Compact adaptive-grid scheme for high numerical resolution simulations of isotachophoresis.

In a previous publication we demonstrated a fast simulation tool for solution of electrophoretic focusing and separation. We here describe the novel mathematical model and numerical algorithms used to create this code. These include the representation of advection-diffusion equations on an adaptive grid, high-resolution discretization of the equations (sixth order compact), a new variational-based approach for controlling the motion of grid points, and new boundary conditions which enable solution in a moving frame of reference. We discuss the advantages of combining a high-resolution discretization with an adaptive grid in accurately resolving sharp interfaces in isotachophoresis, and provide verification against known analytical solutions and comparison with prevailing exiting numerical algorithms.

[1]  Bohuslav Gas,et al.  Simul 5 – Free dynamic simulator of electrophoresis , 2006, Electrophoresis.

[2]  D. Westerlund,et al.  Detectability improvements in capillary zone electrophoresis by combining single capillary isotachophoretic preconcentration and frequency doubled argon ion laser‐induced fluorescence detection , 1998, Electrophoresis.

[3]  J. Beckers,et al.  Isotachophoresis : theory, instrumentation and applications , 1976 .

[4]  W. Thormann,et al.  Dynamic simulator for capillary electrophoresis with in situ calculation of electroosmosis , 1995 .

[5]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[6]  T. Hirokawa,et al.  Isotachophoretic determination of mobility and pKa by means of computer simulation : II. Evaluation of mo and pKa of 65 anions , 1982 .

[7]  D. Saville,et al.  Computer simulation and experimental validation of the electrophoretic behavior of proteins. , 1989, Analytical chemistry.

[8]  O A Palusinski,et al.  Numerical technique and computational procedure for isotachophoresis , 1990, Electrophoresis.

[9]  R. Alberty.  Moving Boundary Systems Formed by Weak Electrolytes. Theory of Simple Systems Formed by Weak Acids and Bases , 1950 .

[10]  F. Kohlrausch,et al.  Ueber Concentrations-Verschiebungen durch Electrolyse im Inneren von Lösungen und Lösungsgemischen , 1897 .

[11]  M Bier,et al.  Electrophoresis: mathematical modeling and computer simulation. , 1983, Science.

[12]  M. Jaros,et al.  Eigenmobilities in background electrolytes for capillary zone electrophoresis: III. Linear theory of electromigration , 2004, Electrophoresis.

[13]  T. Jovin.  Multiphasic zone electrophoresis. I. Steady-state moving-boundary systems formed by different electrolyte combinations. , 1973, Biochemistry.

[14]  Andreas Manz,et al.  Miniaturised isotachophoresis analysis. , 2006, Lab on a chip.

[15]  O. A. Palusinski,et al.  Theory of electrophoretic separations. Part II: Construction of a numerical simulation scheme and its applications , 1986 .

[16]  Moran Bercovici,et al.  Open source simulation tool for electrophoretic stacking, focusing, and separation. , 2009, Journal of chromatography. A.

[17]  W. Spotz.  Formulation and experiments with high‐order compact schemes for nonuniform grids , 1998 .

[18]  T. Hirokawa,et al.  Numerical simulation for capillary electrophoresis: I. Development of a simulation program with high numerical stability , 1998 .

[19]  T. Sounart,et al.  Simulation of electrophoretic separations by the flux-corrected transport method. , 2000, Journal of chromatography. A.

[20]  Y. Chou,et al.  High‐resolution modeling of isotachophoresis and zone electrophoresis , 2008, Electrophoresis.

[21]  J. H. Martens,et al.  Transient modelling of capillary electrophoresis, isotachophoresis , 1997 .

[22]  W. Thormann,et al.  Modeling of the impact of ionic strength on the electroosmotic flow in capillary electrophoresis with uniform and discontinuous buffer systems. , 1998, Analytical chemistry.

[23]  Darwin R. Reyes,et al.  Micro total analysis systems. 2. Analytical standard operations and applications. , 2002, Analytical chemistry.

[24]  P. Righetti,et al.  Numerical algorithms for capillary electrophoresis , 1994 .

[25]  O. A. Palusinski,et al.  Theory of electrophoretic separations. Part I: Formulation of a mathematical model , 1986 .

[26]  L. G. Longsworth,et al.  Transference Numbers by the Method of Moving Boundaries. , 1932 .

[27]  A. Manz,et al.  Micro total analysis systems. Latest advancements and trends. , 2006, Analytical chemistry.

[28]  M. Breadmore,et al.  High-resolution computer simulations of stacking of weak bases using a transient pH boundary in capillary electrophoresis. 1. Concept and impact of sample ionic strength. , 2006, Analytical chemistry.

[29]  Juan G Santiago,et al.  Sample zone dynamics in peak mode isotachophoresis. , 2008, Analytical chemistry.

[30]  G. Moore.  Theory of isotachophoresis development of concentration boundaries , 1975 .

[31]  G. Guiochon,et al.  High-resolution modeling of capillary zone electrophoresis and isotachophoresis , 1991 .