A one-dimensional model for ion transport in a flame with two absorbing surfaces

This paper presents numerical and asymptotic analytical solutions for the current-voltage characteristic of a flame using a one-dimensional ion transport model with boundary conditions that include detailed treatment of sheath formation. Non-dimensional conservation equations are presented for the free electron, the hydronium ion, and the electrical potential in a one-dimensional flow field with uniform velocity, electrical mobility, and diffusivity, but allowances are made for non-equilibrium electron temperature. In this study, the size and location of the ion formation region and the electric Reynolds numbers are changed, and their impacts are studied. The model predicts the formation of charged sheaths at both ends of the domain, which are responsible for saturation events that are reliably observed in experiments. A new saturation regime can be made to appear in the model, but its absence from the experiment is argued to have implications on transport near absorbing surfaces in the experiment. For example, the Reynolds numbers at which the current-voltage characteristic converges to the shape and magnitude observed in the experiment implies that the sheaths form in the low-velocity region in the real flow that reduces the apparent Reynolds number.