References:

[1] M. Daneshvar Garmroodi and I. Karimfazli, “Mixing in heterogeneous fluids: An examination of fluid property variations,” J. Non-Newton. Fluid Mech., vol. 325, p. 105196, 2024.
[2] B. Singh, Z. Szamosi, and Z. Siménfalvi, “State of the art on mixing in an anaerobic digester: A review,” Renewable Energy, vol. 141, pp. 922–936, 2019.
[3] D. Dapelo, Gas mixing in anaerobic digestion. PhD thesis, University of Birmingham,
2016.
[4] Canada-wide strategy for the management of municipal wastewater effluent. Canadian
Council of Ministers of the Environment, 2007.
[5] P. A. Chambers, M. Allard, S. Walker, J. Marsalek, J. Lawrence, M. Servos, J. Busnarda,
K. Munger, K. Adare, C. Jefferson, et al., “Impacts of municipal wastewater effluents on
canadian waters: a review,” Water Quality Research Journal, vol. 32, no. 4, pp. 659–714,
1997.
[6] D. G. Cyr, R. Hausler, and V. Yargeau, Examination report by independent experts
on the technical and scientific information regarding the planned discharge of untreated
wastewater effluent into the St. Lawrence by the City of Montreal. Environment Canada,
2015.
[7] 2011 Municipal Water Use Report: Municipal Water Use 2009 Statistics. Environment
Canada, 2000.
[8] Data Sources and Methods: Municipal Wastewater Treatment Indicator. Environment
Canada, 2000.
[9] P. J. Cullen, R. J. Romañach, N. Abatzoglou, and C. D. Rielly, Pharmaceutical blending
and mixing. John Wiley & Sons, 2015.
[10] E. L. Paul, V. A. Atiemo-Obeng, and S. M. Kresta, Handbook of Industrial Mixing.
Wiley Online Library, 2004.
[11] P. J. Cullen, Food mixing: Principles and Applications. John Wiley & Sons, 2009.
[12] N. Balmforth, I. Frigaard, and G. Ovarlez, “Yielding to stress: recent developments in
viscoplastic fluid mechanics,” Annual Review of Fluid Mechanics, vol. 46, pp. 121–146,
2014.
[13] N. News, “Ketchup bottle stock image,” 2017. Accessed: 2025-03-14.
[14] Baamboozle, “Untitled image from baamboozle,” 2025. Accessed: 2025-03-14.
[15] Sovcombank, “Untitled image from sovcombank media library,” 2025. Accessed: 2025-
03-14.
[16] Gismeteo, “Weather-related image from gismeteo,” 2021. Accessed: 2025-03-14.
[17] C. Sandu and B. Wright, “Innovative solutions for processing shale oils,” Hydrocarbon
Processing, 2013.
[18] Kimsel, “Shutterstock image from kimsel,” 2025. Accessed: 2025-03-14.
[19] Dreamstime, “Shaving cream and razor image,” 2025. Accessed: 2025-03-14.
[20] Pinterest, “Image from pinterest,” 2025. Accessed: 2025-03-14.
[21] S. S. Desserts, “Shutterstock dessert image from sweet street desserts,” 2021. Accessed:
2025-03-14.
[22] E. C. Bingham, Fluidity and plasticity. McGraw-Hill, 1922.
[23] W. H. Herschel and R. Bulkley, “Konsistenzmessungen von gummi-benzollösungen,”
Kolloid-Zeitschrift, vol. 39, pp. 291–300, 1926.
[24] G. Ovarlez and S. Hormozi, Lectures on visco-plastic fluid mechanics. Springer, 2019.
[25] M. Allouche, I. Frigaard, and G. Sona, “Static wall layers in the displacement of two
visco-plastic fluids in a plane channel,” Journal of Fluid Mechanics, vol. 424, pp. 243–
277, 2000.
[26] M. Bercovier and M. Engelman, “A finite-element method for incompressible non-
newtonian flows,” Journal of Computational Physics, vol. 36, no. 3, pp. 313–326, 1980.
[27] T. C. Papanastasiou, “Flows of materials with yield,” Journal of rheology, vol. 31, no. 5,
pp. 385–404, 1987.
