A computational study of the effect of particle migration on the low-flow limit in slot coating of particle suspensions

  • Ivan R. SiqueiraEmail author
  • Marcio S. Carvalho


Slot coating of particle suspensions is commonly used in the manufacturing of a wide variety of products. An important limit in this process is known as low-flow limit, which refers to the minimum wet film thickness that can be coated at a given substrate velocity. Recent studies have shown that shear-induced particle migration leads to a highly non-uniform particle distribution in the coating bead, playing an important role in the flow dynamics in slot coating of particulate systems. In this work, we extend the previous analyses to investigate the effects of particle migration on the low-flow limit in slot coating of particle suspensions at both dilute and concentrated conditions. As a first approximation, the suspension is modeled as a Newtonian liquid with a concentration-dependent viscosity, and shear-induced particle migration is described according to the diffusive flux model. The resulting set of governing equations is solved with a stabilized finite element method coupled with the elliptic mesh generation method for the free-boundary problem. The results show that particle migration changes the liquid viscosity near the downstream meniscus and strongly affects the force balance that sets the critical operating conditions at the low-flow limit. Remarkably, it was found that particle migration enlarges the operating window of the process when the suspensions are compared to a Newtonian liquid with the same bulk properties, especially at high concentrations.


Slot coating Suspensions Particle migration Low-flow limit Finite element method 



This work was supported by the Brazilian Research Council (CNPq) and the Industrial Partnership for Research in Interfacial & Materials Engineering of the University of Minnesota (IPRIME).


