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Forced spreading of films and droplets of colloidal suspensions

Published online by Cambridge University Press:  21 February 2014

Leonardo Espín  and
Satish Kumar
Leonardo Espín
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Satish Kumar*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: kumar030@umn.edu
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Abstract

When a thin film of a colloidal suspension flows over a substrate, uneven distribution of the suspended particles can lead to an uneven coating. Motivated by this phenomenon, we analyse the flow of perfectly wetting films and droplets of colloidal suspensions down an inclined plane. Lubrication theory and the rapid-vertical-diffusion approximation are used to derive a coupled pair of one-dimensional partial differential equations describing the evolution of the interface height and particle concentration. Precursor films are assumed to be present, the colloidal particles are taken to be hard spheres, and particle and liquid dynamics are coupled through a concentration- dependent viscosity and diffusivity. We find that for sufficiently high Péclet numbers, even small initial concentration inhomogeneities produce viscosity gradients that cause the film or droplet front to evolve continuously in time instead of travelling without changing shape as happens in the absence of colloidal particles. At high enough particle concentrations, particle diffusion can lead to the formation of long-lived secondary flow fronts in films. Our results suggest that particle concentration gradients can have a dramatic influence on interface evolution in flowing films and droplets, a finding which may be relevant for understanding the onset of patterns that are observed experimentally.

JFM classification

Materials Processing Flows: Coating Complex Fluids: Colloids Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 495 - 519
Copyright
© 2014 Cambridge University Press 

