Continuum theory of spherical electrostatic probes (frozen chemistry)

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Abstract
Continuum theory is adopted to describe the steady, spherically symmetric flow of an unbounded expanse of quiescent, slightly ionized fluid about a perfectly catalytic conductor. The negative charge carrier is taken to be an electron, the potential bias of the probe φP is taken to be negative, and recombination and ionization effects are taken to be negligible. Matched asymptotic expansions are used to study the limit of small Debye number ∈, where ∈ is the ratio of Debye length to conductor radius. The current collected at the probe is found for three ranges of applied potential: small bias, including φp = O(1); moderate bias in which φP = O(log(1/∈)); and large bias in which φP = O(log(1/∈);). The current collected does not saturate (become independent of φP) for the range of c studied here; however, for φP, the current collected remains of order unity while the potential bias varies over several orders of magnitude. The previous asymptotic treatments of this problem, principally due to Su & Lam and to Cohen, are critically reviewed and compared with the results developed here.