Abstract
Particle shape and particle-size distribution (PSD) are important factors for pigment packing and water retention in the pigment coating process, being closely associated with many runnability problems. Diverse experimental investigations on the packing and dewatering of pigment slurries have been made. However, theoretical approaches remain lacking. This paper presents a joint experimental and theoretical analysis of the influence of pigment shape and PSD on pigment packing and dewatering. The relative viscosities of very dilute pigment slurries were measured and used to determine the intrinsic viscosity, based on the Einstein equation. The deviation of pigment shape from spherical caused an increase in viscosity of the slurries. Acicular precipitated calcium carbonates gave lower shape factor values than platy clay particles, which indicated that the needle-like particles could rotate more easily around their long axes under shearing conditions. The packing of pigments, which determines porosity, permeability, light scattering, and mechanical properties, was examined. The packing volumes of nonspherical pigments were estimated based on their respective PSDs, using an algorithm developed for spherical particles, modified with a correction factor. This model is based on the close random-packing volume fraction (\(\emptyset_{\text{p}}^{ 2}\)) of particles of uniform size being an independent variable, regardless of their shape. Therefore, it was valid as long as the particles always achieve the same close random-packing volume (\(\emptyset_{\text{p}}^{ 1}\)) by sedimentation or tapping. Overall, the effect of the particle shape and PSD on the dewatering and filter-cake permeability (Kf) was analyzed. The dewatering rates were measured with a common pressure filtration method, and the permeability of the filter cakes was obtained by fitting the data to a filtration equation. The particle size and PSD were found to influence the permeability constant, but there was little correlation between the permeability and particle shape.
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References
Lohmander, S, “Aspect Ratios of Pigment Particles Determined by Different Methods.” Nord. Pulp Pap. Res J., 15 (4) 300–305 (2000)
Weigl, J, Grossmann, H, “Factors Impeding High-Speed Runnability of Blade Coaters.” TAPPI J., 80 (11) 223–232 (1997)
Einstein, A, “Eine Neue Bestimmung der Moleküldimensionen.” Ann. Physik, 19 (2) 289–306 (1906); “Corrections, Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen.” Ann. Physik, 34 (3) 591–592 (1911)
Barnes, HA, Hutton, JF, Walters, K, An Introduction to Rheology. Elsevier, New York (1989)
Lindhjem, C, “Particle Packing and Shape Effects on the Rheological Characteristics of Paper Coating Pigments.” TAPPI Coating Conference Proceedings, Atlanta, GA, May 1991
Westman, AER, Hugill, HR, “The Packing of Particles.” J. Am. Ceram. Soc., 13 (10) 767–779 (1930)
Furnas, CC, “Mathematical Relations for Beds of Broken Solids of Maximum Density.” Ind. Eng. Chem., 23 (9) 1052–1058 (1931)
McGeary, RK, “Mechanical Packing of Spherical Particles.” J. Am. Ceram. Soc., 44 (10) 513–522 (1961)
Yerazunis, S, Bartlett, JW, Nissan, AH, “Packing of Binary Mixtures of Spheres and Irregular Particles.” Nature, 195 33–35 (1962)
Lee, DI, “Packing of Spheres and Its Effect on the Viscosity of Suspensions.” J. Paint Technol., 42 (550) 579–587 (1970)
Haughey, DP, Beveridge, GSG, “Structural Properties of Packed Beds: A Review.” Can. J. Chem. Eng., 47 (2) 130–140 (1969)
Gupta, RK, Seshadri, SG, “Maximum Loading Levels in Filled Liquid Systems.” J. Rheol., 30 (3) 503–508 (1986)
Eksi, G, Bousfield, DW, “Modeling of Coating Structure Development.” TAPPI J., 80 (2) 125–135 (1997)
Cumberland, DJ, Crawford, RJ, The Packing of Particles. Elsevier, Amsterdam (1987)
German, RM, Particle Packing Characteristics. Metal Powder Industries Federation, Princeton, NJ (1987)
Dodds, JA, “The Porosity and Contact Point in Multicomponent Random Sphere Packing Calculated by a Simple Statistical Geometric Model.” J. Colloid Interface Sci., 77 (2) 317–327 (1980)
Ouchiyama, N, Tanaka, T, “Porosity of a Mass of Solid Particle Having a Range of Sizes.” Ind. Eng. Chem. Fundam., 20 (1) 66–71 (1981)