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References

Bertozzi, A. L. & Brenner, M. P. 1997 Linear stability and transient growth in driven contact lines. Phys. Fluids 9, 530.CrossRefGoogle Scholar
Brady, J. F. 1993 The rheological behavior of concentrated colloidal dispersions. J. Chem. Phys. 99, 567.CrossRefGoogle Scholar
Brown, P. N., Hindmarsh, A. C. & Petzold, L. R. 1994 Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 1467.CrossRefGoogle Scholar
Buchanan, M., Molenaar, D., Villiers, S. D. & Evans, R. 2007 Pattern formation in draining thin film suspensions. Langmuir 23, 3732.CrossRefGoogle ScholarPubMed
Cook, B., Bertozzi, A. & Hosoi, A. 2008 Shock solutions for particle-laden thin films. SIAM J. Appl. Maths 68, 760.CrossRefGoogle Scholar
Craster, R. & Matar, O. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131.CrossRefGoogle Scholar
Craster, R. V., Matar, O. K. & Sefiane, K. 2009 Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir 25, 3601.CrossRefGoogle ScholarPubMed
Diez, J. A., Kondic, L. & Bertozzi, A. 2001 Global models for moving contact lines. Phys. Rev. E 63, 011208.Google ScholarPubMed
Fan, H. & Striolo, A. 2012 Nanoparticle effects on the water–oil interfacial tension.. Phys. Rev. E 86, 051610.Google ScholarPubMed
Fraštia, L., Archer, A. J. & Thiele, U. 2012 Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions. Soft Matt. 8, 11363.CrossRefGoogle Scholar
Goodwin, R. & Homsy, G. M. 1991 Viscous flow down a slope in the vicinity of a contact line. Phys. Fluids A 3, 515.CrossRefGoogle Scholar
Han, J. & Kim, C. 2012 Spreading of a suspension drop on a horizontal surface. Langmuir 28, 2680.CrossRefGoogle ScholarPubMed
Hewitt, D. R. & Balmforth, N. J. 2013 Thixotropic gravity currents. J. Fluid Mech. 727, 56.CrossRefGoogle Scholar
Hiemenz, P. C. & Rajagopalan, R. 1997 Principles of Colloid and Surface Chemistry. CRC.Google Scholar
Huppert, H. E. 1982 Flow and instability of a viscous current down a slope. Nature 300, 427.CrossRefGoogle Scholar
Jeong, H. J., Hwang, W. R., Kim, C. & Kim, S. J. 2010 Numerical simulations of capillary spreading of a particle laden-droplet on a solid surface. J. Mater. Process. Tech. 210, 297.CrossRefGoogle Scholar
Kondic, L. & Diez, J. 2001 Pattern formation in the flow of thin films down an incline: Constant flux configuration. Phys. Fluids 13, 3168.CrossRefGoogle Scholar
Kondiparty, K., Nikolov, A. D., Wasan, D. & Liu, K. 2012 Dynamic spreading of nanofluids on solids. Part I: experimental. Langmuir 28, 14618.CrossRefGoogle ScholarPubMed
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. J. Rheol. 3, 137.Google Scholar
Liu, K., Kondiparty, K., Nikolov, A. D. & Wasan, D. 2012 Dynamic spreading of nanofluids on solids Part II: modeling. Langmuir 28, 16274.CrossRefGoogle ScholarPubMed
Maki, K. L. & Kumar, S. 2011 Fast evaporation of spreading droplets of colloidal suspensions. Langmuir 27, 11347.CrossRefGoogle ScholarPubMed
Matar, O., Craster, R. & Sefiane, K. 2007 Dynamic spreading of droplets containing nanoparticles. Phys. Rev. E 76, 056315.CrossRefGoogle ScholarPubMed
Moriarty, J. A., Schwartz, L. W. & Tuck, E. O. 1991 Unsteady spreading of thin liquid films with small surface tension. Phys. Fluids A 3, 733.CrossRefGoogle Scholar
Murisic, N., Pausader, B., Peschka, D. & Bertozzi, A. L. 2013 Dynamics of particle settling and resuspension in viscous liquid films. J. Fluid Mech. 717, 203.CrossRefGoogle Scholar
Ohara, P. C. & Gelbart, W. M. 1998 Interplay between hole instability and nanoparticle array formation in ultrathin liquid films. Langmuir 14, 3418.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931.CrossRefGoogle Scholar
Popescu, M. N., Oshanin, G., Dietrich, S. & Cazabat, A.-M. 2012 Precursor films in wetting phenomena. J. Phys.: Condens. Matter 24, 243102.Google ScholarPubMed
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1995 Colloidal Dispersions. Cambridge University Press.Google Scholar
Schmidt, H. 2001 Nanoparticles by chemical synthesis, processing to materials and innovative applications. Appl. Organomet. Chem. 15, 331.CrossRefGoogle Scholar
Schwartz, W. L., Roux, D. & Cooper-White, J. 2005 On the shapes of droplets that are sliding on a vertical wall. Physica D 209, 236.CrossRefGoogle Scholar
Schwartz, L. W. 1998 Hysteretic effects in droplet motions on heterogeneous substrates: Direct numerical simulation. Langmuir 14, 3440.CrossRefGoogle Scholar
Schwartz, L. W. & Eley, R. R. 1998 Simulation of droplet motion on low-energy and heterogeneous surfaces. J. Colloid Interface Sci. 202, 173.CrossRefGoogle Scholar
Smith, P. C. 1973 A similarity solution for slow viscous flow down an inclined plane. J. Fluid Mech. 58, 275.CrossRefGoogle Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D 12, 1473.CrossRefGoogle Scholar
Trokhymchuk, A., Henderson, D., Nikolov, A. & Wasan, D. T. 2001 A simple calculation of structural and depletion forces for fluids/suspensions confined in a film. Langmuir 17, 4940.CrossRefGoogle Scholar
Tsai, B., Carvalho, M. S. & Kumar, S. 2010 Leveling of thin films of colloidal suspensions. J. Colloid Interface Sci. 343, 306.CrossRefGoogle ScholarPubMed
Tuck, E. O. & Schwartz, L. W. 1990 A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. SIAM Rev. 32, 453.CrossRefGoogle Scholar
Warner, M. R. E., Craster, R. V. & Matar, O. K. 2003 Surface patterning via evaporation of ultrathin films containing nanoparticles. J. Colloid Interface Sci. 267, 92.CrossRefGoogle ScholarPubMed
Wasan, D., Nikolov, A. & Kondiparty, K. 2011 The wetting and spreading of nanofluids on solids: Role of the structural disjoining pressure. Curr. Opin. Colloid Interface Sci. 16, 344.CrossRefGoogle Scholar
Ye, Y. & Chang, H. C. 1999 A spectral theory for fingering on a prewetted plane. Phys. Fluids 11, 2494.CrossRefGoogle Scholar
Yiantsios, S. G. & Higgins, B. G. 2006 Marangoni flows during drying of colloidal films. Phys. Fluids 18, 082103.CrossRefGoogle Scholar
Zhou, J., Dupuy, B., Bertozzi, A. & Hosoi, A. 2005 Theory for shock dynamics in particle-laden thin films. Phys. Rev. Lett. 94, 117803.CrossRefGoogle ScholarPubMed