Improvements in Numerical Simulations of Isotachophoresis by Using Adaptive Mesh Refinement

Abstract

Isotachophoresis (ITP) belongs to a wide group of analytical techniques named as Electrophoretic separations, which also includes capillary electrophoresis, isoelectric focusing and free flow electrophoresis. Electrophoretic separations are based on the dissimilar mobility of ionic species under the action of an external electric field. In particular in ITP assays, the sample is introduced between a fast leading electrolyte and a slow terminating electrolyte. After applying a difference of electric potential, a low electrical field is created in the leading electrolyte and a high electrical field in the terminating electrolyte. The constituents will completely separate from each other, and concentrate at an equilibrium point, surrounded by sharp electrical field differences. These sharpnesses in the electric field give place to spurious oscillations due to the high local values of the Pèclet number. In order to avoid this oscillations, a large amount of nodes in the mesh are required. The additions of points have to be cleverly done in order to avoid a substantial increase in the computational costs. This is achieved by using an h-adaptive mesh refinement (AMR) method. In this work, we present two examples of ITP in microfluidic chips, in order to show the advantages of using AMR in these kind of problems. Examples were solved by using a generalized numerical model of electrophoresis on microfluidic devices previously presented. The model is based on the set of equations that governs electrical phenomena (Poisson equation), fluid dynamics (Navier-Stokes equations), mass transport (Nerst-Planck equation) and chemical reactions. The numerical simulations were carried out by using PETSc-FEM (Portable Extensible Toolkit for Scientific Computation - Finite Elements Method), in a Python environment using high performance parallel computing and solving techniques based on domain decomposition methods.