[28] R. Tanner and J. Milthorpe, “Numerical simulation of the flow of fluids with yield
stress,” Numer Meth Lami Turb Flow Seattle, pp. 680–690, 1983.
[29] A. Ahmadi and I. Karimfazli, “A quantitative evaluation of viscosity regularization
in predicting transient flows of viscoplastic fluids,” Journal of Non-Newtonian Fluid
Mechanics, vol. 287, p. 104429, 2021.
[30] H. Ameur, “Agitation of yield stress fluids in different vessel shapes,” Engineering
Science and Technology, an International Journal, vol. 19, no. 1, pp. 189–196, 2016.
[31] A. Kazemzadeh, F. Ein-Mozaffari, A. Lohi, and L. Pakzad, “Intensification of mixing
of shear-thinning fluids possessing yield stress with the coaxial mixers composed of
two different central impellers and an anchor,” Chemical Engineering and Processing:
Process Intensification, vol. 111, pp. 101–114, 2017.
[32] A. Russell, L. Kahouadji, K. Mirpuri, A. Quarmby, P. Piccione, O. Matar, P. Luckham,
and C. Markides, “Mixing viscoplastic fluids in stirred vessels over multiple scales: A
combined experimental and cfd approach,” Chem. Eng. Sci., vol. 208, p. 115129, 2019.
[33] H. Ameur, “Newly modified curved-bladed impellers for process intensification: Energy
saving in the agitation of hershel-bulkley fluids,” Chemical Engineering and Processing-
Process Intensification, vol. 154, p. 108009, 2020.
[34] H. Ameur and C. Vial, “Modified scaba 6srgt impellers for process intensification:
Cavern size and energy saving when stirring viscoplastic fluids,” Chemical Engineering
and Processing-Process Intensification, vol. 148, p. 107795, 2020.
[35] J. Solomon, T. Elson, A. Nienow, and G. Pace, “Cavern sizes in agitated fluids with
a yield stress,” Chemical Engineering Communications, vol. 11, no. 1-3, pp. 143–164,
1981.
[36] J. Boujlel, F. Pigeonneau, E. Gouillart, and P. Jop, “Rate of chaotic mixing in localized
flows,” Physical Review Fluids, vol. 1, no. 3, p. 031301, 2016.
[37] H. Ameur, “Modifications in the rushton turbine for mixing viscoplastic fluids,” J. Food
Eng., vol. 233, pp. 117–125, 2018.
[38] J. Derksen, “Simulations of mobilization of bingham layers in a turbulently agitated
tank,” J. Non-Newton. Fluid Mech., vol. 191, pp. 25–34, 2013.
[39] P. Arratia, J. Kukura, J. Lacombe, and F. Muzzio, “Mixing of shear-thinning fluids
with yield stress in stirred tanks,” AIChE journal, vol. 52, no. 7, pp. 2310–2322, 2006.
[40] P. Prajapati and F. Ein-Mozaffari, “CFD investigation of the mixing of yield-
pseudoplastic fluids with anchor impellers,” Chemical Engineering & Technology:
Industrial Chemistry-Plant Equipment-Process Engineering-Biotechnology, vol. 32,
no. 8, pp. 1211–1218, 2009.
[41] J. Sossa-Echeverria and F. Taghipour, “Effect of mixer geometry and operating
conditions on flow mixing of shear thinning fluids with yield stress,” AIChE Journal,
vol. 60, no. 3, pp. 1156–1167, 2014.
[42] J. Sossa-Echeverria and F. Taghipour, “Computational simulation of mixing flow of
shear thinning non-newtonian fluids with various impellers in a stirred tank,” Chemical
Engineering and Processing: Process Intensification, vol. 93, pp. 66–78, 2015.
[43] D. M. Wendell, F. Pigeonneau, E. Gouillart, and P. Jop, “Intermittent flow in yield-
stress fluids slows down chaotic mixing,” Physical Review E, vol. 88, no. 2, p. 023024,
2013.
[44] Y. Fan, N. Phan-Thien, and R. I. Tanner, “Tangential flow and advective mixing of
viscoplastic fluids between eccentric cylinders,” Journal of Fluid Mechanics, vol. 431,
pp. 65–89, 2001.
[45] F. Savreux, P. Jay, and A. Magnin, “Viscoplastic fluid mixing in a rotating tank,”
Chemical Engineering Science, vol. 62, no. 8, pp. 2290–2301, 2007.
