<p>The air bubble dispersion in whipping cream during agitation has been imaged by fuzzy phase classification implemented in electrical impedance tomography (<i>f</i>EIT) for internal morphological structure visualization. The <i>f</i>EIT consists of non-linear conductivity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\sigma\:\)</EquationSource> </InlineEquation> reconstruction and fuzzy phase classification to classify <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\sigma\:\)</EquationSource> </InlineEquation> into a probabilistic cluster <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{u}_{j}\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:j=1\)</EquationSource> </InlineEquation>: oil-in-water phase, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:j=2\)</EquationSource> </InlineEquation>: air bubble). In the experiments, probabilistic air bubble cluster <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{u}_{2}\)</EquationSource> </InlineEquation> of whipping cream with five milk fat (MF) contents were reconstructed by <i>f</i>EIT during agitation to image the air bubble dispersion. The <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{u}_{2}\)</EquationSource> </InlineEquation> demonstrated the air bubble dispersion within the sensor area caused by agitation. The spatial average <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\langle{u}_{2}\rangle\)</EquationSource> </InlineEquation> was increased and then decreased due to the incorporation and subsequent departure of air bubbles during agitation. The peak <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq9.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\langle{u}_{2}\rangle}_{\:}\)</EquationSource> </InlineEquation> time <i>t</i><sub><i>s</i></sub>, which represents the critical saturation point of air bubbles, was decreased as MF content increased, which was verified by OR measurement and microscope observation. Compared to <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\sigma\:\)</EquationSource> </InlineEquation> reconstructed by EIT influenced by the liquid water phase, fat and air bubbles, <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_3773_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\langle{u}_{2}\rangle\)</EquationSource> </InlineEquation> reconstructed by <i>f</i>EIT successfully imaged air bubble dispersion in whipping cream. Furthermore, <i>f</i>EIT demonstrated comparable performance to OR measurements in evaluating the internal morphological structure of whipping cream during agitation, while providing the advantage of inline measurement.</p>

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Air bubble dispersion imaging in whipping cream with specified fat contents by fuzzy phase classification implemented in electrical impedance tomography

  • Songshi Li,
  • Prima Asmara Sejati,
  • Ryuichi Fukumoto,
  • Masahiro Takei

摘要

The air bubble dispersion in whipping cream during agitation has been imaged by fuzzy phase classification implemented in electrical impedance tomography (fEIT) for internal morphological structure visualization. The fEIT consists of non-linear conductivity \(\:\sigma\:\) reconstruction and fuzzy phase classification to classify \(\:\sigma\:\) into a probabilistic cluster \(\:{u}_{j}\) ( \(\:j=1\) : oil-in-water phase, \(\:j=2\) : air bubble). In the experiments, probabilistic air bubble cluster \(\:{u}_{2}\) of whipping cream with five milk fat (MF) contents were reconstructed by fEIT during agitation to image the air bubble dispersion. The \(\:{u}_{2}\) demonstrated the air bubble dispersion within the sensor area caused by agitation. The spatial average \(\:\langle{u}_{2}\rangle\) was increased and then decreased due to the incorporation and subsequent departure of air bubbles during agitation. The peak \(\:{\langle{u}_{2}\rangle}_{\:}\) time ts, which represents the critical saturation point of air bubbles, was decreased as MF content increased, which was verified by OR measurement and microscope observation. Compared to \(\:\sigma\:\) reconstructed by EIT influenced by the liquid water phase, fat and air bubbles, \(\:\langle{u}_{2}\rangle\) reconstructed by fEIT successfully imaged air bubble dispersion in whipping cream. Furthermore, fEIT demonstrated comparable performance to OR measurements in evaluating the internal morphological structure of whipping cream during agitation, while providing the advantage of inline measurement.