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Macrotransport in nonlinear, reactive, shear flows
1. | Department of Mathematics, University of Montana-Western, 710 S. Atlantic Street Dillon, MT 59725-3598, United States |
References:
[1] |
R. Aris, On the dispersion of a solute in a fluid flowing through a tube, Proc. Roy. Soc. London A, 235 (1956), 67-77.
doi: 10.1098/rspa.1956.0065. |
[2] |
R. Aris, On the dispersion of a solute in a pulsating flow through a tube, Proc. Roy. Soc. London A, 259 (1960), 370-376.
doi: 10.1098/rspa.1960.0231. |
[3] |
V. Balakotaiah and H. Chang, Dispersion of chemical solutes in cromatographs and reactors, Phil. Trans. R. Soc. Lond. A, 351 (1995), 39-75.
doi: 10.1098/rsta.1995.0025. |
[4] |
B. Bloechle, "On the Taylor Dispersion of Reactive Solutes in a Parallel-Plate Fracture-Matrix System,'' PhD thesis, University of Colorado at Boulder - Department of Applied Mathematics, 2001. |
[5] |
H. Brenner and D. Edwards, "Macrotransport Processes,'' Butterworth, Boston, 1993. |
[6] |
L. H. Dill and H. Brenner, A general theory of Taylor dispersion phenomena. iii, J. Colloid Interface Sci., 85 (1982), 101-117.
doi: 10.1016/0021-9797(82)90239-9. |
[7] |
L. H. Dill and H. Brenner, A general theory of Taylor dispersion phenomena. vi, J. Colloid Interface Sci., 93 (1983), 343-365.
doi: 10.1016/0021-9797(83)90419-8. |
[8] |
K. D. Dorfman and H. Brenner, Generalized Taylor-Aris dispersion in spatially periodic microfluidic networks. chemical reactions, SIAM J. Appl. Math., 63 (2003), 962-986.
doi: 10.1137/S0036139902401872. |
[9] |
S. R. Dungan, M. Shapiro and H. Brenner, Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems, Proc. R. Soc. Lond. A, 429 (1990), 639-671.
doi: 10.1098/rspa.1990.0077. |
[10] |
D. A. Edwards, M. Shapiro and H. Brenner, Dispersion and reaction in two-dimensional model porous media, Phys. Fluids A, 5 (1993), 837-848.
doi: 10.1063/1.858631. |
[11] | |
[12] |
P. Fife and K. Nicholes, Dispersion in flow through small tubes, Proc. Roy. Soc. London A, 344 (1975), 131-145.
doi: 10.1098/rspa.1975.0094. |
[13] |
P. C. Fife, Singular perturbation problems whose degenerate forms have many solutions, Applicable Analysis, 1 (1972), 331-358.
doi: 10.1080/00036817208839022. |
[14] |
Avner Friedman, "Partial Differential Equations,'' Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London,1969. |
[15] |
W. N. Gill, A note on the solution of transient dispersion problems, Proc. Roy. Soc. London A, 298 (1967), 335-339.
doi: 10.1098/rspa.1967.0107. |
[16] |
W. N. Gill and R. Sankarasubramanian, Exact analysis of unsteady convective diffusion, Proc. Roy. Soc. London A, 316 (1970), 341-350.
doi: 10.1098/rspa.1970.0083. |
[17] |
L. E. Johns and A. E. Degance, Dispersion approximations to the multicomponent convective diffusion equation for chemically active systems, Chemical Engineering Science, 30 (1975), 1065-1067.
doi: 10.1016/0009-2509(75)87008-4. |
[18] |
C. Li and E. S. Wright, Modeling chemical reactions in rivers: A three component reaction, Discrete and Continuous Dynamical Systems, 7 (2001), 377-384.
