Generalized Taylor-Aris dispersion in spatially periodic microfluidic networks. Chemical reactions

SIAM Journal on Applied Mathematics

Volumn 63, Issue 3, 2003, Pages 962-986

  Dorfman, K D ^a,b   Brenner, H ^a  

^a Massachusetts Institute of Technology   (United States)

^b INSTITUT CURIE   (France)

Author keywords

Asymptotics; Stochastic processes; Taylor dispersion

Indexed keywords

COMPUTATIONAL METHODS; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POROSITY; SEPARATION;

MICROFLUIDIC NETWORKS;

FLUIDICS;

EID: 0037828218     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902401872     Document Type: Article

References (40)

1. P. M. ADLER AND H. BRENNER, Transport processes in spatially periodic capillary networks. I. Geometrical description and linear flow hydrodynamics., PhysicoChem. Hydrodyn., 5 (1984), pp. 245-268.
2. V. ALVARADO, H. T. DAVIS, AND L. E. SCRIVEN, Effects of pore-level reaction on dispersion in porous media, Chem. Eng. Sci., 52 (1997), pp. 2865-2881.
3. J. S. ANDRADE, D. A. STREET, Y. SHIBUSA, S. HAVLIN, AND H. E. STANLEY, Diffusion and reaction in percolating pore networks, Phys. Rev. E, 55 (1997), pp. 772-777.
4. B. E. AVILES AND M. D. LEVAN, Network models for nonuniSciform flow and adsorption in fixed beds, Chem. Eng. Sci., 46 (1991), pp. 1935-1944.
5. V. BALAKOTAIAH AND H.-C. CHANG, Dispersion of chemical solutes in chromatographs and reactors, Philos. Trans. R. Soc. Lond. Ser. A, 351 (1995), pp. 39-75.
6. V. BALAKOTAIAH AND S. M. S. DOMMETI, Effective models for packed-bed catalytic reactors, Chem. Eng. Sci., 54 (1999), pp. 1621-1638.
7. R. P. BATYCKY, D. A. EDWARDS, AND H. BRENNER, On the need for fictitious initial conditions in effective medium theories of transient nonconservative transport phenomena. Some elementary unsteady-state heat conduction examples, Chem. Eng. Comm., 152-153 (1996), pp. 173-187.
8. B. BOLLOBAS, Graph Theory: An Introductory Course, Springer-Verlag, New York, 1979.
9. H. BRENNER AND D. A. EDWARDS, Macrotransport Processes, Butterworth-Heinemann, Boston, 1993.
10. R. I. CUKIER, Diffusion controlled processes among stationary reactive sinks: Effective medium approach, J. Chem. Phys., 78 (1983), pp. 2573-2578.
11. R. I. CUKIER, Effective medium theory of rate processes among stationary reactive sinks with the radiation boundary condition, J. Phys. Chem., 87 (1983), pp. 582-586.
12. K. D. DORFMAN AND H. BRENNER, Generalized Taylor-Aris dispersion in discrete spatially periodic networks. Microfluidic applications, Phys. Rev. E, 65 (2002), p. 021103.
13. K. D. DORFMAN AND H. BRENNER, Modeling DNA electrophoresis in microfluidic entropic trapping devices, Biomed. Microdev., 4 (2002), pp. 237-244.
14. S. R. DUNGAN, M. SHAPIRO, AND H. BRENNER, Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems, Proc. R. Soc. Lond. Ser. A, 429 (1990), pp. 639-671.
15. D. A. EDWARDS, M. SHAPIRO, AND H. BRENNER, Dispersion and reaction in two-dimensional model porous media, Phys. Fluids A. 5 (1993), pp. 837-848.
16. T. R. GINN, Stochastic-convective transport with nonlinear reactions and mixing: Finite streamtube ensemble formulation for multicomponent reaction systems with intrastreamtube dispersion, J. Contam. Hydrol., 47 (2001), pp. 1-28.
17. M. P. HOLLEWAND AND L. F. GLADDEN, Modeling of diffusion and reaction in porous catalysts using a random 3-dimensional network model, Chem. Eng. Sci., 47 (1992), pp. 1761-1770.
