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Dip coating of bidisperse particulate suspensions

Published online by Cambridge University Press:  15 February 2022

Deok-Hoon Jeong Open the ORCID record for Deok-Hoon Jeong [Opens in a new window] ,
Michael Ka Ho Lee ,
Virgile Thiévenaz Open the ORCID record for Virgile Thiévenaz [Opens in a new window] ,
Martin Z. Bazant Open the ORCID record for Martin Z. Bazant [Opens in a new window]  and
Alban Sauret Open the ORCID record for Alban Sauret [Opens in a new window]
Deok-Hoon Jeong
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Michael Ka Ho Lee
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Virgile Thiévenaz
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Martin Z. Bazant
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Saint-Gobain Research North America, Northborough, MA 01532, USA
Alban Sauret*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: [email protected]
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Abstract

Dip coating consists of withdrawing a substrate from a bath to coat it with a thin liquid layer. This process is well understood for homogeneous fluids, but heterogeneities, such as particles dispersed in liquid, lead to more complex situations. Indeed, particles introduce a new length scale, their size, in addition to the thickness of the coating film. Recent studies have shown that, at first order, the thickness of the coating film for monodisperse particles can be captured by an effective capillary number based on the viscosity of the suspension, providing that the film is thicker than the particle diameter. However, suspensions involved in most practical applications are polydisperse, characterized by a wide range of particle sizes, introducing additional length scales. In this study, we investigate the dip coating of suspensions having a bimodal size distribution of particles. We show that the effective viscosity approach is still valid in the regime where the coating film is thicker than the diameter of the largest particles, although bidisperse suspensions are less viscous than monodisperse suspensions of the same solid fraction. We also characterize the intermediate regime that consists of a heterogeneous coating layer and where the composition of the film is different from the composition of the bath. A model to predict the probability of entraining the particles in the liquid film depending on their sizes is proposed and captures our measurements. In this regime, corresponding to a specific range of withdrawal velocities, capillarity filters the large particles out of the film.

JFM classification

Interfacial Flows (free surface): Capillary flows Materials Processing Flows: Coating Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A36
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Berteloot, G., Daerr, A., Lequeux, F. & Limat, L. 2013 Dip coating with colloids and evaporation. Chem. Engng Process 68, 69–73.CrossRefGoogle Scholar
Bonnoit, C., Bertrand, T., Clément, E. & Lindner, A. 2012 Accelerated drop detachment in granular suspensions. Phys. Fluids 24 (4), 043304.CrossRefGoogle Scholar
Bonnoit, C., Darnige, T., Clement, E. & Lindner, A. 2010 Inclined plane rheometry of a dense granular suspension. J. Rheol. 54 (1), 65–79.CrossRefGoogle Scholar
Bretherton, F.P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (2), 166–188.CrossRefGoogle Scholar
Château, J., Guazzelli, É. & Lhuissier, H. 2018 Pinch-off of a viscous suspension thread. J. Fluid Mech. 852, 178–198.CrossRefGoogle Scholar
