Numerical Measurement of the Effective Electrical Conductivity of Electrolyte-Gas Bubble Dispersions

Abstract

Bubble formation during water electrolysis is inevitable. Apart from mass and heat transfer limitations, the presence of these bubbles causes a decrease in the local electrical conductivity of the electrolyte, thereby contributing further to the ohmic resistance of the system. Experimental and theoretical studies have shown that the effective electrical conductivity of an electrolyte-gas bubble dispersion depends on the volume fraction of gas bubbles. However, these studies do not provide insight into the dependence of conductivity on the geometric and spatial parameters of the dispersion, such as the size distribution of the bubbles or their spatial arrangement.Experimentally, the conductivity of such dispersions can be measured using the four-electrode conductivity measurement technique. In this talk, I will present a numerical rendition of this experimental technique to measure the conductivity of an electrolyte dispersed with gas bubbles, using the lattice Boltzmann method. The computational nature of the method lends itself well to investigating systems with different bubble size distributions and spatial configurations. The model also offers the flexibility to specify the surface charge density of the dispersed bubbles. The visualization of the ionic flux around these dispersed bubbles provides insights into the motion of ions along the paths of least resistance, and therefore a better understanding of the behavior of such systems.The effective conductivity of bubble dispersions with varying degrees of randomness in their spatial arrangement has been measured, ranging from a regularly packed array of bubbles to a completely random packing. We observed that the numerically measured conductivity deviates from that predicted theoretically at high bubble volume fractions. Moreover, for the same bubble volume fraction, different spatial arrangements yield different values of conductivity, thus highlighting the influence of spatial arrangement of the bubbles on the effective conductivity of the dispersion. Additionally, the spread (standard deviation) of the numerically measured conductivity about the mean value for a given bubble volume fraction is observed to be larger at moderate volume fractions, in comparison to very dilute and densely packed dispersions. This can be explained by the fact that at moderate bubble volume fractions, there is a larger probability for the formation of random bubble clusters that hinder the movement of ions. Such clusters are unlikely in dilute cases and are universal in the dense limit, and as a consequence, less variation in the resulting effective conductivity is observed for the two limiting cases. This furthermore indicates the importance of spatial arrangement on the effective conductivity of such dispersions.