18. S. G. JAKEWAY, A. J. DE MELLO, AND E. L. RUSSELL, Miniaturized total analysis systems for biological analysis, Fresenius J. Anal. Chem., 366 (2000), pp. 525-539.
19. K. JENSEN, Microreaction engineering - Is smaller better?, Chem. Eng. Sci., 56 (2001), pp. 293-303.
20. M. KRISHNAN, V. NAMASIVAYAM, R. S. LIN, R. PAL, AND M. A. BURNS, Microfabricated reaction and separation systems, Curr. Opin. Biotechnol., 12 (2001), pp. 92-98.
21. J. KRUGER, Effective medium theory for diffusion-controlled reactions among stationary perfect sinks, Physica A, 166 (1990), pp. 206-219.
22. J. KRUGER, Effective medium theory of diffusion and chemical-reaction in the presence of stationary sinks, Physica A, 169 (1990), pp. 393-406.
23. J. P. KUTTER, Current developments in electrmicrofabricatedophoretic and Chromatographic separation methods on microfabricated devices, Trac-Trends Anal. Chem., 19 (2000), pp. 352-363.
24. M. LEITZELEMENT, P. MAJ, J. A. DODDS, AND J. L. GREFFE, Deep bed filtration in a network of random tubes, in Solid-Liquid Separation, J. Gregory, ed., Ellis Horwood, Chichester, U.K., 1984, pp. 273-296.
25. G. Y. Li AND H. RABITZ, A general lumping analysis of a reaction system coupled with diffusion, Chem. Eng. Sci., 46 (1991), pp. 2041-2053.
26. K. MATTERN AND B. U. FELDERHOF, Rate of diffusion-controlled reactions in a random array of spherical sinks, Physica A, 143 (1987), pp. 1-20.
27. R. MAURI, Dispersion, convection, and reaction in porous-media, Phys. Fluids, 3 (1991), pp. 743-756.
28. K. N. MEHTA, M. C. TIWARI, AND K. D. P. NIGAM, Effect of permeability and chemical-reaction on laminar dispersion of a solute, Int. J. Eng. Fluid Mech., 1 (1988), pp. 351-364.
29. M. MUTHUKUMAR, Concentration dependence of diffusion controlled processes among static traps, J. Chem. Phys., 76 (1982), pp. 2667-2671.
30. D. PAL, Effect of chemical reaction on the dispersion of a solute in a porous medium, Appl. Math. Model., 23 (1999), pp. 557-566.
31. S. H. PARK AND Y. G. KIM, The effect of chemical-reaction on effective diffusivity within biporous catalysts. I. Theoretical development, Chem. Eng. Sci., 39 (1984), pp. 523-531.
32. S. D. REGE AND H. S. FOGLER, A network model for deep bed filtration of solid particles and emulsion drops, AIChE J., 34 (1988), pp. 1761-1772.
33. D. RYAN, R. G. CARBONELL, AND S. WHITAKER, Effective diffusivities for catalyst pellets under reactive conditions, Chem. Eng. Sci., 35 (1980), pp. 10-16.
34. M. SAHIMI, G. GAVALAS, AND T. T. TSOTSIS, Statistical and continuum models of fluid-solid reactions in porous media, Chem. Eng. Sci., 45 (1990), pp. 1443-1502.
35. M. SHAPIRO AND H. BRENNER, Taylor dispersion of chemically reactive species: Irreversible first-order reactions in bulk and on boundaries, Chem. Eng. Sci., 41 (1986), pp. 1417-1433.
36. M. SHAPIRO AND H. BRENNER, Chemically reactive generalized Taylor dispersion phenomena, AIChE J., 33 (1987), pp. 1155-1167.
37. M. SHAPIRO AND H. BRENNER, Dispersion of a chemically reactive solute in a spatially periodic model of a porous medium, Chem. Eng. Sci., 43 (1988), pp. 551-571.
38. B. J. SUCHOMEL, B. M. CHEN, AND M. B. ALLEN, Network model of flow, transport and biofilm effects in porous media, Transp. Porous Media, 30 (1998), pp. 1-23.
39. N. WAKAD AND Y. NARDSE, Effective diffusivities and dead-end pores, Chem. Eng. Sci., 29 (1973), pp. 1304-1306.
40. L. ZHANG AND N. A. SEATON, The application of continuum equations to diffusion and reaction in pore networks, Chem. Eng. Sci., 49 (1994), pp. 41-50.