[46] A. Amanullah, S. Hjorth, and A. Nienow, “A new mathematical model to predict
cavern diameters in highly shear thinning, power law liquids using axial flow impellers,”
Chemical Engineering Science, vol. 53, no. 3, pp. 455–469, 1998.
[47] Q. Xiao, N. Yang, J. Zhu, and L. Guo, “Modeling of cavern formation in yield stress
fluids in stirred tanks,” AIChE Journal, vol. 60, no. 8, pp. 3057–3070, 2014.
[48] S. Jegatheeswaran, F. Ein-Mozaffari, and J. Wu, “Process intensification in a chaotic
smx static mixer to achieve an energy-efficient mixing operation of non-newtonian
fluids,” Chemical Engineering and Processing-Process Intensification, vol. 124, pp. 1–10,
2018.
[49] D. Lester and A. Chryss, “Topological mixing of yield stress materials,” Physical Review
Fluids, vol. 4, no. 6, p. 064502, 2019.
[50] A. Metzner and R. Otto, “Agitation of non-newtonian fluids,” AIChE J., vol. 3, no. 1,
pp. 3–10, 1957.
[51] E. Galindo, M. Argüello, D. Velasco, V. Albiter, and A. Martínez, “A comparison of
cavern development in mixing a yield stress fluid by rushton and intermig impellers,”
Chem. Eng. Technol., vol. 19, no. 4, pp. 315–323, 1996.
[52] P. Tanguy, F. Bertrand, R. Labrie, and E. Brito-De La Fuente, “Numerical modelling
of the mixing of viscoplastic slurries in a twin-blade planetary mixer,” Chem. Eng. Res.
Des., vol. 74, no. 4, pp. 499–504, 1996.
[53] L. Pakzad, F. Ein-Mozaffari, S. R. Upreti, and A. Lohi, “A novel and energy-efficient
coaxial mixer for agitation of non-newtonian fluids possessing yield stress,” Chemical
Engineering Science, vol. 101, pp. 642–654, 2013.
[54] H. Aref, “Stirring by chaotic advection,” J. Fluid Mech., vol. 143, p. 1–21, 1984.
[55] J. Ottino, The kinematics of mixing: stretching, chaos, and transport, vol. 3. Cambridge
University Press, 1989.
[56] T. Niederkorn and J. Ottino, “Chaotic mixing of shear-thinning fluids,” AIChE J.,
vol. 40, no. 11, pp. 1782–1793, 1994.
[57] E. Paul, V. Atiemo-Obeng, and S. Kresta, eds., Handbook of Industrial Mixing: Science
and Practice. Wiley-Interscience, 2004.
[58] V. Uhl, Mixing V1: Theory and practice. Elsevier, 2012.
[59] K. Craig, M. Nieuwoudt, and L. J. Niemand, “Cfd simulation of anaerobic digester with
variable sewage sludge rheology,” Water research, vol. 47, no. 13, pp. 4485–4497, 2013.
[60] L. Pakzad, F. Ein-Mozaffari, and P. Chan, “Using computational fluid dynamics
modeling to study the mixing of pseudoplastic fluids with a scaba 6srgt impeller,”
Chemical Engineering and Processing: Process Intensification, vol. 47, no. 12, pp. 2218–
2227, 2008.
[61] K. M. Stewart, E. Stonecipher, H. Ning, and S. B. Pillay, “Mixing rules for high density
polyethylene-polypropylene blends,” The Canadian Journal of Chemical Engineering,
vol. 101, no. 9, pp. 5395–5407, 2023.
[62] M. Ramírez-de Santiago, “Viscosity of binary liquid mixtures: A comparative analysis of
mixing rules,” Industrial & Engineering Chemistry Research, vol. 63, no. 51, pp. 22470–
22480, 2024.
[63] G. Centeno, G. Sánchez-Reyna, J. Ancheyta, J. A. Muñoz, and N. Cardona, “Testing
various mixing rules for calculation of viscosity of petroleum blends,” Fuel, vol. 90,
no. 12, pp. 3561–3570, 2011.
[64] OpenFOAM | Open Source Computational Fluid Dynamics, “OpenFOAM Licensing.”