Château, J. & Lhuissier, H. 2019 Breakup of a particulate suspension jet. Phys. Rev. Fluids 4 (1), 012001.CrossRefGoogle Scholar
Colosqui, C.E., Morris, J.F. & Stone, H.A. 2013 Hydrodynamically driven colloidal assembly in dip coating. Phys. Rev. Lett. 110 (18), 188302.CrossRefGoogle ScholarPubMed
Couturier, É., Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 686, 26–39.CrossRefGoogle Scholar
De Ryck, A. & Quéré, D. 1998 Fluid coating from a polymer solution. Langmuir 14 (7), 1911–1914.CrossRefGoogle Scholar
Delacotte, J., Montel, L., Restagno, F., Scheid, B., Dollet, B., Stone, H.A., Langevin, D. & Rio, E. 2012 Plate coating: influence of concentrated surfactants on the film thickness. Langmuir 28 (8), 3821–3830.CrossRefGoogle ScholarPubMed
Derjaguin, B. 1943 On the thickness of liquid layer adhering to walls of vessels after emptying and the theory of photo- and motion picture film coating. Dokl. Akad. Nauk SSSR 39, 13–16.Google Scholar
Dincau, B.M., Bazant, M.Z., Dressaire, E. & Sauret, A. 2019 Capillary sorting of particles by dip coating. Phys. Rev. Appl. 12 (1), 011001.CrossRefGoogle Scholar
Dincau, B.M., Mai, E., Magdelaine, Q., Lee, J.A., Bazant, M.Z. & Sauret, A. 2020 Entrainment of particles during the withdrawal of a fibre from a dilute suspension. J. Fluid Mech. 903, A38.CrossRefGoogle Scholar
Dörr, A., Sadiki, A. & Mehdizadeh, A. 2013 A discrete model for the apparent viscosity of polydisperse suspensions including maximum packing fraction. J. Rheol. 57 (3), 743–765.CrossRefGoogle Scholar
Dressaire, E. & Sauret, A. 2017 Clogging of microfluidic systems. Soft Matt. 13 (1), 37–48.CrossRefGoogle Scholar
Fornari, W., Brandt, L., Chaudhuri, P., Lopez, C.U., Mitra, D. & Picano, F. 2016 Rheology of confined non-brownian suspensions. Phys. Rev. Lett. 116 (1), 018301.CrossRefGoogle ScholarPubMed
Furbank, R.J. & Morris, J.F. 2004 An experimental study of particle effects on drop formation. Phys. Fluids 16 (5), 1777–1790.CrossRefGoogle Scholar
Gamonpilas, C., Morris, J.F. & Denn, M.M. 2016 Shear and normal stress measurements in non-brownian monodisperse and bidisperse suspensions. J. Rheol. 60 (2), 289–296.CrossRefGoogle Scholar
Gans, A., Dressaire, E., Colnet, B., Saingier, G., Bazant, M.Z. & Sauret, A. 2019 Dip-coating of suspensions. Soft Matt. 15 (2), 252–261.CrossRefGoogle ScholarPubMed
Ghosh, M., Fan, F. & Stebe, K.J. 2007 Spontaneous pattern formation by dip coating of colloidal suspensions on homogeneous surfaces. Langmuir 23 (4), 2180–2183.CrossRefGoogle ScholarPubMed
Gondret, P. & Petit, L. 1997 Dynamic viscosity of macroscopic suspensions of bimodal sized solid spheres. J. Rheol. 41 (6), 1261–1274.CrossRefGoogle Scholar
Grosso, D. 2011 How to exploit the full potential of the dip-coating process to better control film formation. J. Mater. Chem. 21 (43), 17033–17038.CrossRefGoogle Scholar
Guazzelli, É. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Gutfinger, C. & Tallmadge, J.A. 1965 Films of non-newtonian fluids adhering to flat plates. AIChE J. 11 (3), 403–413.CrossRefGoogle Scholar
Guy, B.M., Ness, C., Hermes, M., Sawiak, L.J., Sun, J. & Poon, W.C.K. 2020 Testing the wyart–cates model for non-brownian shear thickening using bidisperse suspensions. Soft Matt. 16 (1), 229–237.CrossRefGoogle ScholarPubMed
Hewson, R.W., Kapur, N. & Gaskell, P.H. 2009 A model for film-forming with newtonian and shear-thinning fluids. J. Non-Newtonian Fluid Mech. 162 (1-3), 21–28.CrossRefGoogle Scholar
Jeong, D.-H., Kvasnickova, A., Boutin, J.-B., Cébron, D. & Sauret, A. 2020 Deposition of a particle-laden film on the inner wall of a tube. Phys. Rev. Fluids 5 (11), 114004.CrossRefGoogle Scholar
