Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T07:35:42.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Marangoni circulation by UV light modulation on sessile drop for particle agglomeration

Published online by Cambridge University Press:  20 June 2019

Tianyi Li ,
Aravinda Kar  and
Ranganathan Kumar Open the ORCID record for Ranganathan Kumar [Opens in a new window]
Tianyi Li
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA
Aravinda Kar
Affiliation:
The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816, USA
Ranganathan Kumar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA
*
†Email address for correspondence: Ranganathan.Kumar@ucf.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical solution of a biharmonic equation is presented in axisymmetric toroidal coordinates for Stokes flow due to surface tension gradient on the free surface of sessile drops. The stream function profiles exhibit clockwise and counter-clockwise toroidal volumes. The ring or dot formed by the downward dividing streamlines between these volumes predicts the experimentally deposited particle ring or dot well. This finding suggests that the downward dividing streamline can be taken to be a reasonable indicator of where deposition occurs. Different light patterns directed at different locations of the droplet can give rise to a single spot or ring. A relationship between the positions of the light intensity peak and possible locations of particle deposition is analysed to demonstrate that the streamlines can be generated on-demand to achieve particle deposition at predetermined locations on the substrate. Toroidal corner vortices called Moffatt eddies have appeared in other corner flows and develop in this optical Marangoni flow as well near the contact line.

