Deposition by random diffusion occurs as a consequence of thermally driven Brownian motion. The root mean square displacement (A) of a particle moving by diffusion is given by [240]:

where Dp is its diffusivity and t is the residence time of the particle in the lung. For a particle with diameter d in a fluid of viscosity h, Dp is given by the Stokes -

Einstein equation:

where k is the Boltzmann constant, T is the absolute temperature, and Cs is the slip correction factor. Combining Eqs. (5) and (6), one finds diffusional transport is proportional to (t/d)05, where t is the residence time of the particle in the lung and d is the geometric diameter of the particle. Note that diffusional transport is independent of particle density, such that aerodynamic diameter is not a significant parameter in deposition by diffusion. Therefore, increasing particle residence time and decreasing geometric size increases the probability that a particle will deposit by diffusional transport. However, diffusion is only an effective deposition mechanism for submicrometer-sized particles (< 0.5 mm) [221]. Additionally, low flowrates are necessary for diffusion to be significant; therefore, deposition by diffusion occurs mainly in the alveolar region of the lung, where velocities are typically on the order of 0-0.3 cm/sec (compared, for example, to velocities of 390 cm/sec in the trachea. 52-430 cm/sec in the bronchi, and 1.9-14 cm/sec in the bronchioles at a flowrate of 60L/sec) [241]. Increasing tidal volume (at a given flowrate) and/or breath holding both increase the residence time of particles within the smaller airways, thus increasing diffusional deposition [242-244].

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