Confinement of paramagnetic ions under magnetic field influence: Lorentz- versus concentration gradient force based explanations

Concentration variations observed at circular electrodes with their axis parallel to a magnetic and normal to the gravitational field have previously been attributed elsewhere to the concentration gradient force only. The present paper aims to show that Lorentz force driven convection is a more likely explanation. preprint, finally published in Electrochemistry Communications 9 (2007), 2479–2483 In magnetoelectrochemistry, i.e. in electrochemistry inside a magnetic field, different forces of magnetic origin and their relative importance are actively debated. An overview of the forces under discussion can be found in [1]. Recently, the so called “concentration gradient force” or “paramagnetic gradient force” [1] ~ F∇c = χmB 2 2μ0 ~ ∇c (1) has attracted a great deal of attention, see, e.g. [2–10]. In Eq. (1) χm denotes the molar susceptibility, B the magnitude of the magnetic induction ~ B, μ0 the vacuum permeability and c the concentration of the electroactive species, respectively. ~ F∇c is considered in the literature as a true body force. Main arguments in favor of the existence of this force result from unexpected low deposition rates, e.g. of cobalt ions, in presence of ~ B [5]. A more established and generally accepted force is the Lorentz force ~ FL = ~j × ~ B (2) where ~j is the current density and ~ B the magnetic induction. Changes in mass transfer, i.e. the limiting current density, are usually attributed to convection generated or influenced by the Lorentz force. Sometimes, this is called the “MHD effect”, where MHD is an acronym for magnetohydrodynamics. Especially in cases, where the magnetic induction is normal to the working electrode (WE) surface, Lorentz forces are often assumed to be absent. Even if this might be true in the direct vicinity of the electrode, Lorentz forces can originate anywhere in the cell, when electric and magnetic fields are not strictly parallel. Convection arising from those Lorentz forces will influence the mass transfer at the electrode since it is generally not confined to its origin only. This is even more so in small cells which have to be used in the narrow gaps of electromagnets. Unfortunately, in the vast majority of papers on magnetic field effects on electrochemical reactions, convection is either assumed or neglected a priori but rarely directly observed. Flow visualizations are a valuable step towards flow measurement, but might be misleading if not interpreted with care, as shown by e.g. [11]. However, with the advent of Particle Image Velocimetry (PIV) an easily applicable measurement technique for flow fields is readily available. Interferometry has been used by O’Brien and coworkers, e.g. [2, 12], to measure concentration fields in electrochemical cells under magnetic field influence. If one tries to dodge the considerable experimental effort related with interferometry, synthetic schlieren [13], i.e. background oriented schlieren (BOS) [14], is one of several alternative solutions and especially attractive if a PIV system is already available since it uses the same components and algorithms. White and coworkers [15–18] have shown that Lorentz forces are generated at disc microelectrodes (diameter 6 ≤ d ≤ 250μm) whose axes are parallel to a magnetic field. These azimuthal Lorentz forces are due to radial current densities at the perimeter of the electrodes and drive an azimuthal primary flow which in turn generates secondary flows. Somewhat in contrast to these findings, Leventis et al. [7, 9] claim absence of convection at millielectrodes (diameter 0.5 ≤ d ≤ 3mm). Based on this assumption, Leventis et al. [7, 9] attribute the indeed surprising pinning of buoyant boundary layers in presence of ~ B to the sole action of ~ F∇c.