JFM classification

Drops and Bubbles: Drops Convection: Marangoni convection Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 72 - 88
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anyfantakis, M. & Baigl, D. 2014 Dynamic photocontrol of the coffee-ring effect with optically tunable particle stickiness. Angewandte Chemie 126 (51), 14301–14305.Google Scholar
Anyfantakis, M., Varanakkottu, S. N., Rudiuk, S., Morel, M. & Baigl, D. 2017 Evaporative optical Marangoni assembly: tailoring the three-dimensional morphology of individual deposits of nanoparticles from sessile drops. ACS Appl. Mater. Interfaces 9 (42), 37435–37445.Google Scholar
Armstrong, E., Khunsin, W., Osiak, M., Blömker, M., Torres, C. M. S. & O’Dwyer, C. 2014 Ordered 2D colloidal photonic crystals on gold substrates by surfactant-assisted fast-rate dip coating. Small 10 (10), 1895–1901.Google Scholar
Biswas, S. & Kalita, J. C. 2018 Moffatt eddies in the driven cavity: a quantification study by an HOC approach. Comput. Maths Applics. 76 (3), 471–487.Google Scholar
Brown, P., Butts, C. P. & Eastoe, J. 2013 Stimuli-responsive surfactants. Soft Matt. 9 (8), 2365–2374.Google Scholar
Chevallier, E., Mamane, A., Stone, H. A., Tribet, C., Lequeux, F. & Monteux, C. 2011 Pumping-out photo-surfactants from an air–water interface using light. Soft Matt. 7 (17), 7866–7874.Google Scholar
Deegan, R. D. 2000 Pattern formation in drying drops. Phys. Rev. E 61 (1), 475–485.Google Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389 (6653), 827–829.Google Scholar
Diddens, C., Tan, H., Lv, P., Versluis, M., Kuerten, J. G. M., Zhang, X. & Lohse, D. 2017 Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking. J. Fluid Mech. 823, 470–497.Google Scholar
El-Kareh, A. W. & Secomb, T. W. 1996 Stokes flow impinging on a spherical cap on a plane wall. Q. J. Mech. Appl. Maths 49 (2), 179–183.Google Scholar
Fischer, B. J. 2002 Particle convection in an evaporating colloidal droplet. Langmuir 18 (1), 60–67.Google Scholar
Gelderblom, H., Bloemen, O. & Snoeijer, J. H. 2012 Stokes flow near the contact line of an evaporating drop. J. Fluid Mech. 709, 69–84.Google Scholar
Happel, J. & Brenner, H. 2012 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, vol. 1. Springer Science & Business Media.Google Scholar
Hu, H. & Larson, R. G. 2005a Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21 (9), 3972–3980.Google Scholar
Hu, H. & Larson, R. G. 2005b Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21 (9), 3963–3971.Google Scholar
Huang, X., Zhou, J., Fu, M., Li, B., Wang, Y., Zhao, Q., Yang, Z., Xie, Q. & Li, L. 2007 Binary colloidal crystals with a wide range of size ratios via template-assisted electric-field-induced assembly. Langmuir 23 (17), 8695–8698.Google Scholar
Jeong, J.-T. & Moffatt, H. K. 1992 Free-surface cusps associated with flow at low Reynolds number. J. Fluid Mech. 241, 1–22.Google Scholar
Kim, J. J., Li, Y., Lee, E. J. & Cho, S. O. 2011 Fabrication of size-controllable hexagonal non-close-packed colloidal crystals and binary colloidal crystals by pyrolysis combined with plasma-electron coirradiation of polystyrene colloidal monolayer. Langmuir 27 (6), 2334–2339.Google Scholar
Lee, C. T., Smith, K. A. & Hatton, T. A. 2004 Photoreversible viscosity changes and gelation in mixtures of hydrophobically modified polyelectrolytes and photosensitive surfactants. Macromolecules 37 (14), 5397–5405.Google Scholar
Marin, A., Liepelt, R., Rossi, M. & Kähler, C. J. 2016 Surfactant-driven flow transitions in evaporating droplets. Soft Matt. 12 (5), 1593–1600.Google Scholar
Masoud, H. & Felske, J. D. 2009a Analytical solution for inviscid flow inside an evaporating sessile drop. Phys. Rev. E 79 (1), 016301.Google Scholar
Masoud, H. & Felske, J. D. 2009b Analytical solution for stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes. Phys. Fluids 21 (4), 042102.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1.Google Scholar
Moon, P. & Spencer, D. E. 1971 Field Theory Handbook: Including Coordinate Systems, Differential Equations and their Solutions. Springer.Google Scholar
Ristenpart, W. D., Kim, P. G., Domingues, C., Wan, J. & Stone, H. A. 2007 Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99 (23), 234502.Google Scholar
Scriven, L. E. & Sternling, C. V. 1964 On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19 (3), 321–340.Google Scholar
Shankar, P. N. 1993 The eddy structure in stokes flow in a cavity. J. Fluid Mech. 250, 371–383.Google Scholar
Shtern, V. 2018 Cellular Flows: Topological Metamorphoses in Fluid Mechanics. Cambridge University Press.Google Scholar
Silverman, R. A. & others 1972 Special Functions and their Applications. Courier Corporation.Google Scholar
Tam, D., von Arnim, V., McKinley, G. H. & Hosoi, A. E. 2009 Marangoni convection in droplets on superhydrophobic surfaces. J. Fluid Mech. 624, 101–123.Google Scholar
Varanakkottu, S. N., Anyfantakis, M., Morel, M., Rudiuk, S. & Baigl, D. 2015 Light-directed particle patterning by evaporative optical Marangoni assembly. Nano Lett. 16 (1), 644–650.Google Scholar
Vogel, N., Retsch, M., Fustin, C-A., del Campo, A. & Jonas, U. 2015 Advances in colloidal assembly: the design of structure and hierarchy in two and three dimensions. Chem. Rev. 115 (13), 6265–6311.Google Scholar
Zeng, D., Latham, W. P. & Kar, A. 2006 Shaping of annular laser intensity profiles and their thermal effects for optical trepanning. Opt. Engng 45 (1), 014301.Google Scholar
Zhang, X., Zhang, J., Zhu, D., Li, X., Zhang, X., Wang, T. & Yang, B. 2010 A universal approach to fabricate ordered colloidal crystals arrays based on electrostatic self-assembly. Langmuir 26 (23), 17936–17942.Google Scholar