# Ian Frigaard

#### Professor

B.Sc. (Univ. of Wales), M.Sc. (Oxon), D.Phil. (Oxon), C.Math.

phone: |
(604) 822-1316 |

fax: |
(604) 822-2403 |

email: |
frigaard@math.ubc.ca |

website: |
blogs.ubc.ca/frigaard |

office: |
ICCS 177 |

### Research Interests

My research falls into two main categories:

**Non-Newtonian fluid mechanics:**Subjects recently studied with yield stress fluids include: Suspension flows, Wavy-walled channels and fouling, Shear instabilities, Rayleigh-Bénard flows, Bubble propagation, particle sedimentation, visco-plastic lubrication, miscible displacement flows. Research in these areas is ongoing.**Industrial mathematical modelling:**This work is industry-driven. Broadly, I have been interested in processes combing thermal and fluid dynamic effects. Examples: oilfield cementing, spray deposition/forming, injection molding, continuous casting, Czrochalski crystal growth, image processing, wellbore hydraulics, slurry transport, well control.

### Current Research Work

**Non-Newtonian fluid mechanics:**Subjects recently studied with yield stress fluids include: Shear instabilities, Rayleigh-Bénard flows, Bubble propagation, particle sedimentation, visco-plastic lubrication, miscible displacement flows, dispersion, Taylor-Couette instabilities, regularization methods. Research in these areas is ongoing.**Industrial mathematical modelling:**Subjects recently studied include: InSb crystal growth, injection molding, reactive displacement flows, waxy crude oil pipeline restarts, cementing displacement flows.

