Mobility of power-law and Carreau fluids through fibrous media
The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or p...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/100456 https://orcid.org/0000-0003-4395-523X https://orcid.org/0000-0001-8323-2779 |
| _version_ | 1826216891772829696 |
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| author | Shahsavari, Setareh McKinley, Gareth H |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Shahsavari, Setareh McKinley, Gareth H |
| author_sort | Shahsavari, Setareh |
| collection | MIT |
| description | The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers. |
| first_indexed | 2024-09-23T16:54:46Z |
| format | Article |
| id | mit-1721.1/100456 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:54:46Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1004562022-09-29T22:23:13Z Mobility of power-law and Carreau fluids through fibrous media Shahsavari, Setareh McKinley, Gareth H Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Hatsopoulos Microfluids Laboratory Shahsavari, Setareh McKinley, Gareth H. The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ɛ≃0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers. National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Award DMR-0819762) 2015-12-21T17:02:07Z 2015-12-21T17:02:07Z 2015-12 2015-09 2015-12-10T23:00:06Z Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/100456 Shahsavari, Setareh, and Gareth H. McKinley. "Mobility of power-law and Carreau fluids through fibrous media." Phys. Rev. E 92, 063012 (December 2015). © 2015 American Physical Society https://orcid.org/0000-0003-4395-523X https://orcid.org/0000-0001-8323-2779 en http://dx.doi.org/10.1103/PhysRevE.92.063012 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Shahsavari, Setareh McKinley, Gareth H Mobility of power-law and Carreau fluids through fibrous media |
| title | Mobility of power-law and Carreau fluids through fibrous media |
| title_full | Mobility of power-law and Carreau fluids through fibrous media |
| title_fullStr | Mobility of power-law and Carreau fluids through fibrous media |
| title_full_unstemmed | Mobility of power-law and Carreau fluids through fibrous media |
| title_short | Mobility of power-law and Carreau fluids through fibrous media |
| title_sort | mobility of power law and carreau fluids through fibrous media |
| url | http://hdl.handle.net/1721.1/100456 https://orcid.org/0000-0003-4395-523X https://orcid.org/0000-0001-8323-2779 |
| work_keys_str_mv | AT shahsavarisetareh mobilityofpowerlawandcarreaufluidsthroughfibrousmedia AT mckinleygarethh mobilityofpowerlawandcarreaufluidsthroughfibrousmedia |