Kao, J.C.T. & Hosoi, A.E. 2012 Spinodal decomposition in particle-laden landau-levich flow. Phys. Fluids 24 (4), 041701.CrossRefGoogle Scholar
Krechetnikov, R. 2010 On application of lubrication approximations to nonunidirectional coating flows with clean and surfactant interfaces. Phys. Fluids 22 (9), 092102.CrossRefGoogle Scholar
Krechetnikov, R. & Homsy, G.M. 2005 Experimental study of substrate roughness and surfactant effects on the Landau-Levich law. Phys. Fluids 17 (10), 102108.CrossRefGoogle Scholar
Krechetnikov, R. & Homsy, G.M. 2006 Surfactant effects in the Landau–Levich problem. J. Fluid Mech. 559, 429–450.CrossRefGoogle Scholar
Kulkarni, S.D., Metzger, B. & Morris, J.F. 2010 Particle-pressure-induced self-filtration in concentrated suspensions. Phys. Rev. E 82 (1), 010402.CrossRefGoogle ScholarPubMed
Levich, B. & Landau, L. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. URSS 17, 42.Google Scholar
Mahadik, S.A., Vhatkara, R.S., Mahadik, D.B., Kavale, M.S., Wagh, P.B., Gupta, S., Gurav, J., et al. 2013 Superhydrophobic silica coating by dip coating method. Appl. Surf. Sci. 277, 67–72.CrossRefGoogle Scholar
Maillard, M., Boujlel, J. & Coussot, P. 2014 Solid-solid transition in landau-levich flow with soft-jammed systems. Phys. Rev. Lett. 112 (6), 068304.CrossRefGoogle ScholarPubMed
Maillard, M., Boujlel, J. & Coussot, P. 2015 Flow characteristics around a plate withdrawn from a bath of yield stress fluid. J. Non-Newtonian Fluid Mech. 220, 33–43.CrossRefGoogle Scholar
Maleki, M., Reyssat, M., Restagno, F., Quéré, D. & Clanet, C. 2011 Landau–Levich menisci. J. Colloid Interface Sci. 354 (1), 359–363.CrossRefGoogle ScholarPubMed
Mechiakh, R., Ben Sedrine, N., Chtourou, R. & Bensaha, R. 2010 Correlation between microstructure and optical properties of nano-crystalline tio2 thin films prepared by sol-gel dip coating. Appl. Surf. Sci. 257 (3), 670–676.CrossRefGoogle Scholar
Ninfa, A.J., Ballou, D.P. & Benore, M. 2009 Fundamental Laboratory Approaches for Biochemistry and Biotechnology. John Wiley & Sons.Google Scholar
Ouchiyama, N. & Tanaka, T. 1984 Porosity estimation for random packings of spherical particles. Ind. Engng Chem. Fundam. 23 (4), 490–493.CrossRefGoogle Scholar
Palma, S. & Lhuissier, H. 2019 Dip-coating with a particulate suspension. J. Fluid Mech. 869, R3.CrossRefGoogle Scholar
Pednekar, S., Chun, J. & Morris, J.F. 2018 Bidisperse and polydisperse suspension rheology at large solid fraction. J. Rheol. 62 (2), 513–526.CrossRefGoogle Scholar
Peyla, P. & Verdier, C. 2011 New confinement effects on the viscosity of suspensions. Europhys. Lett. 94 (4), 44001.CrossRefGoogle Scholar
Probstein, R.F., Sengun, M.Z. & Tseng, T.-C. 1994 Bimodal model of concentrated suspension viscosity for distributed particle sizes. J. Rheol. 38 (4), 811–829.CrossRefGoogle Scholar
Quemada, D. 1977 Rheology of concentrated disperse systems and minimum energy dissipation principle. Rheol. Acta 16 (1), 82–94.CrossRefGoogle Scholar
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31 (1), 347–384.CrossRefGoogle Scholar
Raux, P.S., Troger, A., Jop, P. & Sauret, A. 2020 Spreading and fragmentation of particle-laden liquid sheets. Phys. Rev. Fluids 5 (4), 044004.CrossRefGoogle Scholar
Rio, E. & Boulogne, F. 2017 Withdrawing a solid from a bath: how much liquid is coated? Adv. Colloid Interface Sci. 247, 100–114.CrossRefGoogle ScholarPubMed
Ro, J.S. & Homsy, G.M. 1995 Viscoelastic free surface flows: thin film hydrodynamics of hele-shaw and dip coating flows. J. Non-Newtonian Fluid Mech. 57 (2–3), 203–225.CrossRefGoogle Scholar
