Polarization-dependent LIF/Mie ratio for sizing of micrometric ethanol droplets doped with Nile red
Matthias Koegl, Hongfei Dai, Kevin Baderschneider, Hannah Ulrich, Lars Zigan
Abstract
The present study deals with droplet sizing based on laser-induced fluorescence (LIF) and Mie scattering for varied polarization of the utilized laser (parallel or perpendicular). The polarization-dependent LIF/Mie ratio is studied for micrometric droplets (25–60 µm) produced with a droplet generator. The investigations were carried out with the dye Nile red dissolved in ethanol and ethanol/iso-octane mixtures. A spectral absorption and fluorescence characterization at various dye and ethanol concentrations is carried out in a cuvette in order to identify reabsorption effects. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> droplet images (index <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:math> : parallel polarization) show a more homogeneous intensity distribution in the droplets and slightly stronger morphology-dependent resonances (MDRs) in comparison to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:msub> </mml:mrow> </mml:math> (index <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:math> : perpendicular polarization). The spectral LIF emissions reveal a dependence of the MDR on the ethanol admixture. The larger the ethanol content, the lower the MDR peak, which is also shifted further to the red part of the spectrum. The Mie droplet signal images are mainly characterized by two distinct glare points, one at the entrance of the laser light (reflection) and one at the exit (first-order refraction). The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:msub> </mml:mrow> </mml:math> images show a more pronounced entrance glare point, in comparison to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , where the exit glare point is more pronounced. These observations are in accordance with the theory. The calibration curve of the micro droplet signals revealed a volumetric trend of the LIF signals and a slightly higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:msub> </mml:mrow> </mml:math> signal and sensitivity in comparison to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . The signal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:math> follows roughly a quadratic trend on average, while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:math> follows a linear trend. Consequently, the calculated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mi mathvariant="normal">⊥</mml:mi> </mml:math> ratio shows a linear trend, whereas the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">L</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">F</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:math> ratio shows a quadratic trend, which confirms theoretical calculations. A numerical simulation of the Mie signal at various detection angles shows a good agreement with the experimental data at large apertures.