Analysis of breakthrough dynamics in rectangular channels of arbitrary aspect ratio

Adsorption in rectangular and square channels is attracting great interest from various fields of research. In particular, in large scale applications the main interest is in the prediction of the performance of monoliths composed of several individual channels, while, in the field of microengineering, particular interest is in the separation performance of individual channels for the development of small-scale analytical devices, that is, the lab on a chip. The design of all these units is based on the accurate representation of the breakthrough dynamics and the performance of the unit can be represented conveniently by the height equivalent to a theoretical plate (HETP). General simplified equations for the calculation of the HETP are derived for rectangular channels of arbitrary aspect ratio. The dispersion in the solid phase is corrected to take into account the effect of the adsorptive capacity in the four corners of the solid phase. A corrected thickness of the walls of the channels is predicted and shown to yield the exact HETP by comparing the analytical solution to the full 3-D numerical solution. Numerical simulations are presented for representative gas and liquid systems.

[1]  G. Spangler.  Relationships for modeling the performance of rectangular gas chromatographic columns , 2001 .

[2]  G. Baron,et al.  Chromatographic explanation for the side-wall induced band broadening in pressure-driven and shear-driven flows through channels with a high aspect-ratio rectangular cross-section. , 2002, Journal of chromatography. A.

[3]  D. Ruthven.  Past Progress and Future Challenges in Adsorption Research , 2000 .

[4]  G. Baron,et al.  Computational fluid dynamics simulations yielding guidelines for the ideal internal structure of monolithic liquid chromatography columns. , 2003, Journal of chromatography. A.

[5]  S. Terry,et al.  A gas chromatographic air analyzer fabricated on a silicon wafer , 1979, IEEE Transactions on Electron Devices.

[6]  E. S. Kolesar,et al.  Silicon-micromachined gas chromatography system used to separate and detect ammonia and nitrogen dioxide. I. Design, fabrication, and integration of the gas chromatography system , 1994 .

[7]  Octave Levenspiel,et al.  Engineering Flow and Heat Exchange , 1984 .

[8]  D. Ruthven,et al.  Performance of a parallel passage adsorbent contactor , 1997 .

[9]  J. C. Giddings,et al.  Capillary liquid chromatography in field flow fractionation-type channels , 1983 .

[10]  R. Aris,et al.  On the dispersion of a solute by diffusion, convection and exchange between phases , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  F. Regnier,et al.  Analysis of channel-geometry effects on separation efficiency in rectangular-capillary electrochromatography columns. , 2000, Journal of chromatography. A.

[13]  R. J. Cornish,et al.  Flow in a Pipe of Rectangular Cross-Section , 1928 .

[14]  Stefano Brandani,et al.  Adsorption Kinetics and Dynamic Behavior of a Carbon Monolith , 2004 .

[15]  M. Golay.  The height equivalent to a theoretical plate of retentionless rectangular tubes , 1981 .

[16]  D. Leighton,et al.  Dispersion in large aspect ratio microchannels for open-channel liquid chromatography. , 2003, Analytical chemistry.

[17]  Glenn E. Spangler.  Height Equivalent to a Theoretical Plate Theory for Rectangular GC Columns , 1998 .

[18]  P. C. Chatwin,et al.  The effect of aspect ratio on longitudinal diffusivity in rectangular channels , 1982, Journal of Fluid Mechanics.

[19]  D. Ruthven,et al.  Moments analysis of the zero length column method , 1996 .

[20]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.