Proceedings of 15th International Symposium on Industrial Crystallization : September, 15-18, Sorrento, Italy / promoted by: The Working Party on Crystallization, EFCE: the European Federation of Chemical Engineering, Vol. 2; Chianese A.(Ed.). - Milano, Italy: AIDC (2002) 909-914.

Cite this paper

Friedhelm Schönfeld, Klaus S. Drese, Steffen Hardt, CµFD: Simulation of Microfluidic Systems, NAFEMS International Journal of CFD Case Studies, Volume 5, 2006, Pages 57-73, https://doi.org/10.59972/5f1ncmu3

Document Details

ReferenceCFDJ5-6
AuthorsSchönfeld. F Drese. K Hardt. S
LanguageEnglish
TypeJournal Article
Date 2nd January 2006
OrganisationDarmstadt University of Technology

Download

Purchase Download

Order RefCFDJ5-6 Download
Non-member Price £5.00 | $6.33 | €6.02

Back to Previous Page