### Abstract

An alternative method, called the Martin-Synge algorithm, is introduced to calculate numerical solutions of the equilibrium-dispersive (ED) model. The developed algorithm is based on the earlier work of Friday and Levan [1] and on the continuous plate model of Martin and Synge [2]. The column is divided evenly into a series of virtual vessels in which a simplified mass balance equation is solved accurately by the Runge-Kutta-Fehlberg method and the elution profile is given by the numerical solution for the last vessel. The dispersion of the compound during the elution process is controlled by adjusting the number of virtual vessels into which the column is divided. Solving the ED model under linear conditions with this method gives exactly the same profile as the analytical solution of the Martin-Synge plate model. The Martin-Synge method gives better results than the Rouchon method (1) when the isotherms involved are sigmoidal or anti-Langmuir; and, more importantly, (2) in the case of multi-component problems. Finally, the Martin-Synge method proves to be more robust and faster than the OCFE method that, until now, was considered to be one of the most robust and accurate algorithms. The developed algorithm was used for the calculation of the coefficients of the isotherm of butyl benzoate by the inverse method, using a simplex optimization algorithm.

Original language | English |
---|---|

Pages (from-to) | 8127-8135 |

Number of pages | 9 |

Journal | Journal of Chromatography A |

Volume | 1217 |

Issue number | 52 |

DOIs | |

Publication status | Published - Dec 24 2010 |

### Fingerprint

### Keywords

- Equilibrium-dispersive model
- Inverse method
- Martin-Synge plate model
- Mass balance equation

### ASJC Scopus subject areas

- Analytical Chemistry
- Organic Chemistry
- Biochemistry

### Cite this

*Journal of Chromatography A*,

*1217*(52), 8127-8135. https://doi.org/10.1016/j.chroma.2010.10.035

**Martin-Synge algorithm for the solution of equilibrium-dispersive model of liquid chromatography.** / Horváth, K.; Fairchild, Jacob N.; Kaczmarski, Krzysztof; Guiochon, Georges.

Research output: Contribution to journal › Article

*Journal of Chromatography A*, vol. 1217, no. 52, pp. 8127-8135. https://doi.org/10.1016/j.chroma.2010.10.035

}

TY - JOUR

T1 - Martin-Synge algorithm for the solution of equilibrium-dispersive model of liquid chromatography

AU - Horváth, K.

AU - Fairchild, Jacob N.

AU - Kaczmarski, Krzysztof

AU - Guiochon, Georges

PY - 2010/12/24

Y1 - 2010/12/24

N2 - An alternative method, called the Martin-Synge algorithm, is introduced to calculate numerical solutions of the equilibrium-dispersive (ED) model. The developed algorithm is based on the earlier work of Friday and Levan [1] and on the continuous plate model of Martin and Synge [2]. The column is divided evenly into a series of virtual vessels in which a simplified mass balance equation is solved accurately by the Runge-Kutta-Fehlberg method and the elution profile is given by the numerical solution for the last vessel. The dispersion of the compound during the elution process is controlled by adjusting the number of virtual vessels into which the column is divided. Solving the ED model under linear conditions with this method gives exactly the same profile as the analytical solution of the Martin-Synge plate model. The Martin-Synge method gives better results than the Rouchon method (1) when the isotherms involved are sigmoidal or anti-Langmuir; and, more importantly, (2) in the case of multi-component problems. Finally, the Martin-Synge method proves to be more robust and faster than the OCFE method that, until now, was considered to be one of the most robust and accurate algorithms. The developed algorithm was used for the calculation of the coefficients of the isotherm of butyl benzoate by the inverse method, using a simplex optimization algorithm.

AB - An alternative method, called the Martin-Synge algorithm, is introduced to calculate numerical solutions of the equilibrium-dispersive (ED) model. The developed algorithm is based on the earlier work of Friday and Levan [1] and on the continuous plate model of Martin and Synge [2]. The column is divided evenly into a series of virtual vessels in which a simplified mass balance equation is solved accurately by the Runge-Kutta-Fehlberg method and the elution profile is given by the numerical solution for the last vessel. The dispersion of the compound during the elution process is controlled by adjusting the number of virtual vessels into which the column is divided. Solving the ED model under linear conditions with this method gives exactly the same profile as the analytical solution of the Martin-Synge plate model. The Martin-Synge method gives better results than the Rouchon method (1) when the isotherms involved are sigmoidal or anti-Langmuir; and, more importantly, (2) in the case of multi-component problems. Finally, the Martin-Synge method proves to be more robust and faster than the OCFE method that, until now, was considered to be one of the most robust and accurate algorithms. The developed algorithm was used for the calculation of the coefficients of the isotherm of butyl benzoate by the inverse method, using a simplex optimization algorithm.

KW - Equilibrium-dispersive model

KW - Inverse method

KW - Martin-Synge plate model

KW - Mass balance equation

UR - http://www.scopus.com/inward/record.url?scp=78649887154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649887154&partnerID=8YFLogxK

U2 - 10.1016/j.chroma.2010.10.035

DO - 10.1016/j.chroma.2010.10.035

M3 - Article

C2 - 21092975

AN - SCOPUS:78649887154

VL - 1217

SP - 8127

EP - 8135

JO - Journal of Chromatography

JF - Journal of Chromatography

SN - 0021-9673

IS - 52

ER -