Mathematical model for transient isoelectric focusing of simple ampholytes

Theory of ion transport with fast acid-base equilibrations in bioelectrochemical systems

Bioelectrochemical systems recover valuable components and energy in the form of hydrogen or electricity from aqueous organic streams. We derive a one-dimensional steady-state model for ion transport in a bioelectrochemical system, with the ions subject to diffusional and electrical forces. Since most of the ionic species can undergo acid-base reactions, ion transport is combined in our model with infinitely fast ion acid-base equilibrations. The model describes the current-induced ammonia evaporation and recovery at the cathode side of a bioelectrochemical system that runs on an organic stream containing ammonium ions. We identify that the rate of ammonia evaporation depends not only on the current but also on the flow rate of gas in the cathode chamber, the diffusion of ammonia from the cathode back into the anode chamber, through the ion exchange membrane placed in between, and the membrane charge density.

Steady state electrolysis and isoelectric focusing

The properties of pH gradients formed by stationary electrolysis of weak mobile or fixed electrolytes are analyzed. The model uses the appropriate balance equations and those of chemical equilibria. It is shown how the equation of the current density has to be modified for considering that fraction of current that is associated with the diffusion of neutral buffer molecules within a pH gradient. Furthermore it is shown that the pH gradients themselves give rise to water production within the gradient and that essential properties of the steady state are related to chemical reactions between the electrolyte constituents. The differential equations describing the gradients of the concentration of a given component, the pH, conductivity and potential are explicitly formulated in relation to those reactions. The equations are solved numerically and the significance of the results for isoelectric focusing is discussed. The experimental conditions to reach shallow and smooth pH gradients exhibiting sufficient ionic strength are formulated.

pH gradients generated by polyprotic buffers. I. Theory and computer simulation

This paper presents the general equations for computing pH, dissociation coefficients, buffering power and ionic strength of pure polyelectrolyte solutions (polyacids, polybases and zwitterionic species with any number of dissociable groups) and mixtures of any number of these species. A program has been written for simulating the behaviour of mixtures containing up to 50 species (including buffers and titrants), each of them with up to 10 dissociable groups. This allowed one to check the equations with the available data on a few oligoprotic species.

Generalized finite element solution to one-dimensional flux problems

A finite element numerical solution to the general one-dimensional flow equation is derived in a form that provides a convenient and general means to simulate a wide variety of one-dimensional flow techniques of interest to biological scientists, e.g., ultracentrifugation, electrophoresis, chromatography, etc. Diverse physical models defined in terms of column geometry, solute interactions, and the dependence of transport parameters on column position, time, or concentrations of one or more solutes, can be accommodated. A particularly useful aspect of the formulation is that a wide variety of boundary conditions can be simply applied to the end result, without rederivation of the solution for each new case. The numerical solution is expressed as matrix equations that are sufficiently general so that incorporation of particular models can be effected by substitution of appropriate quantities into the final result.

Electrophoresis: mathematical modeling and computer simulation

A mathematical model of electrophoretic separation processes has been developed and adapted for computer simulations. The model is used to predict the characteristic behavior of a variety of electrophoretic techniques from a knowledge of chemical equilibria and physical transport phenomena. The model provides a unifying basis for a rational classification of all electrophoretic processes.