Experimental investigations of turbulent fragmenting stresses in a rotor-stator mixer. Part 2. Probability distributions of instantaneous stresses

Chemical Engineering Science

Volumn 171, Issue , 2017, Pages 638-649

  Håkansson, Andreas ^a   Andersson, Ronnie ^b   Mortensen, Hans Henrik ^c   Innings, Fredrik ^c,d  

^a KRISTIANSTAD UNIVERSITY   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^c Tetra Pak AB   (Sweden)

^d LUND UNIVERSITY   (Sweden)

Author keywords

Emulsification; Fragmentation; High shear mixer; Intermittency; Mixing; Rotor stator mixer; Turbulence

Indexed keywords

DROPS; EMULSIFICATION; MIXERS (MACHINERY); MIXING; PROBABILITY; STATORS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TURBULENCE; VELOCITY; VELOCITY MEASUREMENT;

EXPERIMENTAL INVESTIGATIONS; EXPONENTIAL DECAY MODELS; FRAGMENTATION; HIGH SHEAR MIXERS; INTERMITTENCY; PARTICLE IMAGE VELOCIMETRIES; ROTOR-STATOR MIXER; STOCHASTIC VARIATION;

PROBABILITY DISTRIBUTIONS;

EID: 85021756180     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2017.06.038     Document Type: Article

References (45)

