## R

contrasts with the above. There must therefore be a particle diameter for which both processes have a combined minimum value; this occurs with particles approximately 0.5 pm in diameter. Particles of this size have the minimum probability of deposition in the upper respiratory tract.

### Inertial impaction

When, during breathing, the airflow suddenly changes direction, a drug particle will continue in its original direction of flow owing to its inertia. In this way the particle may impact on the channel wall. In curved tubes the particle in an airstream which experiences a sudden bend suffers a similar fate, and the effective stopping distance at right-angles to the direction of travel, hs, is given by ptp sin 0

The probability of deposition by sedimentation is proportional to this ratio; the closer pt t is to 2R/cos y, the greater the likelihood of deposition by this mechanism. If the particles are evenly distributed over the cross-section of an airstream, it is theoretically possible to calculate the probability of deposition in tubular airways and in a spherical alveolus. Individual tubes are of course randomly positioned with reference to the horizontal and therefore an average value of y is used. Airflow is also not always laminar, and orderly deposition will not always occur, but in spite of these problems the following calculations of percentage sedimentation (S) may usefully be quoted. If S = 55% when d = 2 pm and the deposition diameter is 1.0 pm, then for 1 pm particles S = 29%, and for 0.5 pm particles S = 10%. Sedimentation, of course, reduces in importance as the drug particle size decreases.

### Diffusion

The effectiveness of deposition by diffusion increases as particle size is reduced, which where p is the velocity of the airstream with particles approaching a bend of angle 0. The term p sin 0 is therefore a component of initial particle velocity at right-angles to the direction of airflow. The probability of inertial deposition, I, is proportional to the ratio of stopping distance, hs, to the radius, R, of the airway; that is hs ptp sin 0 T- s--^ (9.28)

0 0