Ruckenstein, E. 2002 Scaling analysis of coating of a plate or a fiber. J. Colloid Interface Sci. 246 (2), 393–400.CrossRefGoogle ScholarPubMed
Ruschak, K.J. 1985 Coating flows. Annu. Rev. Fluid Mech. 17 (1), 65–89.CrossRefGoogle Scholar
Sauret, A., Barney, E.C., Perro, A., Villermaux, E., Stone, H.A. & Dressaire, E. 2014 Clogging by sieving in microchannels: Application to the detection of contaminants in colloidal suspensions. Appl. Phys. Lett. 105 (7), 074101.CrossRefGoogle Scholar
Sauret, A., Gans, A., Colnet, B., Saingier, G., Bazant, M.Z. & Dressaire, E. 2019 Capillary filtering of particles during dip coating. Phys. Rev. Fluids 4 (5), 054303.CrossRefGoogle Scholar
Sauret, A., Somszor, K., Villermaux, E. & Dressaire, E. 2018 Growth of clogs in parallel microchannels. Phys. Rev. Fluids 3 (10), 104301.CrossRefGoogle Scholar
Scriven, L.E. 1988 Physics and applications of dip coating and spin coating. Mater. Res. Soc. 121, 717.CrossRefGoogle Scholar
Seiwert, J., Clanet, C. & Quéré, D. 2011 Coating of a textured solid. J. Fluid Mech. 669, 55–63.CrossRefGoogle Scholar
Shapiro, A.P. & Probstein, R.F. 1992 Random packings of spheres and fluidity limits of monodisperse and bidisperse suspensions. Phys. Rev. Lett. 68 (9), 1422.CrossRefGoogle ScholarPubMed
Shen, A.Q., Gleason, B., McKinley, G.H. & Stone, H.A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14 (11), 4055–4068.CrossRefGoogle Scholar
Smit, W.J., Kusina, C., Joanny, J.-F. & Colin, A. 2019 Stress field inside the bath determines dip coating with yield-stress fluids in cylindrical geometry. Phys. Rev. Lett. 123 (14), 148002.CrossRefGoogle ScholarPubMed
Stickel, J.J. & Powell, R.L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Svarovsky, L. 2000 Solid–Liquid Separation. Elsevier.Google Scholar
Thiévenaz, V., Rajesh, S. & Sauret, A. 2021 Droplet detachment and pinch-off of bidisperse particulate suspensions. Soft Matt. 17, 6202–6211.CrossRefGoogle ScholarPubMed
Thiévenaz, V. & Sauret, A. 2021 Pinch-off of viscoelastic particulate suspensions. Phys. Rev. Fluids 6 (6), L062301.CrossRefGoogle Scholar
Urfer, D., Huck, P.M., Booth, S.D.J. & Coffey, B.M. 1997 Biological filtration for bom and particle removal: a critical review. J. Am. Water Works Assoc. 89 (12), 83–98.CrossRefGoogle Scholar
White, D.A. & Tallmadge, J.A. 1965 Static menisci on the outside of cylinders. J. Fluid Mech. 23 (2), 325–335.CrossRefGoogle Scholar
Wu, T., Yang, Z., Hu, R., Chen, Y.-F., Zhong, H., Yang, L. & Jin, W. 2021 Film entrainment and microplastic particles retention during gas invasion in suspension-filled microchannels. Water Res. 194, 116919.CrossRefGoogle ScholarPubMed
Wyss, H.M., Blair, D.L., Morris, J.F., Stone, H.A. & Weitz, D.A. 2006 Mechanism for clogging of microchannels. Phys. Rev. E 74 (6), 061402.CrossRefGoogle ScholarPubMed
Yu, Y.E., Khodaparast, S. & Stone, H.A. 2018 Separation of particles by size from a suspension using the motion of a confined bubble. Appl. Phys. Lett. 112 (18), 181604.CrossRefGoogle Scholar
Zarraga, I.E., Hill, D.A. & Leighton, D.T. Jr. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44 (2), 185–220.CrossRefGoogle Scholar
Zhang, Z., Salamatin, A., Peng, F. & Kornev, K.G. 2022 Dip coating of cylinders with Newtonian fluids. J. Colloid Interface Sci. 607, 502–513.CrossRefGoogle ScholarPubMed
Zhao, M., Oléron, M., Pelosse, A., Limat, L., Guazzelli, E. & Roché, M. 2020 Spreading of granular suspensions on a solid surface. Phys. Rev. Res. 2 (2), 022031.CrossRefGoogle Scholar