Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization
Mass transport in textiles is crucial. Knowledge of effective mass transport properties of textiles can be used to improve processes and applications where textiles are used. Mass transfer in knitted and woven fabrics strongly depends on the yarn used. In particular, the permeability and effective d...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Materials |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1996-1944/16/5/2014 |
| _version_ | 1797614933729345536 |
|---|---|
| author | Lukas Maier Lars Kufferath-Sieberin Leon Pauly Manuel Hopp-Hirschler Götz T. Gresser Ulrich Nieken |
| author_facet | Lukas Maier Lars Kufferath-Sieberin Leon Pauly Manuel Hopp-Hirschler Götz T. Gresser Ulrich Nieken |
| author_sort | Lukas Maier |
| collection | DOAJ |
| description | Mass transport in textiles is crucial. Knowledge of effective mass transport properties of textiles can be used to improve processes and applications where textiles are used. Mass transfer in knitted and woven fabrics strongly depends on the yarn used. In particular, the permeability and effective diffusion coefficient of yarns are of interest. Correlations are often used to estimate the mass transfer properties of yarns. These correlations commonly assume an ordered distribution, but here we demonstrate that an ordered distribution leads to an overestimation of mass transfer properties. We therefore address the impact of random ordering on the effective diffusivity and permeability of yarns and show that it is important to account for the random arrangement of fibers in order to predict mass transfer. To do this, Representative Volume Elements are randomly generated to represent the structure of yarns made from continuous filaments of synthetic materials. Furthermore, parallel, randomly arranged fibers with a circular cross-section are assumed. By solving the so-called cell problems on the Representative Volume Elements, transport coefficients can be calculated for given porosities. These transport coefficients, which are based on a digital reconstruction of the yarn and asymptotic homogenization, are then used to derive an improved correlation for the effective diffusivity and permeability as a function of porosity and fiber diameter. At porosities below 0.7, the predicted transport is significantly lower under the assumption of random ordering. The approach is not limited to circular fibers and may be extended to arbitrary fiber geometries. |
| first_indexed | 2024-03-11T07:18:14Z |
| format | Article |
| id | doaj.art-1593e12ec0e64ab28cf220cdf0e31162 |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-11T07:18:14Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-1593e12ec0e64ab28cf220cdf0e311622023-11-17T08:06:02ZengMDPI AGMaterials1996-19442023-02-01165201410.3390/ma16052014Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic HomogenizationLukas Maier0Lars Kufferath-Sieberin1Leon Pauly2Manuel Hopp-Hirschler3Götz T. Gresser4Ulrich Nieken5Institute of Chemical Process Engineering, University of Stuttgart, Boeblinger Strasse 78, 70199 Stuttgart, GermanyInstitute of Chemical Process Engineering, University of Stuttgart, Boeblinger Strasse 78, 70199 Stuttgart, GermanyGerman Institutes of Textile and Fiber Research Denkendorf (DITF), Körschtalstraße 26, 73770 Denkendorf, GermanyInstitute of Chemical Process Engineering, University of Stuttgart, Boeblinger Strasse 78, 70199 Stuttgart, GermanyGerman Institutes of Textile and Fiber Research Denkendorf (DITF), Körschtalstraße 26, 73770 Denkendorf, GermanyInstitute of Chemical Process Engineering, University of Stuttgart, Boeblinger Strasse 78, 70199 Stuttgart, GermanyMass transport in textiles is crucial. Knowledge of effective mass transport properties of textiles can be used to improve processes and applications where textiles are used. Mass transfer in knitted and woven fabrics strongly depends on the yarn used. In particular, the permeability and effective diffusion coefficient of yarns are of interest. Correlations are often used to estimate the mass transfer properties of yarns. These correlations commonly assume an ordered distribution, but here we demonstrate that an ordered distribution leads to an overestimation of mass transfer properties. We therefore address the impact of random ordering on the effective diffusivity and permeability of yarns and show that it is important to account for the random arrangement of fibers in order to predict mass transfer. To do this, Representative Volume Elements are randomly generated to represent the structure of yarns made from continuous filaments of synthetic materials. Furthermore, parallel, randomly arranged fibers with a circular cross-section are assumed. By solving the so-called cell problems on the Representative Volume Elements, transport coefficients can be calculated for given porosities. These transport coefficients, which are based on a digital reconstruction of the yarn and asymptotic homogenization, are then used to derive an improved correlation for the effective diffusivity and permeability as a function of porosity and fiber diameter. At porosities below 0.7, the predicted transport is significantly lower under the assumption of random ordering. The approach is not limited to circular fibers and may be extended to arbitrary fiber geometries.https://www.mdpi.com/1996-1944/16/5/2014homogenizationtextilesyarnsrandom fiberspermeabilityeffective diffusion |
| spellingShingle | Lukas Maier Lars Kufferath-Sieberin Leon Pauly Manuel Hopp-Hirschler Götz T. Gresser Ulrich Nieken Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization Materials homogenization textiles yarns random fibers permeability effective diffusion |
| title | Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization |
| title_full | Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization |
| title_fullStr | Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization |
| title_full_unstemmed | Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization |
| title_short | Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization |
| title_sort | constitutive correlations for mass transport in fibrous media based on asymptotic homogenization |
| topic | homogenization textiles yarns random fibers permeability effective diffusion |
| url | https://www.mdpi.com/1996-1944/16/5/2014 |
| work_keys_str_mv | AT lukasmaier constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization AT larskufferathsieberin constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization AT leonpauly constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization AT manuelhopphirschler constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization AT gotztgresser constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization AT ulrichnieken constitutivecorrelationsformasstransportinfibrousmediabasedonasymptotichomogenization |