Reynolds number effects in a simple planetary mixer
Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the...
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| Published in | Chemical engineering science Vol. 59; no. 16; pp. 3371 - 3379 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Oxford
Elsevier Ltd
01.08.2004
Elsevier |
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| Abstract | Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces. Experiments performed at low Reynolds number (
Re≪1) show good agreement with corresponding numerical simulations, but as the Reynolds number is increased, the agreement between experiments and Stokes-flow numerics worsens, in a manner that reflects improving experimental mixing quality. Specifically, we find that islands of poor mixing shrink as
Re increases. Our results suggest that, while numerical simulations in the Stokes flow regime may be used as a ‘sieve’ to select good mixing protocols at small
Re, experiments or computational fluid dynamics simulations are required properly to evaluate mixing protocols operated at finite Reynolds numbers. |
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| AbstractList | Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces. Experiments performed at low Reynolds number (Re < < 1) show good agreement with corresponding numerical simulations, but as the Reynolds number is increased, the agreement between experiments and Stokes-flow numerics worsens, in a manner that reflects improving experimental mixing quality. Specifically, we find that islands of poor mixing shrink as Re increases. Our results suggest that, while numerical simulations in the Stokes flow regime may be used as a "sieve" to select good mixing protocols at small Re, experiments or computational fluid dynamics simulations are required properly to evaluate mixing protocols operated at finite Reynolds numbers. Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary mixer, and a comparison with numerical simulations based on a simple mathematical model of the flow. The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces. Experiments performed at low Reynolds number ( Re≪1) show good agreement with corresponding numerical simulations, but as the Reynolds number is increased, the agreement between experiments and Stokes-flow numerics worsens, in a manner that reflects improving experimental mixing quality. Specifically, we find that islands of poor mixing shrink as Re increases. Our results suggest that, while numerical simulations in the Stokes flow regime may be used as a ‘sieve’ to select good mixing protocols at small Re, experiments or computational fluid dynamics simulations are required properly to evaluate mixing protocols operated at finite Reynolds numbers. |
| Author | Finn, M.D Cox, S.M Clifford, M.J |
| Author_xml | – sequence: 1 givenname: M.J surname: Clifford fullname: Clifford, M.J email: Mike.Clifford@nottingham.ac.uk organization: School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, University Park, Nottingham NG7 2RD, UK – sequence: 2 givenname: S.M surname: Cox fullname: Cox, S.M email: scox@maths.adelaide.edu.au organization: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK – sequence: 3 givenname: M.D surname: Finn fullname: Finn, M.D email: Matthew.Finn@maths.nottingham.ac.uk organization: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK |
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| Cites_doi | 10.1023/A:1011840630170 10.1098/rspa.1986.0115 10.1103/PhysRevLett.81.3395 10.1063/1.1458932 10.1017/S0022112094001539 10.1103/PhysRevA.40.7182 10.1017/S0022112089003186 10.1017/S002211200000118X 10.1023/A:1009940909377 10.1016/S0167-2789(99)00018-4 10.1016/S0923-0467(98)00065-7 10.1017/S0022112084001233 10.1063/1.868853 10.1103/PhysRevA.42.5873 10.1142/S0218348X9700036X 10.1016/S0997-7546(99)00119-3 10.1205/026387699526241 10.1063/1.1490135 10.1016/S0009-2509(99)00333-4 10.1103/PhysRevLett.63.47 10.1002/aic.690481005 10.1063/1.865828 10.1016/0169-5983(94)00018-U 10.1017/S0022112003005858 10.1063/1.866449 10.1016/S0009-2509(02)00122-7 10.1002/aic.690401102 10.1017/S0022112099007107 10.1205/026387600527491 10.1023/B:ENGI.0000011930.55539.69 |
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| Keywords | Fluid mechanics Nonlinear dynamics Mixing Laminar flow Chaotic advection Stokes flow Numerical simulation Computational fluid dynamics Reynolds number Mixing quality |
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| Snippet | Planetary mixers are widely used in a diverse range of industrial applications. This paper presents an experimental investigation of mixing in a planetary... |
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| SubjectTerms | Applied sciences Chaotic advection Chemical engineering Exact sciences and technology Fluid mechanics Laminar flow Mixing Nonlinear dynamics Stokes flow |
| Title | Reynolds number effects in a simple planetary mixer |
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