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We analyze the escape of Brownian particles over potential barriers using theFokker-Planck equation in a similar way to that of Chandrasekhar (Rev. ModernPhys., 1943), deriving a formula for the particle deposition velocity to asurface as a function of the particle response time. For very small particleresponse times, the particle deposition velocity reduces to that obtained usinga quasi-steady solution of Smoluchowski's equation and for very large particleresponse times, the deposition velocity corresponds to that based on thetransition state method (E. Wigner, Trans. Faraday Soc., 1938).

Evaluation of the rate constant and deposition velocity for the escape of Brownian particles over potential barriers