1. Andersson, R., Andersson, B., Modeling the breakup of fluid particles in turbulent flows. AIChE J. 52:6 (2006), 2031–2038, 10.1002/aic.10832.
2. Andersson, R., Helmi, A., Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows. Appl. Math. Model. 38:17–18 (2014), 4186–4196, 10.1016/j.apm.2014.01.005.
3. Angelidou, C., Psimopoulos, M., Jameson, G.J., Size distribution functions of dispersions. Chem. Eng. Sci. 37 (1979), 671–676, 10.1016/0009-2509(79)85112-X.
4. Ashar, M., Innings, F., Andersson, R., 2017. Single drop breakup visualizations in a rotor-stator mixer. Submitted to Journal (Submitted for publication).
5. Atiemo-Obeng, V.A., Calabrese, R., Rotor-stator mixing devices. Paul, E.L., Atiemo-Obeng, V.A., Kresta, S.M., (eds.) Handbook of Industrial Mixing, 2004, Wiley, Hoboken, 479–505.
6. Atiemo-Obeng, V.A., Calabrese, R., Rotor-stator mixing devices. Kresta, S.M., Etchells, A.W., Dickey, D.S., Atiemo-Obeng, V.A., (eds.) Advances in Industrial Mixing, 2016, Wiley, Hoboken, 255–502.
7. Baldyga, J., Podgorska, W., Drop break-up in intermittent turbulence: maximum stable and transient sizes of drops. Cana. J. Chem. Eng. 76 (1998), 456–470, 10.1002/cjce.5450760316.
8. Baldyga, J., Bourne, J.R., Some consequences for turbulent mixing of fine-scale intermittency. Chem. Eng. Sci. 47:15–16 (1992), 3943–3948, 10.1016/0009-2509(92)85143-Y.
9. Baldyga, J., Bourne, J.R., Interpretation of turbulent mixing using fractals and multifractals. Chem. Eng. Sci. 50:3 (1995), 381–400, 10.1016/0009-2509(94)00217-F.
10. Bisten, A., Schuchmann, H.P., Optical measuring methods for the investigation of high-pressure homogenization. Processes, 4, 2016, 41, 10.3390/pr4040041.
11. Boxall, J.A., Kohn, C.A., Sloan, E.D., Sum, A.K., Wu, D.T., Droplet size scaling of water-in-oil emulsions under turbulent flow. Langmuir, 28, 2012, 10.1021/la202293t 204-110.
12. Cheng, Q., Xu, S., Shi, J., Li, W., Zhang, J., Pump capacity and power consumption of two commercial in-line high shear mixers. Ind. Eng. Chem. Res. 52:1 (2012), 525–537, 10.1021/ie3023274.
13. Calabrese, R.V., Chang, T.P.K., Dang, P.T., Drop breakup in turbulent stirred-tank contactors. Part I: Effect of dispersed-phase viscosity. AIChE J. 32:4 (1986), 657–666, 10.1002/aic.690320416.
14. Cooke, M., Rodgers, T.L., Kowalski, A.J., Power consumption characteristics of an in-line silverson high shear mixer. AIChE J. 58 (2012), 1683–1692, 10.1002/aic.12703.
15. Coulaloglou, C.A., Tavlarides, L.L., Description of interaction process in agitated liquid-liquid dispersions. Chem. Eng. Sci. 32 (1977), 1289–1297, 10.1016/0009-2509(77)85023-9.
16. Davies, J.T., Drop sizes of emulsions related to turbulent energy dissipation rates. Chem. Eng. Sci. 40:5 (1985), 839–842, 10.1016/0009-2509(85)85036-3.
17. Gabriele, A., Nienow, A.W., Simmons, M.J.H., Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank. Chem. Eng. Sci. 64 (2009), 126–143, 10.1016/j.ces.2008.09.018.
18. Ghasempour, F., Andersson, R., Andersson, B., Bergstrom, D.J., Number density of turbulent vortices in the entire energy spectrum. AIChE J. 60:11 (2014), 3989–3995, 10.1002/aic.14622.
19. Ghasempour, F., Andersson, R., Andersson, B., Multidimensional turbulence spectra – statistical analysis of turbulent vortices. Appl. Math. Model. 38 (2014), 4226–4237, 10.1016/j.apm.2014.03.003.
20. Gupta, A., Eral, H.B., Hatton, T.A., Doyle, P.S., Nanoemulsions: formation, properties and applications. Soft Matter 12 (2016), 2826–2841, 10.1039/C5SM02958A.
21. Hagsaether, L., Jakobsen, H.A., Svendsen, H.F., A model for turbulent binary breakup of dispersed fluid particles. Chem. Eng. Sci. 57 (2002), 3251–3267, 10.1016/S0009-2509(02)00197-5.
22. Håkansson, A., Fuchs, L., Innings, F., Revstedt, J., Trägårdh, C., Bergenståhl, B., High resolution experimental measurement of turbulent flow field in a high pressure homogenizer model its implication on turbulent drop fragmentation. Chem. Eng. Sci. 66 (2011), 1790–1801, 10.1016/j.ces.2011.01.026.
23. Håkansson, A., Chaudhry, Z., Innings, F., Model emulsion to study the mechanism of industrial mayonnaise emulsification. Food Bioprod. Process. 98 (2016), 189–195, 10.1016/j.fbp.2016.01.011.
