The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories

This study presents a theoretical model for the thermoelastic response in transmission-mode photoacoustic systems that feature a two-layer structure. The model incorporates volumetric optical absorption in both layers and is based on classical heat conduction theory, hyperbolic generalized heat cond...

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Main Authors: Marica N. Popovic, Slobodanka P. Galovic, Ervin K. Lenzi, Aloisi Somer
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/9/7/456
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author Marica N. Popovic
Slobodanka P. Galovic
Ervin K. Lenzi
Aloisi Somer
author_facet Marica N. Popovic
Slobodanka P. Galovic
Ervin K. Lenzi
Aloisi Somer
author_sort Marica N. Popovic
collection DOAJ
description This study presents a theoretical model for the thermoelastic response in transmission-mode photoacoustic systems that feature a two-layer structure. The model incorporates volumetric optical absorption in both layers and is based on classical heat conduction theory, hyperbolic generalized heat conduction theory, and fractional heat conduction models including inertial memory in Generalizations of the Cattaneo Equation (GCEI, GCEII, and GCEIII). To validate the model, comparisons were made with the existing literature models. Using the proposed model, the thermoelastic photoacoustic response of a two-layer system composed of a 3D-printed porous polyamide (PA12) substrate coated with a thin, highly absorptive protective dye layer is analyzed. We obtain that the thickness and thermal conduction in properties of the coating are very important in influencing the thermoelastic component and should not be overlooked. Furthermore, the thermoelastic component is affected by the selected fractional model—whether it is subdiffusion or superdiffusion—along with the value of the order of the fractional derivative, as well as the optical absorption coefficient of the layer being investigated. Additionally, it is concluded that the phase has a greater impact than the amplitude when selecting the appropriate theoretical heat conduction model.
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publishDate 2025-07-01
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spelling doaj-art-e53aae8d2e2c4b2ebf98cf046b4d872f2025-08-20T03:58:26ZengMDPI AGFractal and Fractional2504-31102025-07-019745610.3390/fractalfract9070456The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction TheoriesMarica N. Popovic0Slobodanka P. Galovic1Ervin K. Lenzi2Aloisi Somer3Institute of Physics Belgrade, National Institute of the Republic of Serbia, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia“VINČA” Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, P.O. Box 522, 11000 Belgrade, SerbiaDepartamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá 87020-900, BrazilDepartamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, BrazilThis study presents a theoretical model for the thermoelastic response in transmission-mode photoacoustic systems that feature a two-layer structure. The model incorporates volumetric optical absorption in both layers and is based on classical heat conduction theory, hyperbolic generalized heat conduction theory, and fractional heat conduction models including inertial memory in Generalizations of the Cattaneo Equation (GCEI, GCEII, and GCEIII). To validate the model, comparisons were made with the existing literature models. Using the proposed model, the thermoelastic photoacoustic response of a two-layer system composed of a 3D-printed porous polyamide (PA12) substrate coated with a thin, highly absorptive protective dye layer is analyzed. We obtain that the thickness and thermal conduction in properties of the coating are very important in influencing the thermoelastic component and should not be overlooked. Furthermore, the thermoelastic component is affected by the selected fractional model—whether it is subdiffusion or superdiffusion—along with the value of the order of the fractional derivative, as well as the optical absorption coefficient of the layer being investigated. Additionally, it is concluded that the phase has a greater impact than the amplitude when selecting the appropriate theoretical heat conduction model.https://www.mdpi.com/2504-3110/9/7/456anomalous diffusionfractional thermal conductionfractional calculus
spellingShingle Marica N. Popovic
Slobodanka P. Galovic
Ervin K. Lenzi
Aloisi Somer
The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
Fractal and Fractional
anomalous diffusion
fractional thermal conduction
fractional calculus
title The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
title_full The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
title_fullStr The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
title_full_unstemmed The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
title_short The Thermoelastic Component of the Photoacoustic Response in a 3D-Printed Polyamide Coated with Pigment Dye: A Two-Layer Model Incorporating Fractional Heat Conduction Theories
title_sort thermoelastic component of the photoacoustic response in a 3d printed polyamide coated with pigment dye a two layer model incorporating fractional heat conduction theories
topic anomalous diffusion
fractional thermal conduction
fractional calculus
url https://www.mdpi.com/2504-3110/9/7/456
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