doi: 10.3934/dcds.2001.7.373. |
[19] |
C. Li and E. S. Wright, Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics, Communications on Pure and Applied Analysis, 1 (2002), 77-84. |
[20] |
R. Mauri, Dispersion, convection, and reaction in porous-media, Phys. Fluids, 3 (1991), 743-756.
doi: 10.1063/1.858007. |
[21] |
G. N. Mercer and A. J. Roberts, A center manifold description of contaminant dispersion in channels with varying flow properties, SIAM J. appl. Math, 50 (1990), 1547-1565.
doi: 10.1137/0150091. |
[22] |
M. Pagitsas, A. Nadim and H. Brenner, Projection operator analysis of macrotransport processes, J. Chem. Phys., 84 (1986), 2901-2807.
doi: 10.1063/1.450305. |
[23] |
M. Shapiro and H. Brenner, Taylor dispersion of chemically reactive species: irreversible first order reactions in bulk and on boundaries, Chem. Engng Sci., 41 (1986), 1417-1433.
doi: 10.1016/0009-2509(86)85228-9. |
[24] |
M. Shapiro and H. Brenner, Taylor dispersion of chemically reactive solute in a spatially periodic model of a porous medium, Chem. Engng Sci., 43 (1988), 551-571.
doi: 10.1016/0009-2509(88)87016-7. |
[25] |
G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. of London A, 219 (1953), 186-203.
doi: 10.1098/rspa.1953.0139. |
[26] |
G. I. Taylor, Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular dispersion, Proc. Roy. Soc. London A, 225 (1954), 473-477.
doi: 10.1098/rspa.1954.0216. |
[27] |
S. D. Watt and A. J. Roberts, The accurate dynamic modelling of contaminant dispersion in channels, SIAM J. Appl Math, 55 (1995), 1016-1038.
doi: 10.1137/S0036139993257971. |
[28] |
T. Yamanaka, Projection operator theoretical approach to unsteady convective diffusion phenomena, Journal of Chemical Engineering of Japan, 16 (1983), 29-35.
doi: 10.1252/jcej.16.29. |
[29] |
T. Yamanaka and S. Inui, Taylor dispersion models involving nonlinear irreversible reactions, Journal of Chemical Engineering of Japan, 27 (1994), 434-435.
doi: 10.1252/jcej.27.434. |
show all references
References:
[1] |
R. Aris, On the dispersion of a solute in a fluid flowing through a tube, Proc. Roy. Soc. London A, 235 (1956), 67-77.
doi: 10.1098/rspa.1956.0065. |
[2] |
R. Aris, On the dispersion of a solute in a pulsating flow through a tube, Proc. Roy. Soc. London A, 259 (1960), 370-376.
doi: 10.1098/rspa.1960.0231. |
[3] |
V. Balakotaiah and H. Chang, Dispersion of chemical solutes in cromatographs and reactors, Phil. Trans. R. Soc. Lond. A, 351 (1995), 39-75.
doi: 10.1098/rsta.1995.0025. |
[4] |
B. Bloechle, "On the Taylor Dispersion of Reactive Solutes in a Parallel-Plate Fracture-Matrix System,'' PhD thesis, University of Colorado at Boulder - Department of Applied Mathematics, 2001. |
[5] |
H. Brenner and D. Edwards, "Macrotransport Processes,'' Butterworth, Boston, 1993. |
[6] |
L. H. Dill and H. Brenner, A general theory of Taylor dispersion phenomena. iii, J. Colloid Interface Sci., 85 (1982), 101-117.
doi: 10.1016/0021-9797(82)90239-9. |
[7] |
L. H. Dill and H. Brenner, A general theory of Taylor dispersion phenomena. vi, J. Colloid Interface Sci., 93 (1983), 343-365.
doi: 10.1016/0021-9797(83)90419-8. |
[8] |
K. D. Dorfman and H. Brenner, Generalized Taylor-Aris dispersion in spatially periodic microfluidic networks. chemical reactions, SIAM J. Appl. Math., 63 (2003), 962-986.
doi: 10.1137/S0036139902401872. |
[9] |
S. R. Dungan, M. Shapiro and H. Brenner, Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems, Proc. R. Soc. Lond. A, 429 (1990), 639-671.
