A generalized theoretical model for the response of a phase–Doppler particle analyzer (PDPA) to homogeneous, spherical particles passing at arbitrary locations through a crossed beam measurement volume is presented. The model is based on the arbitrary beam theory [J. Appl. Phys. 64, 1632 (1988)] and is valid for arbitrary particle size and complex refractive index. In contrast to classical Lorenz–Mie theory, the arbitrary beam approach has the added capability of accounting for effects that are due to the presence of the finite-size crossed incident beams that are used in the PDPA measurement technique.
The theoretical model is used to compute phase shift as a function of both the particle position within the measurement volume and particle diameter (1.0 μm < diameter water droplets < 10.0 μm for both resonant and nonresonant sizes) for 30° off-axis receiver configuration. Results indicate that trajectory effects are most pronounced for particle trajectories through the edge of the crossed beam measurement volume on the side opposite the detector. Trajectories through the center of the probe volume gave phase shifts that are nearly identical to those obtained with Lorenz–Mie plane-wave theory. Phase shifts calculated for particle diameters corresponding to electric-wave resonances showed the largest deviation from the corresponding nonresonance diameter phase shifts. Phase shifts for droplets at magnetic wave resonance conditions showed smaller effects, closely following the behavior of nonresonant particle sizes. The major influence of aerosol trajectory on actual particle size determination (for both resonant and nonresonant particle sizes) is that the measured aerosol size distributions will appear broader than the actual size distribution that exists within a spray.
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