Theory of electrophoretic separations. Part II: Construction of a numerical simulation scheme and its applications

Abstract

The mathematical model outlined in Part I is recast in a form suitable for numerical computation. The spatial derivatives are replaced by finite-difference expressions, which leads to a set of ordinary differential equations coupled to a set of nonlinear algebraic relations. This system is solved using existing integration techniques. The resulting algorithm simulates the characteristic behavior of the classical modes of electrophoresis, which is shown by examples involving moving boundary electrophoresis and isoelectric focusing. In the first example two different integration schemes are used and their accuracy and stability investigated. The second example illustrates the versatility of the methodology. 0. SCOPEIn the model presented in Part I (Saville and Palusinski), the electrophoresis of amphoteric compounds is described by a set of partial differential equations coupled to a system of algebraic equations. Separation of sample components arises from interactions between the chemical equilibria and the transport processes. These interactions alter the effective mobilities of the various species and induce them to separate under the action of the electric field in nonequilibrium processes such as isotachophoresis. In equilibrium processes such as isoelectric focusing, the action of the field produces a pH gradient and the amphoteric constituents move to positions where they are isoelectric. In either case, the evolution of the process is best followed by numerical methods. The purpose of this paper is twofold: 1. To show how the mathematical model derived in Part I can be expressed in a form suitable for numerical computation. 2.To demonstrate the model depicts the detailed characteristics of electrophoretic processes.The numerical algorithm selected employs a five-point finite-difference expression to approximate the spatial derivatives at a set of mesh points. This converts the set of partial differential equations into a set of ordinary differential equations describing the temporal evolution of the concentration fields at each mesh point. These equations can be integrated using any one of a variety of schemes for solving sets of firstorder ordinary differential equations. Boundary conditions at either end of a separation column are incorporated by adjusting the form of the finite-difference expressions at the boundary points. In a similar fashion, the algorithm can easily be adapted for simulation of novel separation methods such as the use of immobilized ampholytes, molecular sieving, or ion-selective membranes at the boundaries. CONCLUSIONS AND SIGNIFICANCEThe implementation of the algorithm describing electrophoretic transport processes is illustrated by simulating moving boundary electrophoresis and isoelectric focusing with immobilized species. Both examples are intended to illustrate particular electrophoretic processes using rather simple systems. Attention concentrates on the essential characteristics of a particular mode, For the isoelectric focusing example, the central feature is the migration...

High‐resolution computer simulation of electrophoretic mobilization in isoelectric focusing

“…The isothermal model is 1-D, based upon the principles of electroneutrality and conservation of mass and charge, and represents an extension of the model which was developed at the University of Arizona [26][27][28]. It provides data that are comparable to those obtained with SIMUL5 [29], a recently developed model which is available on the net (www.natur.cuni.cz/gas).…”

Micro freef‐low IEF enhanced by active cooling and functionalized gels

“…In order to simplify the system of equations; this diffusive current was assumed to be negligible compared to the current due to the applied field. To validate the model, previously published results [24,25] were reproduced.…”

“…A 1-D free-flow IEF model was developed similar to Bier et al [24][25][26]. Briefly, for an idealized ionic species undergoing electrophoresis, the general time-dependent 1-D formulation is given by the following system of equations:…”

Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

“…Component fluxes are computed on the basis of electromigration, diffusion and convection (imposed flow and/or electroosmosis). The models are composed of a set of balance laws governing the transport of components in electrophoretic separations [1,37,38,40,41,43] and comprise a coupled set of non-linear partial differential equations describing the appropriate balance laws and algebraic equations describing chemical equilibria. The statement of conservation of charge includes a term for the diffusion current (for importance of diffusion current compare data of [133] with those of [134]).…”

“…This is illustrated here with ZE, ITP, IEF and EKC separation examples. The data shown were produced with GENTRANS, the simulator based on the work of Bier, Mosher, Thormann, Breadmore and coworkers [1,37,38,44,[49][50][51][52][53][54]75].…”