The Phase Rainbow Refractometry (PRR) technique is developed and applied to measure droplet temperature, size and transient size changes and thereafter evaporation rate simultaneously. The nanoscale size change of a micron-sized droplet exactly describes its transient mass transfer, but is difficult to measure because it is smaller than the resolutions of current size measurement techniques. The accurate measurements of droplet temperature, size and evaporation rate are of great importance to characterize the heat and mass transfer during evaporation/condensation processes. The influence of the droplet refractive index on the Möbius shift is also investigated. For the first-order and second-order rainbows, the application ranges are briefly revisited with the current method. For the fourth-order rainbow, the application range of the Lock approximation is 0.99≤a/c≤1.01 for water droplets.
For the third-order rainbow, it is shown that this is the case for the Lock approximation for water droplets (m=1.333) with aspect ratios in the range of 0.97≤a/c≤1.03.
A threshold value of 5% for ΔD is chosen below which the agreement is considered to be good. For this, a parameter ΔD is defined that measures the disagreement between the two methods. The assessment of applicability ranges of the Lock approximation is obtained by comparing with a VRT simulation for a water droplet with the refractive index m=1.333. When the aspect ratio of a spheroidal droplet is small, approximation expressions for calculating the Möbius shift (i.e., deviation of the geometrical rainbow angle for a spheroidal droplet and that for a spherical droplet) were given by Lock and Können. Vector-ray tracing (VRT) is employed to calculate Möbius shifts of the third-order and the fourth-order rainbows for a spheroidal droplet.
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