### Selected Publications

- I.A. Frigaard, “Simple Yield Stress Fluids,”
*Current Opinion in Colloid & Interface Science,*2019. - I.A. Frigaard, C. Nouar, “Onset of flow in a vibrated thin viscoplastic layer,”
*Journal of Non-Newtonian Fluid Mechanics,*2019. - E. Chaparian, A. Wachs, I.A. Frigaard, “Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid,”
*Physics of Fluids*,*30*(3), p.033101, 2018. - A. Etrati, K. Alba, I.A. Frigaard, “Two-layer displacement flow of miscible fluids with viscosity ratio: Experiments,”
*Physics of Fluids*,*30*(5), p.052103, 2018. - A. Etrati, I.A. Frigaard, “A two-layer model for buoyant inertial displacement flows in inclined pipes,”
*Physics of Fluids*,*30*(2), p.022107, 2018. - P. Sarmadi, S. Hormozi, I.A. Frigaard, “Flow development and interface sculpting in stable lubricated pipeline transport,”
*Journal of Non-Newtonian Fluid Mechanics*,*261*, pp.60-80, 2018. - N. Hanachi, A. Maleki, I.A. Frigaard, “A model for foamed cementing of oil and gas wells,”
*Journal of Engineering Mathematics*,*113*(1), pp.93-121, 2018. - A. Renteria, A. Maleki, I.A. Frigaard, B. Lund, A. Taghipour, J.D. Ytrehus, “Displacement Efficiency for Primary Cementing of Washout Sections in Highly Deviated Wells,” In
*SPE Asia Pacific Oil and Gas Conference and Exhibition*. Society of Petroleum Engineers, 2018. - I.A. Frigaard, A. Maleki, “Tracking Fluid Interface in Carbon Capture and Storage Cement Placement Application,” In
*ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering*(pp. V008T11A060-V008T11A060). American Society of Mechanical Engineers, 2018. - A. Maleki, I.A. Frigaard, “Tracking fluid interfaces in primary cementing of surface casing,”
*Physics of Fluids*,*30*(9), p.093104, 2018. - A. Maleki, I.A. Frigaard, “Turbulent displacement flows in primary cementing of oil and gas wells,”
*Physics of Fluids*,*30*(12), p.123101, 2018. - A. Etrati, I.A. Frigaard, “Viscosity effects in density-stable miscible displacement flows: Experiments and simulations,”
*Physics of Fluids*,*30*(12), p.123104, 2018. - T. Treskatis, A. Roustaei, I.A. Frigaard, A. Wachs, “Practical guidelines for fast, efficient and robust simulations of yield-stress flows without regularisation: A study of accelerated proximal gradient and augmented Lagrangian methods,”
*Journal of Non-Newtonian Fluid Mechanics*,*262*, pp.149-164, 2018. - A.S. Shirazi, I.A. Frigaard, “A New Three-Layer Model for Horizontal Slurry Flow,” 2018.
- M. Zare, I.A. Frigaard, “Onset of miscible and immiscible fluids’ invasion into a viscoplastic fluid,”
*Physics of Fluids*,*30*(6), p.063101, 2018. - I.A. Frigaard, K.G. Paso, P.R. de Souza Mendes, “Bingham’s model in the oil and gas industry,”
*Rheologica Acta*,*56*(3), pp.259-282, 2017. - E. Chaparian, I.A. Frigaard, “Yield limit analysis of particle motion in a yield-stress fluid,”
*Journal of Fluid Mechanics*,*819*, pp.311-351, 2017. - A. Maleki, I.A. Frigaard, “Primary cementing of oil and gas wells in turbulent and mixed regimes,”
*Journal of Engineering Mathematics*,*107*(1), pp.201-230, 2017. - E. Chaparian, I.A. Frigaard, “Cloaking: Particles in a yield-stress fluid,”
*Journal of Non-Newtonian Fluid Mechanics*,*243*, pp.47-55, 2017. - I.A. Frigaard, J.A. Iglesias, G. Mercier, C. Pöschl, O. Scherzer, “Critical yield numbers of rigid particles settling in Bingham fluids and Cheeger sets,”
*SIAM Journal on Applied Mathematics*,*77*(2), pp.638-663, 2017. - P. Sarmadi, S. Hormozi, I.A. Frigaard, “Triple-layer configuration for stable high-speed lubricated pipeline transport,”
*Physical Review Fluids*,*2*(4), p.044302, 2017. - G. Goyal, G.J. Elfring, I.A. Frigaard, “Rheology and flow studies of drag-reducing gravel packing fluids,”
*Rheologica Acta*,*56*(11), pp.905-914, 2017. - D.M. Martinez, J.A. Olson, A. Madani, I.A. Frigaard, D. Farajisarir, J. Lockhart, “
*Method and apparatus for continuously fractionating particles contained within a viscoplastic fluid,”*U.S. Patent 9,849,466, 2017. - S.A. Ale Etrati Khosroshahi, I.A. Frigaard, “Buoyant miscible displacement flow of shear-thinning fluids: Experiments and Simulations,” In
*APS Meeting Abstracts,*2017. - P. Sarmadi, S. Hormozi, I.A. Frigaard, “Viscoplastic sculpting in stable triple layer heavy oil transport flow,” In
*APS Meeting Abstracts,*2017. - A. Wachs, I.A. Frigaard, “Particle settling in yield stress fluids: Limiting time, distance and applications,”
*Journal of Non-Newtonian Fluid Mechanics*,*238*, pp.189-204, 2016. - N. J. Balmforth, I. A. Frigaard, G. Ovarlez, “Yielding to stress: Recent developments in viscoplastic fluid mechanics,”
*Annual Review of Fluid Mechanics*, vol. 46, pp. 121–146, 2014. - K. Alba, S.M. Taghavi, I.A. Frigaard, “Miscible density-unstable displacement flows in inclined tubes.”
*Phys. Fluids*, accepted for publication March 2013 and to appear. - A. Roustaei, I.A. Frigaard, “The occurrence of fouling layers in the flow of a yield stress fluid along a wavy-walled channel.”
*J. non-Newt. Fluid Mech.*, accepted for publication, March 2013, to appear. - S.M. Taghavi, I.A. Frigaard, “Estimation of mixing volumes in buoyant miscible displacement flows along near-horizontal pipes.”
*Can. J. Chem. Eng.*, 91(3), pp. 399–412, (2013). - M. Moyers-Gonzalez, K. Alba, S.M. Taghavi, I.A. Frigaard, “Fluid-fluid displacement flows in pipes: development of a semi-analytical closure for stratified interfaces.”
*J. non-Newt. Fluid Mech.*, 193, pp. 49-67, (2013). - K. Alba, S.M. Taghavi, I.A. Frigaard, “A weighted residual method for two-layer non-Newtonian channel flows: steady-state results and their stability”,
*J. Fluid Mech.*731, pp. 509—544, (2013) - A. Madani, D.M. Martinez, J.A. Olson, I.A. Frigaard, “The stability of spiral Poiseuille flows of Newtonian and Bingham fluids in an annular gap.”
*J. non-Newt. Fluid Mech.*, 193, pp. 3-10, (2013). - M. Moyers-Gonzalez, K. Alba, S.M. Taghavi, I.A. Frigaard, “A semi-analytical closure approximation for pipe flows of two Herschel–Bulkley fluids with a stratified interface.”
*J. non-Newt. Fluid Mech.*, 193, 49-67 (2013). - K. Alba, S.M. Taghavi, I.A. Frigaard, “Miscible density-stable displacement flows in inclined tubes.”
*Phys. Fluids*, 24, 123102 (2012) - A. Madani, D.M. Martinez, J.A. Olson, I.A. Frigaard, “The stability of spiral Poiseuille flows of Newtonian and Bingham fluids in an annular gap.”
*J. non-Newt. Fluid Mech.*, doi.org/10.1016/j.jnnfm.2012.02.007, (2012).

**Books:**

- J. Bélair, I.A. Frigaard, H. Kunze, R. Makarov, R. Melnik, R.J. Spiteri,
*Mathematical and computational approaches in advancing modern science and engineering,*Springer, 2017.