  1. 1.
    Ding, X, Liu, J, Harris, TAL, “A Review of the Operating Limits in Slot Die Coating Processes.” AIChE J., 62 (7) 2508–2524 (2016)CrossRefGoogle Scholar
  2. 2.
    Carvalho, MS, Kheshgi, HS, “Low-Flow Limit in Slot Coating: Theory and Experiments.” AIChE J., 46 (10) 1907–1917 (2000)CrossRefGoogle Scholar
  3. 3.
    Ruschak, KJ, “Limiting Flow in a Pre-metered Coating Device.” Chem. Eng. Sci., 31 (11) 1057–1060 (1976)CrossRefGoogle Scholar
  4. 4.
    Higgins, BG, Scriven, LE, “Capillary Pressure and Viscous Pressure Drop Set Bounds on Coating Bead Operability.” Chem. Eng. Sci., 35 (3) 673–682 (1980)CrossRefGoogle Scholar
  5. 5.
    Lee, K-Y, Liu, L-D, Liu, T-J, “Minimum Wet Thickness in Extrusion Slot Coating.” Chem. Eng. Sci., 47 (7) 1703–1713 (1992)CrossRefGoogle Scholar
  6. 6.
    Chang, Y-R, Chang, H-M, Lin, C-F, Liu, T-J, Wu, P-Y, “Three Minimum Wet Thickness Regions of Slot Die Coating.” J. Colloid Interface Sci., 308 (1) 222–230 (2007)CrossRefGoogle Scholar
  7. 7.
    Benkreira, H, Ikin, JB, “Slot Coating Minimum Film Thickness in Air and in Rarefied Helium.” Chem. Eng. Sci., 150 66–73 (2016)CrossRefGoogle Scholar
  8. 8.
    Romero, OJ, Suszynski, WJ, Scriven, LE, Carvalho, MS, “Low-Flow Limit in Slot Coating of Dilute Solutions of High Molecular Weight Polymer.” J. Non-Newton. Fluid Mech., 118 (2–3) 137–156 (2004)CrossRefGoogle Scholar
  9. 9.
    Romero, OJ, Scriven, LE, Carvalho, MS, “Slot Coating of Mildly Viscoelastic Liquids.” J. Non-Newton. Fluid Mech., 138 (2–3) 63–75 (2006)CrossRefGoogle Scholar
  10. 10.
    Bajaj, M, Prakash, JR, Pasquali, M, “A Computational Study of the Effect of Viscoelasticity on Slot Coating Flow of Dilute Polymer Solutions.” J. Non-Newton. Fluid Mech., 149 (1–3) 104–123 (2008)CrossRefGoogle Scholar
  11. 11.
    Ning, C-Y, Tsai, C-C, Liu, T-J, “The Effect of Polymer Additives on Extrusion Slot Coating.” Chem. Eng. Sci., 51 (12) 3289–3297 (1996)CrossRefGoogle Scholar
  12. 12.
    Yang, CK, Wong, DSH, Liu, TJ, “The Effects of Polymer Additives on the Operating Windows of Slot Coating.” Polym. Eng. Sci., 44 (10) 1970–1976 (2004)CrossRefGoogle Scholar
  13. 13.
    Chu, V, Tsai, M-Z, Chang, Y-R, Liu, T-J, Tiu, C, “Effects of the Molecular Weight and Concentration of Poly(Vinyl Alcohol) on Slot Die Coating.” J. Appl. Polym. Sci., 116 (2) 654–662 (2010)CrossRefGoogle Scholar
  14. 14.
    Huang, Y-C, Wang, T-Z, Liu, T-J, Tiu, C, “Operating Window of Solution Casting. II. Non-newtonian Fluids.” J. Appl. Polym. Sci., 132 (5) 41411 (2015)CrossRefGoogle Scholar
  15. 15.
    Campana, DM, Silva, LDV, Carvalho, MS, “Slot Coating Flows of Non-colloidal Particle Suspensions.” AIChE J., 63 (3) 1122–1131 (2017)CrossRefGoogle Scholar
  16. 16.
    Siqueira, IR, Rebouças, RB, Carvalho, MS, “Particle Migration and Alignment in Slot Coating Flows of Elongated Particle Suspensions.” AIChE J., 63 (7) 3187–3198 (2017)CrossRefGoogle Scholar
  17. 17.
    Araujo, SB, Carvalho, MS, “Sedimentation and Marangoni Stress in Slot Coating Flow of Particle Suspension.” J. Non-Newton. Fluid Mech., 247 53–61 (2017)CrossRefGoogle Scholar
  18. 18.
    Rebouças, RB, Siqueira, IR, Carvalho, MS, “Slot Coating Flow of Particle Suspensions: Particle Migration in Shear Sensitive Liquids.” J. Non-Newton. Fluid Mech., 258 22–31 (2018)CrossRefGoogle Scholar
  19. 19.
    Cardinal, CM, Jung, YD, Ahn, KH, Francis, LF, “Drying Regime Maps for Particulate Coatings.” AIChE J., 56 2769–2780 (2010)CrossRefGoogle Scholar
  20. 20.
    Buss, F, Roberts, CC, Crawford, KS, Peters, K, Francis, LF, “Effect of Soluble Polymer Binder on Particle Distribution in a Drying Particulate Coating.” J. Colloid Interface Sci., 359 (1) 112–120 (2011)CrossRefGoogle Scholar
  21. 21.
    Price, KK, Wu, Y, McCormick, AV, Francis, LF, Frisbie, CD, “Stress Development in Hard Particle Coatings in the Absence of Lateral Drying.” J. Am. Ceram. Soc., 98 (7) 2214–2222 (2015)CrossRefGoogle Scholar
  22. 22.
    Baesch, S, Scharfer, P, Schabel, W, Francis, LF, “Influence of the Drying Conditions on the Particle Distribution in Particle-Filled Polymer Films: Predictive Simulation of the Particle Distribution During Drying.” J. Compos. Mater., 51 (24) 3391–3403 (2017)CrossRefGoogle Scholar
  23. 23.
    Wu, Y, Francis, LF, “Effect of Particle Size Distribution on Stress Development and Microstructure of Particulate Coatings.” J. Coat. Technol. Res., 14 (2) 455–465 (2017)CrossRefGoogle Scholar
  24. 24.
    Santamaría-Holek, I, Mendoza, CI, “The Rheology of Concentrated Suspensions of Arbitrarily-Shaped Particles.” J. Colloid Interface Sci., 346 118–126 (2010)CrossRefGoogle Scholar
  25. 25.
    Phillips, RJ, Armstrong, RC, Brown, RA, Graham, AL, Abbott, JR, “A Constitutive Equation for Concentrated Suspensions that Accounts for Shear-Induced Particle Migration.” Phys. Fluids A Fluid Dyn., 4 30–40 (1992)CrossRefGoogle Scholar
  26. 26.
    Siqueira, IR, Carvalho, MS, “Particle Migration in Planar Die-Swell Flows.” J. Fluid Mech., 825 49–68 (2017)CrossRefGoogle Scholar
  27. 27.
    de Santos Avila, JM, “Two-Phase Cocurrent Downflow Through Constricted Passages.” Ph.D. thesis, University of Minnesota, Minneapolis, United States, 1991Google Scholar
  28. 28.
    Pasquali, M, Scriven, LE, “Free Surface Flows of Polymer Solutions with Models Based on the Conformation Tensor.” J. Non-Newton. Fluid Mech., 108 (1–3) 363–409 (2002)CrossRefGoogle Scholar
  29. 29.
    Chu, W-B, Yang, J-W, Wang, Y-C, Liu, T-J, Tiu, C, Guo, J, “The Effect of Inorganic Particles on Slot Die Coating of Poly(Vinyl Alcohol) Solutions.” J. Colloid Interface Sci., 297 215–225 (2006)CrossRefGoogle Scholar

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© American Coatings Association 2019

Authors and Affiliations

  1. 1.Department of Chemical and Biomolecular EngineeringRice UniversityHoustonUSA
  2. 2.Department of Mechanical EngineeringPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil

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