A complete mathematical model for electromigration in paper-based analytical devices is derived, based on differential equations describing the motion of fluids by pressure sources and EOF, the transport of charged chemical species, and the electric potential distribution. The porous medium created by the cellulose fibers is considered like a network of tortuous capillaries and represented by macroscopic parameters following an effective medium approach. The equations are obtained starting from their open-channel counterparts, applying scaling laws and, where necessary, including additional terms. With this approach, effective parameters are derived, describing diffusion, mobility, and conductivity for porous media. While the foundations of these phenomena can be found in previous reports, here, all the contributions are analyzed systematically and provided in a comprehensive way. Moreover, a novel electrophoretically driven dispersive transport mechanism in porous materials is proposed. Results of the numerical implementation of the mathematical model are compared with experimental data, showing good agreement and supporting the validity of the proposed model. Finally, the model succeeds in simulating a challenging case of free-flow electrophoresis in paper, involving capillary flow and electrophoretic transport developed in a 2D geometry.Abbreviations: EDMSD, electrophoretically driven mechanical solute dispersion; µPAD, microfluidic paper-based analytical device; FEM, finite element method; FFE, free-flow\penalty -\@M electrophoresis; FFEIEF, free-flow IEF; FVM, finite volume method; FWHM, full width at half maximum; LE, leading electrolyte; PDE, partial differential equation; TE, trailing electrolyte; ZE, zone electrophoresis of glass, silicon, or polymers [7,8]. The evolution of the open-channel electrophoresis was followed by proper mathematical descriptions of the involved phenomena, required for deep understanding of the methods, for prediction of the outcome of experiments, and for rational design of novel electrophoretic devices [9]. 1D CZE, ITP, and IEF problems where successfully modeled using nonlinear partial differential equations (PDE) describing the charge and mass conservation principles [10]. By using this approach, several software tools have been developed to simulate specific 1D problems [11][12][13]. Improvements to these models were reported in the past decade, appealing to more complex formulations for particular physicochemical conditions [14], and electrically driven flows [15]. Furthermore, particular applications like IEF in nano-channels [16], 2D IEF [17,18], free-flow IEF (FFIEF) [19], and even FFIEF combined with CZE in a 2D lab-on-a-chip device [20] were successfully modeled with computational tools based on the finite element (FEM) or finite volume (FVM) methods. Also, a commercial Color online: See article online to view Figs. 2 and 3 in color.
