Modeling electronegative impurity concentrations in liquid argon detectors

We present a simple mathematical model of the dynamics of impurity distribution in liquid argon detectors. This model considers the dominant sources, sinks, and transport of the impurity between and within the gas and liquid phases of a large detector. We use this model to extract Henry's coefficients for oxygen and water from the time dependence of the impurity concentration in the liquid phase, while the gas in the detector volume is being purified. We find that Henry's coefficient for oxygen in liquid argon is 0.9, in agreement with previous measurements by other methods. For water we obtain the first measured value of Henry's coefficient in liquid argon of ~ 1.0. This value is in reasonable agreement with the value estimated from the ideal solution theory using an extrapolation of the water vapor pressure.