[65] R. Glowinski, Numerical methods for nonlinear variational problems. Springer-Verlag,
New York, 1984.
[66] M. Zare, A. Roustaei, and I. Frigaard, “Buoyancy effects on micro-annulus formation:
Density stable displacement of newtonian–bingham fluids,” Journal of Non-Newtonian
Fluid Mechanics, vol. 247, pp. 22–40, 2017.
[67] R. Kronig and J. Brink, “On the theory of extraction from falling droplets,” Applied
Scientific Research, vol. 2, pp. 142–154, 1951.
[68] C. Christov and G. Homsy, “Enhancement of transport from drops by steady and
modulated electric fields,” Physics of Fluids, vol. 21, no. 8, p. 083102, 2009.
[69] J. Ottino, “Mixing and chemical reactions a tutorial,” Chemical Engineering Science,
vol. 49, no. 24, pp. 4005–4027, 1994.
[70] L. Cortelezzi, A. Adrover, and M. Giona, “Feasibility, efficiency and transportability of
short-horizon optimal mixing protocols,” J. Fluid Mech., vol. 597, pp. 199–231, 2008.
[71] S. Cerbelli, A. Adrover, F. Creta, and M. Giona, “Foundations of laminar chaotic mixing
and spectral theory of linear operators,” Chem. Eng. Sci., vol. 61, no. 9, pp. 2754–2761,
2006. Fluid Mixing VIII International Conference.
[72] O. Gubanov and L. Cortelezzi, “On the cost efficiency of mixing optimization,” J. Fluid
Mech., vol. 692, pp. 112–136, 2012.
[73] Z. Lin, J.-L. Thiffeault, and C. R. Doering, “Optimal stirring strategies for passive
scalar mixing,” J. Fluid Mech., vol. 675, pp. 465–476, 2011.
[74] L. J. Cullen, I. S. Fernandes, M. S. Brito, M. M. Dias, J. C. B. Lopes, R. J. Santos, and
V. J. Vilar, “Flow dynamics studies in the netmix reactor for a large range of flowrate
ratios between feed streams,” Chemical Engineering Science, p. 120339, 2024.
[75] L. Schembri, G. Caputo, M. Ciofalo, F. Grisafi, S. Lima, and F. Scargiali, “Cfd
simulations of the transition between non-aerated and aerated conditions in uncovered
unbaffled stirred tanks,” Chemical Engineering Science, vol. 302, p. 120824, 2025.
[76] X. Tang, F.-c. Qiu, P. Liu, H. Li, and Z. Liu, “Revealing chaotic advection dynamics in
the chaotic mixing of non-newtonian fluids within a stirred tank employing a twisted-
punched impeller,” Industrial & Engineering Chemistry Research, vol. 63, no. 32,
pp. 14259–14274, 2024.
[77] S. Wang, T. Meng, S. Cen, P. Liu, Y. Wang, S. Qin, Y. Wang, and Z. Liu,
“Hydrodynamic intensification and interfacial regulation strategy for the mixing process
of non-newtonian fluids,” Chemical Engineering Journal, vol. 493, p. 152691, 2024.
[78] A. A. Arosemena, H. Ali, and J. Solsvik, “Characterization of vortical structures in a
stirred tank,” Physics of Fluids, vol. 34, no. 2, 2022.
[79] A. Roshko, “On the development of turbulent wakes from vortex streets,” tech. rep.,
1954.
[80] R. Tanner and J. Milthorpe, “Numerical simulation of the flow of fluids with yield
stress,” Numer. Meth. Lam. Turb. Flow Seattle, pp. 680–690, 1983.
[81] R. Thompson and E. Soares, “Viscoplastic dimensionless numbers,” J. Non-Newton.
Fluid Mech., vol. 238, pp. 57–64, 2016.
[82] A. Ahmadi, H. Olleik, and I. Karimfazli, “Rayleigh–bénard convection of carbopol
microgels: Are viscoplastic models adequate?,” J. Non-Newton. Fluid Mech., vol. 300,
p. 104704, 2022.
[83] I. Frigaard and C. Nouar, “On the usage of viscosity regularisation methods for visco-
plastic fluid flow computation,” Journal of non-newtonian fluid mechanics, vol. 127,
no. 1, pp. 1–26, 2005.