Adaptive mesh simulations of ionic systems in microcapillaries based on the estimation of transport times

We present results of testing an empirical algorithm of mesh adaptation for modeling of spatially one-dimensional reaction-transport systems with initially separated components and large moving gradients. The algorithm combines newly developed procedures of r-refinement and standard FEMLAB procedures. The developed method uses an expansion of a dense mesh in neighborhoods of localized large gradients and estimates the mesh adaptation interval (based on the evaluation of transport times). The size of the neighborhood is dynamically controlled. The adaptation method has been tested on systems of parabolic–elliptic PDEs with extremely large moving gradients of concentrations and electric potential. We have found that CPU time requirements are comparable to other mesh adaptation solvers. The simplicity of the empirical procedure of the mesh adaptation and its easy implementation in standard dynamic solvers represent main advantages of the proposed method.The studied system, called an “electrolyte diode”, is described by four mass balances of the electrolyte components (parabolic PDEs) and by Poisson equation of electrostatics (an elliptic PDE). Dynamics of formation of open and closed modes of the electrolyte diode are described and current–voltage characteristics are explained. The results obtained with the developed solver agree with the results of steady state analysis.Our tests prove that the proposed algorithm of mesh adaptation can be used in modeling of microfluidics application, e.g., DNA chips, capillary electrophoresis and isoelectrical focusing, where formation of extremely large gradients of electric potential and concentrations of the electrolyte components is expected.