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An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids
An analysis of the flow about a sphere rotating slowly in a Rivlin-Ericksen fluid contained in a stationary outer concentric sphere is presented. An application of the conformal mapping technique is proposed. The technique is used to obtain the radial and axial velocity components for the flow about...
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| Format: | Thesis |
| Language: | English |
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Department of Chemical Engineering
2016
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| _version_ | 1867613165329580032 |
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| access_status_str | Open Access |
| author | Cairncross, Eugene Kenneth |
| author2 | Hansford, Geoffrey Spearing |
| author_browse | Cairncross, Eugene Kenneth Hansford, Geoffrey Spearing |
| author_facet | Hansford, Geoffrey Spearing Cairncross, Eugene Kenneth |
| author_sort | Cairncross, Eugene Kenneth |
| collection | Thesis |
| description | An analysis of the flow about a sphere rotating slowly in a Rivlin-Ericksen fluid contained in a stationary outer concentric sphere is presented. An application of the conformal mapping technique is proposed. The technique is used to obtain the radial and axial velocity components for the flow about a disc rotating within an outer oblate spheroidal shell from the solution to the corresponding problem of the flow about a sphere rotating within an outer spherical shell. The results are compared with an existing rigorous analysis for a disc rotating in an infinite sea of the Third Order fluid. They are also used to estimate wall effects in experimental situations. Tangential and radial velocity profiles are measured for the flow about a sphere rotating slowly in a Newtonian liquid. Velocities are determined from enlarged streak photographs of aluminium particles moving in a collimated 'sheet' of light, at several planes throughout the flow field. Similar velocity profiles are measured for the flow of a 1,50% Natrosol 250 H solution about two spheres of different diameters rotating in tanks with different dimensions. A set of velocity distributions is also measured for a sphere rotating in a 0,9% Natrosol 250 H solution; a dye tracer study of the flow about a sphere rotating in this liquid is presented as well. Velocity profiles are presented for the flow of the 1,50% Natrosol solution about a rotating disc and the flow of the 0,9% solution about a second rotating disc of different diameter. Both Natrosol solutions exhibited viscoelastic behaviour in all cases. The Newtonian fluid study is at a Reynolds number of 1,2: all viscoelastic fluid studies are within the range of Reynolds numbers of 0,05 to 1,24. The zero shear viscosities of the Natrosol solutions are measured using the falling sphere method. The non-Newtonian material parameters are obtained by fitting the theoretical curves to the measured velocity data. The values of the elastic and shear thinning parameters for the two fluids obtained in the different geometrical and dynamical systems are compared. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17705 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:48.735Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Chemical Engineering |
| publisherStr | Department of Chemical Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17705 An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids Cairncross, Eugene Kenneth Hansford, Geoffrey Spearing Chemical Engineering An analysis of the flow about a sphere rotating slowly in a Rivlin-Ericksen fluid contained in a stationary outer concentric sphere is presented. An application of the conformal mapping technique is proposed. The technique is used to obtain the radial and axial velocity components for the flow about a disc rotating within an outer oblate spheroidal shell from the solution to the corresponding problem of the flow about a sphere rotating within an outer spherical shell. The results are compared with an existing rigorous analysis for a disc rotating in an infinite sea of the Third Order fluid. They are also used to estimate wall effects in experimental situations. Tangential and radial velocity profiles are measured for the flow about a sphere rotating slowly in a Newtonian liquid. Velocities are determined from enlarged streak photographs of aluminium particles moving in a collimated 'sheet' of light, at several planes throughout the flow field. Similar velocity profiles are measured for the flow of a 1,50% Natrosol 250 H solution about two spheres of different diameters rotating in tanks with different dimensions. A set of velocity distributions is also measured for a sphere rotating in a 0,9% Natrosol 250 H solution; a dye tracer study of the flow about a sphere rotating in this liquid is presented as well. Velocity profiles are presented for the flow of the 1,50% Natrosol solution about a rotating disc and the flow of the 0,9% solution about a second rotating disc of different diameter. Both Natrosol solutions exhibited viscoelastic behaviour in all cases. The Newtonian fluid study is at a Reynolds number of 1,2: all viscoelastic fluid studies are within the range of Reynolds numbers of 0,05 to 1,24. The zero shear viscosities of the Natrosol solutions are measured using the falling sphere method. The non-Newtonian material parameters are obtained by fitting the theoretical curves to the measured velocity data. The values of the elastic and shear thinning parameters for the two fluids obtained in the different geometrical and dynamical systems are compared. 2016-03-14T07:16:26Z 2016-03-14T07:16:26Z 1974 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17705 eng application/pdf Department of Chemical Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Chemical Engineering Cairncross, Eugene Kenneth An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| thesis_degree_str | Doctoral |
| title | An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| title_full | An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| title_fullStr | An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| title_full_unstemmed | An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| title_short | An experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| title_sort | experimental and theoretical study of the flow about spheres and discs rotating slowly in viscoelastic fluids |
| topic | Chemical Engineering |
| url | http://hdl.handle.net/11427/17705 |
| work_keys_str_mv | AT cairncrosseugenekenneth anexperimentalandtheoreticalstudyoftheflowaboutspheresanddiscsrotatingslowlyinviscoelasticfluids AT cairncrosseugenekenneth experimentalandtheoreticalstudyoftheflowaboutspheresanddiscsrotatingslowlyinviscoelasticfluids |