Modeling and high performance simulation of electrophoretic techniques in microfluidic chips

Electrophoretic separations comprise a group of analytical techniques such as capillary zone electrophoresis, isoelectric focusing, isotachophoresis, and free flow electrophoresis. These techniques have been miniaturized in the last years and now represent one of the most important applications of the lab-on-a-chip technology. A 3D and time-dependent numerical model of electrophoresis on microfluidic devices is presented. The model is based on the set of equations that governs electrical phenomena, fluid dynamics, mass transport, and chemical reactions. The relationship between the buffer characteristics (ionic strength and pH) and surface potential of channel walls is taken into consideration. Numerical calculations were performed by using PETSc-FEM, in a Python environment, employing high performance parallel computing. The method includes a set of last generation preconditioners and solvers, especially addressed to 3D microfluidic problems, which significantly improve the numerical efficiency in comparison with typical commercial software for multiphysics. In this work, after discussing two validation examples, the numerical prototyping of a microfluidic chip for two-dimensional electrophoresis is presented.

[1]  Harry Svensson,et al.  Isoelectric Fractionation, Analysis, and Characterization of Ampholytes in Natural pH Gradients. I. The Differential Equation of Solute Concentrations at a Steady State and its Solution for Simple Cases. , 1961 .

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

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

[4]  R. J. Hunter Foundations of Colloid Science , 1987 .

[5]  A. Manz,et al.  Miniaturized total chemical analysis systems: A novel concept for chemical sensing , 1990 .

[6]  S. Mittal,et al.  Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements , 1992 .

[7]  A. Berg,et al.  Micro Total Analysis Systems , 1995 .

[8]  Howard H. Hu,et al.  Numerical simulation of electroosmotic flow. , 1998, Analytical chemistry.

[9]  S. Jacobson,et al.  Computer simulations of electrokinetic transport in microfabricated channel structures. , 1998, Analytical chemistry.

[10]  Tayfun E. Tezduyar,et al.  Finite element stabilization parameters computed from element matrices and vectors , 2000 .

[11]  Mario A. Storti,et al.  A parallel finite element program on a Beowulf cluster , 2000 .

[12]  S. Jacobson,et al.  Computer simulations of electrokinetic injection techniques in microfluidic devices , 2000, Analytical chemistry.

[13]  T. Kenny,et al.  Electroosmotic capillary flow with nonuniform zeta potential , 2000, Analytical Chemistry.

[14]  H. Girault,et al.  Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimensions , 2000, Analytical chemistry.

[15]  Darwin R. Reyes,et al.  Micro total analysis systems. 1. Introduction, theory, and technology. , 2002, Analytical chemistry.

[16]  J. M. MacInnes,et al.  Computation of reacting electrokinetic flow in microchannel geometries , 2002 .

[17]  I. Arnaud,et al.  Finite element simulation of Off‐Gel™ buffering , 2002 .

[18]  David E. Keyes,et al.  Nonlinearly Preconditioned Inexact Newton Algorithms , 2002, SIAM J. Sci. Comput..

[19]  Amy E Herr,et al.  On-chip coupling of isoelectric focusing and free solution electrophoresis for multidimensional separations. , 2003, Analytical chemistry.

[20]  J. A. Deiber,et al.  Modeling the zeta potential of silica capillaries in relation to the background electrolyte composition , 2003, Electrophoresis.

[21]  Athonu Chatterjee,et al.  Generalized numerical formulations for multi-physics microfluidics-type applications , 2003 .

[22]  R. Allen,et al.  Prediction of electrokinetic and pressure flow in a microchannel T-junction , 2003 .

[23]  Dirk Janasek,et al.  Sub-second isoelectric focusing in free flow using a microfluidic device. , 2003, Lab on a chip.

[24]  Armand Ajdari,et al.  Generalized Onsager relations for electrokinetic effects in anisotropic and heterogeneous geometries. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Dongqing Li Electrokinetics in Microfluidics , 2004 .

[26]  E. Hasselbrink,et al.  Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations , 2004, Electrophoresis.

[27]  David Erickson,et al.  Towards numerical prototyping of labs-on-chip: modeling for integrated microfluidic devices , 2005 .

[28]  Dietrich Kohlheyer,et al.  Free-flow zone electrophoresis and isoelectric focusing using a microfabricated glass device with ion permeable membranes. , 2006, Lab on a chip.

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

[30]  Juan G. Santiago,et al.  Convective instability of electrokinetic flows in a cross-shaped microchannel , 2006, Journal of Fluid Mechanics.

[31]  W Thormann,et al.  Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing. , 2007, Journal of chromatography. A.

[32]  T. Sounart,et al.  Lubrication theory for electro-osmotic flow in a non-uniform electrolyte , 2007, Journal of Fluid Mechanics.

[33]  J. Landers Handbook of capillary and microchip electrophoresis and associated microtechniques , 2007 .

[34]  Klavs F Jensen,et al.  Cascaded free-flow isoelectric focusing for improved focusing speed and resolution. , 2007, Analytical chemistry.

[35]  Prashanta Dutta,et al.  Modeling and simulation of IEF in 2‐D microgeometries , 2007, Electrophoresis.

[36]  Claudio L. A. Berli,et al.  Equivalent circuit modeling of electrokinetically driven analytical microsystems , 2008 .

[37]  Youyuan Peng,et al.  Recent innovations in protein separation on microchips by electrophoretic methods , 2008, Electrophoresis.

[38]  William B. Zimmerman,et al.  On slip velocity boundary conditions for electroosmotic flow near sharp corners , 2008 .

[39]  Shuang Yang,et al.  Optimization of sample transfer in two-dimensional microfluidic separation systems. , 2008, Lab on a chip.

[40]  Mario A. Storti,et al.  MPI for Python: Performance improvements and MPI-2 extensions , 2008, J. Parallel Distributed Comput..

[41]  Wei-Cheng Tian,et al.  Microfluidics for Biological Applications , 2008 .

[42]  D. Kohlheyer,et al.  Miniaturizing free‐flow electrophoresis – a critical review , 2008, Electrophoresis.

[43]  P. Spitéri,et al.  Parallel asynchronous iterations for the solution of a 3D continuous flow electrophoresis problem , 2008 .

[44]  Bingcheng Lin,et al.  Electrophoretic separations on microfluidic chips , 2007, Journal of Chromatography A.

[45]  G. Wiederschain Handbook of capillary and microchip electrophoresis and associated microtechniques (3rd Edn.) , 2008, Biochemistry (Moscow).

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

[47]  Samuel Tia,et al.  On-chip technologies for multidimensional separations. , 2009, Lab on a chip.

[48]  Greg J. Sommer,et al.  IEF in microfluidic devices , 2009, Electrophoresis.

[49]  Lisandro Dalcin,et al.  Strong coupling strategy for fluid–structure interaction problems in supersonic regime via fixed point iteration , 2009 .

[50]  R. T. Turgeon,et al.  Micro free-flow electrophoresis: theory and applications , 2009, Analytical and bioanalytical chemistry.

[51]  Lisandro Dalcin,et al.  High performance simulations of electrokinetic flow and transport in microfluidic chips , 2009, Computer Methods in Applied Mechanics and Engineering.

[52]  Dominik P. J. Barz Comprehensive model of electrokinetic flow and migration in microchannels with conductivity gradients , 2009 .