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].

Coping with Asthma

Coping with Asthma

If you suffer with asthma, you will no doubt be familiar with the uncomfortable sensations as your bronchial tubes begin to narrow and your muscles around them start to tighten. A sticky mucus known as phlegm begins to produce and increase within your bronchial tubes and you begin to wheeze, cough and struggle to breathe.

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