Correlations for mixing energy in processes using Rushton turbine mixer‡
-
Grzegorz Story
,
Marian Kordas
Abstract
This study reports the research results on a mixing process using a stirred tank mixer under the action of a rotating magnetic field (RMF). Dimensionless correlations are proposed to predict the power consumption and mixing time for the mixing systems analysed. The results suggest that the mixing behaviour of the experimental set-ups tested may be assessed using the dimensionless mixing energy as the product of the power input and mixing time. In addition, an innovative strategy is proposed on the basis of the synergistic effect of the rotational Rushton turbine and the RMF generator. The values of the dimensionless energy thus obtained were used to compare the mixing process performed by the mixing devices tested. It is shown that the mixing process under the RMF action has significantly higher values of energy consumption than the conventional Rushton turbine. The total energy consumption for the mixing process performed by the RMF mixer may be reduced by concomitant use of a rotational agitator.
Symbols
| a, b | equation coefficient (Eq. (14)) | |
| B | magnetic induction kg A-1 S-2 | |
| C | constant (Eq. (14)) | |
| D | diameter of glass container | m |
| d | diameter of rushton turbine | m |
| emix | mixing energy | J |
| dimensionless mixing energy | ||
| f | frequency of RMF | s-1 |
| H | liquid level in glass container | m |
| I | electrical current | A |
| K | consistency index | Pa sn |
| kMS | Metzner-Otto coefficient | |
| l | characteristic dimension | m |
| M | measured torque | Nm |
| Ne | Newton number | |
| n | rotational speed of agitator | s-1 |
| nF | flow index | |
| P | Power | W |
| Pa | active power | W |
| R, r | radius | m |
| Re | Reynolds number | |
| ΔTtracer | difference between tracer temperature at beginning of process | °C |
| U | voltage | V |
| wφmax | maximum peripheral speed of mixed liquid | m s-1 |
| X(τ) | value of parameter depending on measurement method at measuring point at some instant τ in time | |
| Xo | initial value of parameter depending on measurement method | |
| X∞ | final value of parameter depending on measurement method |
Greek Letters
| γ | strain rate | s−1 | |
| ηa | apparent viscosity | Pa s | |
| Θ | mixing time number | ||
| v | kinematic viscosity | m2 s-1 | |
| Ρ | density | kg m−1 | |
| Σe | electrical conductivity | A s3 kg−1 m−1 | |
| τ | time | s | |
| Ψ | efficiency | ||
| ΩRMF | angular velocity of liquid under action of RMF | rad s−1 | 1 |
| wRMF | angular velocity of rotating magnetic field | rad s−1 |
Abbreviations
| CMC | sodium carboxymethyl cellulose |
| RMF | rotating magnetic field |
| STR | stirred tank reactor |
References
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© 2016 Institute of Chemistry, Slovak Academy of Sciences
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