<p>The planar laser-induced fluorescence (PLIF) method has been widely applied for measuring the thickness of liquid films. To identify the liquid–gas interface, however, PLIF-based methods require an artificial threshold value of brightness or a calibration curve between the thickness and the brightness, limiting its application in measuring unknown film thickness. To overcome the drawbacks, we propose a new method, time-variant PLIF (T-PLIF), which employs an index of time variance of brightness to detect the interface. We first establish the mathematical principle of T-PLIF, wherein the time variance of a phase-dependent variable becomes the maximum exactly at the time-averaged position of the wavy interface. We then perform experiments for a well-controlled downward annular liquid film flow to test the reliability of T-PLIF. We demonstrate that T-PLIF measures liquid film thickness of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_3989_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">$h > 0.2\,\textrm{mm}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo>></mo> <mn>0.2</mn> <mspace width="0.166667em" /> <mtext>mm</mtext> </mrow> </math></EquationSource> </InlineEquation> with the accuracy of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_3989_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$\varepsilon \le 10\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>≤</mo> <mn>10</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> to the theoretical reference and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_3989_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">$h \le 0.2\,\textrm{mm}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo>≤</mo> <mn>0.2</mn> <mspace width="0.166667em" /> <mtext>mm</mtext> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_3989_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">$\varepsilon = 20\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. T-PLIF is able to quantify the film thickness with no need for any pre-/post-calibration or artificial threshold values. We further confirm the applicability of T-PLIF to the wavy film flow sheared by an airflow up to <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_3989_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$30\,\text{m/s}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mspace width="0.166667em" /> <mtext>m/s</mtext> </mrow> </math></EquationSource> </InlineEquation> by measuring the phase velocity and wavelength, which well matches the theoretical results.</p>

Time-variant planar laser-induced fluorescence for thickness measurement of wavy liquid films: a calibration-free and threshold-free method

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发表日期：

2025年2月17日

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Yoshiaki Kamada,
Zhenying Wang,
Chihiro Inoue,
Shigeki Senoo

摘要

The planar laser-induced fluorescence (PLIF) method has been widely applied for measuring the thickness of liquid films. To identify the liquid–gas interface, however, PLIF-based methods require an artificial threshold value of brightness or a calibration curve between the thickness and the brightness, limiting its application in measuring unknown film thickness. To overcome the drawbacks, we propose a new method, time-variant PLIF (T-PLIF), which employs an index of time variance of brightness to detect the interface. We first establish the mathematical principle of T-PLIF, wherein the time variance of a phase-dependent variable becomes the maximum exactly at the time-averaged position of the wavy interface. We then perform experiments for a well-controlled downward annular liquid film flow to test the reliability of T-PLIF. We demonstrate that T-PLIF measures liquid film thickness of $h > 0.2\,\textrm{mm}$ $h > 0.2 mm$ with the accuracy of $\varepsilon \le 10\%$ $ε \leq 10 %$ to the theoretical reference and $h \le 0.2\,\textrm{mm}$ $h \leq 0.2 mm$ with $\varepsilon = 20\%$ $ε = 20 %$ . T-PLIF is able to quantify the film thickness with no need for any pre-/post-calibration or artificial threshold values. We further confirm the applicability of T-PLIF to the wavy film flow sheared by an airflow up to $30\,\text{m/s}$ $30 m/s$ by measuring the phase velocity and wavelength, which well matches the theoretical results.