doi: 10.1098/rspa.1990.0077. |
[10] |
D. A. Edwards, M. Shapiro and H. Brenner, Dispersion and reaction in two-dimensional model porous media, Phys. Fluids A, 5 (1993), 837-848.
doi: 10.1063/1.858631. |
[11] | |
[12] |
P. Fife and K. Nicholes, Dispersion in flow through small tubes, Proc. Roy. Soc. London A, 344 (1975), 131-145.
doi: 10.1098/rspa.1975.0094. |
[13] |
P. C. Fife, Singular perturbation problems whose degenerate forms have many solutions, Applicable Analysis, 1 (1972), 331-358.
doi: 10.1080/00036817208839022. |
[14] |
Avner Friedman, "Partial Differential Equations,'' Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London,1969. |
[15] |
W. N. Gill, A note on the solution of transient dispersion problems, Proc. Roy. Soc. London A, 298 (1967), 335-339.
doi: 10.1098/rspa.1967.0107. |
[16] |
W. N. Gill and R. Sankarasubramanian, Exact analysis of unsteady convective diffusion, Proc. Roy. Soc. London A, 316 (1970), 341-350.
doi: 10.1098/rspa.1970.0083. |
[17] |
L. E. Johns and A. E. Degance, Dispersion approximations to the multicomponent convective diffusion equation for chemically active systems, Chemical Engineering Science, 30 (1975), 1065-1067.
doi: 10.1016/0009-2509(75)87008-4. |
[18] |
C. Li and E. S. Wright, Modeling chemical reactions in rivers: A three component reaction, Discrete and Continuous Dynamical Systems, 7 (2001), 377-384.
doi: 10.3934/dcds.2001.7.373. |
[19] |
C. Li and E. S. Wright, Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics, Communications on Pure and Applied Analysis, 1 (2002), 77-84. |
[20] |
R. Mauri, Dispersion, convection, and reaction in porous-media, Phys. Fluids, 3 (1991), 743-756.
doi: 10.1063/1.858007. |
[21] |
G. N. Mercer and A. J. Roberts, A center manifold description of contaminant dispersion in channels with varying flow properties, SIAM J. appl. Math, 50 (1990), 1547-1565.
doi: 10.1137/0150091. |
[22] |
M. Pagitsas, A. Nadim and H. Brenner, Projection operator analysis of macrotransport processes, J. Chem. Phys., 84 (1986), 2901-2807.
doi: 10.1063/1.450305. |
[23] |
M. Shapiro and H. Brenner, Taylor dispersion of chemically reactive species: irreversible first order reactions in bulk and on boundaries, Chem. Engng Sci., 41 (1986), 1417-1433.
doi: 10.1016/0009-2509(86)85228-9. |
[24] |
M. Shapiro and H. Brenner, Taylor dispersion of chemically reactive solute in a spatially periodic model of a porous medium, Chem. Engng Sci., 43 (1988), 551-571.
doi: 10.1016/0009-2509(88)87016-7. |
[25] |
G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. of London A, 219 (1953), 186-203.
doi: 10.1098/rspa.1953.0139. |
[26] |
G. I. Taylor, Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular dispersion, Proc. Roy. Soc. London A, 225 (1954), 473-477.
doi: 10.1098/rspa.1954.0216. |
[27] |
S. D. Watt and A. J. Roberts, The accurate dynamic modelling of contaminant dispersion in channels, SIAM J. Appl Math, 55 (1995), 1016-1038.
doi: 10.1137/S0036139993257971. |
[28] |
T. Yamanaka, Projection operator theoretical approach to unsteady convective diffusion phenomena, Journal of Chemical Engineering of Japan, 16 (1983), 29-35.
doi: 10.1252/jcej.16.29. |
[29] |
T. Yamanaka and S. Inui, Taylor dispersion models involving nonlinear irreversible reactions, Journal of Chemical Engineering of Japan, 27 (1994), 434-435.
doi: 10.1252/jcej.27.434. |
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