Electrolyte solutes drift velocities

In the binary-electrolyte experiments carried out at large, constant cell potentials, the cell current is ohmically limited. If the conductivity of the solution is proportional to the concentration of electrolyte, the current density at a given overpotential is then proportional to Cb. Under this regime, the concentration cancels out of Eq. (2.3), and the velocity is proportional to the applied potential. For this special case, the velocity can be expressed in terms of the anion drift velocity [27, 28]. For a binary solution, this is equivalent to replacing (1 — t+) by t and i by the ohmically limited current density. 

In an electrolytic solution the electrical current is transported by the ions. When an electrical field E is applied, ions migrate with a constant drift velocity vd ... 

For weak electrolytes, at small concentrations, the electrical conductivity is almost proportional to the electrolyte concentration. For higher concentrations, the degree of dissociation decreases. Consequently, the electrical conductivity reaches a maximum as a function of the electrolyte concentration. For strong electrolytes this maximum also exists, because when the electrolyte concentration is increased, the ionic interaction becomes stronger. This is illustrated for a NaOH solution in Fig. 3.6. In this figure the influence of the electrolyte temperature on the conductivity can be seen. The temperature mainly influences the viscosity of the electrolyte, which influences the drift velocity of the ions. Other effects are the changes in the dielectric function of water and the degree of dissociation of the electrolyte. 

When two electrodes immersed in an electrolyte solution are connected to a power supply, an electric field of strength E is created between them. In this field, a directed mass transport occurs. Anions drift to the positive pole while cations drift to the negative pole. Because the ion velocity, v, is strictly proportional to the electric field strength, the mobility of ions, u (cm V s ), is an independent characteristic ... 

The dominant forces that determine deviations from ideal behaviour of transport processes in electrolytes are the relaxation and electrophoretic forces [16]. The first of these forces was discussed by Debye [6, 17]. When the equilibrium ionic distribution is perturbed by some external force in an ionic solution, electrostatic forces appear, which will tend to restore the equilibrium distribution of the ions. There is also a hydrodynamic effect. It was first discussed by Onsager [2, 3]. Different ions in a solution will respond differently to external forces, and will thus tend to have different drift velocities The hydrodynamic (friction) forces, mediated by the solvent, will tend to equalize these velocities. The electrophoretic ( hydrodynamic) correction can be evaluated by means ofNavier-Stokes equation [18, 19]. Calculating the relaxation effect requires the evaluation of the electrostatic drag of the ions by their surroundings. The time lag of this effect is known as the Debye relaxation time. 

Consider a solution of an electrolyte solute with one cation and one anion. Let the mean velocity of cations be denoted by v+ and the mean velocity of anions be denoted by v. At equilibrium these mean velocities vanish because as many ions will be moving in a given direction as in the opposite direction. In the presence of an electric field v+ and v will be nonzero, in which case they are called drift velocities. The current density is the sum of a cation contribution and an anion contribution. On the average cations no farther from a fixed plane than a distance equal to v+ times 1 second will pass in 1 second. For unit area, the number of cations passing the fixed plane per second is... 

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