Aerodynamic diameter
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Aerodynamic diameter is a physical property of a particle in a viscous fluid such as air. In general, particles have irregular shapes with actual geometric diameters that are difficult to measure. Aerodynamic diameter is an expression of a particle's aerodynamic behavior as if it were a perfect sphere with unit-density and diameter equal to the aerodynamic diameter. Such a model has the same terminal settling velocity.
Aerodynamic diameter is commonly applied to particulate pollutants and inhaled drugs to predict where in the respiratory tract such particles will deposit.
Calculations
Drug particles for pulmonary delivery are typically characterized by aerodynamic diameter rather than geometric diameter. The velocity at which the drug settles is proportional to the aerodynamic diameter, da.
\[d_a = d_e(\frac{\rho_p}{\rho_0\chi})^{\frac{1}{2}}=d_s(\frac{\rho_b}{\rho_0})^{\frac{1}{2}}\]
where \[\ d_e\]= equivalent volume diameter \[\ d_s\]= Stokes’s equivalent diameter \[\ \rho_0\] = standard particle density (1g/cc). \[\ \rho_p\] = particle material density \[\ \rho_b\] = bulk material density (less than \(\rho_p\) if porosity) \[\ \chi\] = shape factor.
For spherical species, χ = 1.
Aerodynamic diameter is the diameter of a sphere of unit density (1g/cc) that has the same gravitational settling velocity as the particle in question. It's given as \[d_a=d_p(\frac{\rho_p}{\rho_0})^{\frac{1}{2}} \]
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