Skip to main content
×
×
Home

On the anisotropic response of a Janus drop in a shearing viscous fluid

  • Misael Díaz-Maldonado (a1) and Ubaldo M. Córdova-Figueroa (a1)
Abstract

The force and couple that result from the shearing motion of a viscous, unbounded fluid on a Janus drop are the subjects of this investigation. A pair of immiscible, viscous fluids comprise the Janus drop and render it with a ‘perfect’ shape: spherical with a flat, internal interface, in which each constituent fluid is bounded by a hemispherical domain of equal radius. The effect of the arrangement of the internal interface (drop orientation) relative to the unidirectional shear flow is explored within the Stokes regime. Projection of the external flow into a reference frame centred on the drop simplifies the analysis to three cases: (i) a shear flow with a velocity gradient parallel to the internal interface, (ii) a hyperbolic flow, and (iii) two shear flows with a velocity gradient normal to the internal interface. Depending on the viscosity of the internal fluids, the Janus drop behaves as a simple fluid drop or as a solid body with broken fore and aft symmetry. The resultant couple arises from both the straining and swirling motions of the external flow in analogy with bodies of revolution. Owing to the anisotropic resistance of the Janus drop, it is inferred that the drop can migrate lateral to the streamlines of the undisturbed shear flow. The grand resistance matrix and Bretherton constant are reported for a Janus drop with similar internal viscosities.

Copyright
Corresponding author
Email address for correspondence: ubaldom.cordova@upr.edu
References
Hide All
Brenner, H. 1963 The Stokes resistance of an arbitrary particle. Chem. Engng Sci. 18, 125.
Bretherton, F. P. 1962 The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14, 284304.
Chervenivanova, E. & Zapryanov, Z. 1989 On the deformation of compound multiphase drops at low Reynolds numbers. Physico-Chem. Hydrodyn. 11, 243259.
Dorrepaal, J. M. 1978 The Stokes resistance of a spherical cap to translational and rotational motions in a linear shear flow. J. Fluid Mech. 84, 265279.
Guzowski, J., Korczyk, P. M., Jakiela, S. & Garstecki, P. 2012 The structure and stability of multiple micro-droplets. Soft Matt. 8, 72697278.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Prentice-Hall.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161179.
Johnson, R. E. & Sadhal, S. S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Annu. Rev. Fluid Mech. 17, 289320.
Kim, S. & Karrila, S. J. 2005 Microhydrodynamics Principles and Selected Applications. Dover.
Manga, M. & Stone, H. A. 1993 Buoyancy-driven interactions between two deformable viscous drops. J. Fluid Mech. 256, 647683.
Morton, D. S., Subramanian, R. S. & Balasubramaniam, R. 1990 The migration of a compound drop due to thermocapillarity. Phys. Fluids A 2, 21192133.
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209223.
Nisisako, T., Torii, T., Takahashi, T. & Takizawa, Y. 2006 Synthesis of monodisperse bicolored Janus particles with electrical anisotropy using a microfluidic co-flow system. Adv. Mater. 18, 11521156.
Ramachandran, A. & Khair, A. S. 2009 The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow. J. Fluid Mech. 633, 233269.
Rosenfeld, L., Lavrenteva, O. M. & Nir, A. 2009 On the thermocapillary motion of partially engulfed compound drops. J. Fluid Mech. 626, 263289.
Rushton, E. & Davies, G. A. 1983 Settling of encapsulated droplets at low Reynolds numbers. Int. J. Multiphase Flow 9, 337342.
Sadhal, S. S. & Oguz, H. N. 1985 Stokes flow past compound multiphase drops: the case of completely engulfed drops/bubbles. J. Fluid Mech. 160, 511529.
Shardt, O., Derksen, J. J. & Mitra, S. K. 2014 Simulations of Janus droplets at equilibrium and in shear. Phys. Fluids 26, 012104.
Shklyaev, S., Ivantsov, A. O., Díaz-Maldonado, M. & Córdova-Figueroa, U. M. 2013 Dynamics of a Janus drop in an external flow. Phys. Fluids 25, 082105.
Stone, H. A. & Leal, L. G. 1990 Breakup of concentric double emulsion droplets in linear flows. J. Fluid Mech. 211, 123156.
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 4148.
Torza, S. & Mason, S. G. 1970 Three-phase interactions in shear and electrical fields. J. Colloid Interface Sci. 33, 6783.
Vuong, S. T. & Sadhal, S. S. 1989 Growth and translation of a liquid–vapour compound drop in a second liquid. Part 1. Fluid mechanics. J. Fluid Mech. 209, 617637.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 3
Total number of PDF views: 63 *
Loading metrics...

Abstract views

Total abstract views: 236 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd April 2018. This data will be updated every 24 hours.