Ouchiyama, N, Tanaka, T, “Porosity Estimation from Particle Size Distribution.” Ind. Eng. Chem. Fundamen., 25 (1) 125–129 (1986)
Stovall, T, De Larrard, F, Buil, M, “Linear Packing Density of Grain Mixtures.” Powder Technol., 48 (1) 1–12 (1986)
Yu, AB, Standish, N, “Porosity Calculation of Multi-component Mixtures of Particle.” Powder Technol., 52 (3) 233–241 (1987)
Yu, AB, Standish, N, “An Analytical Parametric Theory of the Random Packing of Particles.” Powder Technol., 55 (3) 171–186 (1988)
Yu, AB, Standish, N, “Estimation of the Porosity of Particle Mixtures by a Linear-Mixture Packing Model.” Ind. Eng. Chem. Res., 30 (6) 1372–1385 (1991)
Yu, AB, Standish, N, McLean, A, “Porosity Calculation of Binary Mixtures of Nonspherical Particles.” J. Am. Ceram Soc., 76 (11) 2813–2816 (1993)
Zheng, J, Carlson, WB, Reed, JS, “The Packing Density of Binary Powder Mixtures.” J. Eur. Ceram. Soc., 15 479–483 (1995)
Bierwagen, GP, “CPVC (Critical Pigment Volume Concentration) Calculations.” J. Paint Technol., 44 (574) 46–55 (1972)
Yu, AB, Standish, N, “Characterisation of Non-spherical Particles from Their Packing Behavior.” Powder Technol., 74 (3) 205–213 (1993)
Zou, RP, Yu, AB, “Evaluation of the Packing Characteristics of Mono-sized Non-spherical Particles.” Powder Technol., 88 (1) 71–79 (1996)
Yuan, Y, Liu, L, Zhuang, Y, Jin, W, Li, S, “Coupling Effects of Particle Size and Shape on Improving the Density of Disordered Polydisperse Packings.” Physical Review E, 98 042903-1–042903-11 (2018)
Hardy, RE, Carter, D, “Fine Particle Clay Modifications Solve Coater Runnability Problems.” Pulp and Paper (USA) (1994)
Bousfield, DW, “Prediction of Velocity and Coat-Weight Limits Based on Filter-Cake Formation.” TAPPI J., 77 (7) 161–171 (1994)
Sonn, JS, Bousfield, DW, “Modeling Absorption and Rheological Changes as Suspensions are Applied to Porous Substrates.” Chem. Eng. Sci., 123 (17) 579–587 (2015)
Mie, G, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen.” Physik, 330 (3) 377–445 (1908)
Lee, DI, “The Critical Pigment Volume Concentration Concept for Paper Coatings Part 2: Later-Bound Clay; Ground Calcium Carbonate, and Clay–Carbonate Pigment Coatings.” J. Korea Tech. Assoc. Pulp Pap. Ind., 34 (5) 18–38 (2002)
Gane, PAC, McGenity, PM, Watters, P, “Factors Influencing the Runnability of Coating Colors at High Speed.” TAPPI J., 75 (5) 61–73 (1992)
Gane, PAC, Hooper, JJ, Grunwald, A, “Coating Pigment Orientation: A Comparative Analysis of the Application Mechanisms and Properties of Blade and Roll Coatings.” TAPPI J., 80 (2) 109–115 (1997)
Lehtinen, E, Pigment Coating and Surface Sizing of Paper. TAPPI Press, Atlanta (2000)
Krieger, IM, Dougherty, TJ, “A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres.” Trans. Soc. Rheol., 3 (1) 137–152 (1959)
Lee, HK, Joyce, M, Fleming, PD, “Influence of Pigment Particles on Gloss and Printability for Inkjet Paper Coatings.” International Conference on Digital Printing Technologies Proceedings, Salt Lake City, UT, October 2004
Gane, PAC, Matthews, GP, Schoelkopf, J, “Offset Ink Tack and Rheology Correlation Part 1: Ink Rheology as a Function of Concentration.” TAPPI J., 2 (6) 13–19 (2003)
Gane, PAC, Matthews, GP, Schoelkopf, J, “Offset Ink Tack and Rheology Correlation Part 2: Determining in Real Time the Solids Content of Ink-on-Paper Using the Ink Tack Force-Time Integral.” TAPPI J., 2 (7) 23–24 (2003)
Weeks, L, Yum, G, Bousfield, DW, Hayes, P, “Effect of Particle Shape and Latex Particle Size Distributions on Dewatering and Filtercake Permeability.” Advanced Coating Fundamentals Symposium Proceedings, Charlotte, NC, April 2018.
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The authors are grateful to National Research Foundation of Korea (NRF-2017R1D1A1B03031546) for financial support of this work and to Dr. Do Ik Lee for the use of his algorithm for packing calculation.
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Shin, J.Y., Lee, H.L. The influence of different shapes and size distributions of coating pigments on packing and dewatering. J Coat Technol Res 17, 1425–1436 (2020). https://doi.org/10.1007/s11998-020-00371-y
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DOI: https://doi.org/10.1007/s11998-020-00371-y