24. Håkansson, A., Mortensen, H.H., Andersson, R., Innings, F., Experimental investigations of turbulent fragmenting stresses in a Rotor-Stator Mixer. Part 1. Estimation of turbulent stresses and comparison to breakup visualizations. Chem. Eng. Sci. 171 (2017), 625–637.
25. Hall, S., Pacek, A.W., Kowalski, A.J., Cooke, M., Rothman, D., The effect of scale and interfacial tension on liquid-liquid dispersion in in-line Silverson rotor-stator mixers. Chem. Eng. Res. Des. 91 (2013), 2156–2168, 10.1016/j.cherd.2013.04.021.
26. Hinze, J.O., Fundamentals of the hydrodynamic mechanism of splitting in dispersion process. AIChE J. 1 (1955), 289–295, 10.1002/aic.690010303.
27. Jasinska, M., Baldyga, J., Cooke, M., Kowalski, A.J., Specific features of power characteristics of in-line rotor-stator mixers. Chem. Eng. Process. 9 (2015), 143–159, 10.1016/j.cep.2015.03.015.
28. Khan, F.R., Investigation of turbulent flows and instabilities in a stirred vessel using particle image velocimetry. PhD Thesis, 2005, Loughborough University, Loughborough, UK.
29. Kevala, K.R., Kieger, K.T., Calabrese, R.V., PIV study of small scale and transient flow structures for turbulent flow in an inline rotor-stator mixer. 2005, Mixing XX, North American Mixing Federation, Parksville.
30. Kolmogorov, A, N., 1949. On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk. SSSR 66, 825–828. (Originally in Russian. Reprinted and translated in Selected Works of A.N. Kolmogorov, Volume 1: Mathematics and Mechanics, Tikhomirov, V.M. (ed.), 1991, p. 339–343).
31. Kolmogorov, A.N., A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13:1 (1962), 82–85, 10.1017/S0022112062000518.
32. Kresta, S.M., Wood, P.E., The flow field produced by a pitched blade turbine characterization of the turbulence and estimation of the dissipation rate. Chem. Eng. Sci. 48 (1993), 1761–1774, 10.1016/0009-2509(93)80346-R.
33. Lou, H., Svendsen, H.F., Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 42:5 (1996), 1225–1233, 10.1002/aic.690420505.
34. Meneveau, C., Sreenivasan, K.R., The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224 (1991), 429–484, 10.1017/S0022112091001830.
35. Mortensen, H.H., Calabrese, R.V., Innings, F., Rosendahl, L., Characteristics of a batch rotor-stator mixer performance elucidated by shaft torque and angle resolved PIV measurements. Can. J. Chem. Eng. 89 (2011), 1076–1095, 10.1002/cjce.20587.
36. Narsimhan, G., Gupta, J.P., Ramkrishna, D., A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions. Chem. Eng. Sci. 34 (1979), 257–265, 10.1016/0009-2509(79)87013-X.
37. Obukov, A.M., Some specific features of atmospheric turbulence. J. Fluid Mech. 13 (1962), 77–81, 10.1029/JZ067i008p03011.
38. Pope, S.B., Turbulent Flows. 2000, Cambridge University Press, Cambridge.
39. Raffel, M., Kompenhaus, J., Wereley, S.T., Wilert, C.E., 2007. Particle Image Velocimetry: A Practical Guide. Springer, Berlin. DOI: http://dx.doi.org/10.1007/978-3-540-72308-0.
40. Saddoughi, S.G., Veeravalli, S.V., Local isotropy in turbulent boundary layers at high Reynolds numbers. J. Fluid Mech. 268 (1994), 333–372, 10.1017/S0022112094001370.
41. Sheng, J., Meng, H., Fox, R.O., A large eddy PIV method for turbulence dissipation rate estimation. Chem. Eng. Sci. 55 (2000), 4423–4434, 10.1016/S0009-2509(00)00039-7.
42. Sreenivasan, K.R., Possible effects of small-scale intermittency in turbulent reacting flows. Flow, Turbul. Combust. 72 (2004), 115–131, 10.1023/B:APPL.0000044408.46141.26.
43. Utomo, A., Baker, M., Pacek, A.W., The effect of stator geometry on the flow pattern and energy dissipation rate in a rotor-stator mixer. Chem. Eng. Res. Des. 87 (2009), 533–542, 10.1016/j.cherd.2008.12.011.
44. Vankova, N., Tcholakova, S., Denkov, N.D., Ivanov, I.B., Vulchev, V.D., Danner, T., Emulsification in turbulent flow 1. Mean and maximum drop diameters in inertial and viscous regimes. J. Colloid Interface Sci. 312 (2007), 363–380, 10.1016/j.jcis.2007.03.059.
45. Xu, S., Cheng, Q., Li, W., Zhang, J., LDA measurements and CFD simulations of an in-line high shear mixer with ultrafine teeth. AIChE J. 60 (2014), 1143–1155, 10.1002/aic.14315.