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Driven particles at fluid interfaces acting as capillary dipoles

  • Aaron Dörr (a1) and Steffen Hardt (a1)
Abstract

The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line (TCL) and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the linear superposition approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the TCL. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.

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Email address for correspondence: doerr@csi.tu-darmstadt.de
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J. Ally  & A. Amirfazli 2010 Magnetophoretic measurement of the drag force on partially immersed microparticles at air–liquid interfaces. Colloids Surf. A 360, 120128.

C. Berdan II & L. G. Leal 1982 Motion of a sphere in the presence of a deformable interface. Part I. Perturbation of the interface from flat: the effects on drag and torque. J. Colloid Interface Sci. 87 (1), 6280.

B. P. Binks 2002 Particles as surfactants: similarities and differences. Curr. Opin. Colloid Interface Sci. 7, 2141.

H. Brenner 1964 The Stokes resistance of a slightly deformed sphere. Chem. Engng Sci. 19, 519539.

D. Y. C. Chan , J. D. Henry Jr & L. R. White 1981 The interaction of colloidal particles collected at fluid interfaces. J. Colloid Interface Sci. 79 (2), 410418.

W. Chen  & P. Tong 2008 Short-time self-diffusion of weakly charged silica spheres at aqueous interfaces. Eur. Phys. Lett. 84, 28003.

B. Cichocki , M. L. Ekiel-Jeżewska , G. Nägele  & E. Wajnryb 2004 Motion of spheres along a fluid–gas interface. J. Chem. Phys. 121, 23052316.

K. Danov , R. Aust , F. Durst  & U. Lange 1995 Influence of the surface viscosity on the hydrodynamic resistance and surface diffusivity of a large Brownian particle. J. Colloid Interface Sci. 175, 3645.

K. D. Danov , T. D. Gurkov , H. Raszillier  & F. Durst 1998 Stokes flow caused by the motion of a rigid sphere close to a viscous interface. Chem. Engng Sci. 53 (19), 34133434.

K. D. Danov , P. A. Kralchevsky , B. N. Naydenov  & G. Brenn 2005 Interactions between particles with an undulated contact line at a fluid interface: capillary multipoles of arbitrary order. J. Colloid Interface Sci. 287, 121134.

G. Dassios  & P. Vafeas 2001 Connection formulae for differential representations in Stokes flow. J. Comput. Appl. Maths 133, 283294.

K. Du , J. A. Liddle  & A. J. Berglund 2012 Three-dimensional real-time tracking of nanoparticles at an oil–water interface. Langmuir 28, 91819188.

M. A. Fortes 1982 Attraction and repulsion of floating particles. Can. J. Chem. 60, 28892895.

F. Ghezzi , J. C. Earnshaw , M. Finnis  & M. McCluney 2001 Pattern formation in colloidal monolayers at the air–water interface. J. Colloid Interface Sci. 238, 433446.

J. Happel  & H. Brenner 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.

T. S. Horozov , R. Aveyard  & J. H. Clint 2005 Particle zips: vertical emulsion films with particle monolayers at their surfaces. Langmuir 21, 23302341.

C. Huh  & S. G. Mason 1974 The flotation of axisymmetric particles at horizontal liquid interfaces. J. Colloid Interface Sci. 47 (2), 271289.

J. N. Israelachvili 2011 Intermolecular and Surface Forces, 3rd edn. Academic.

P. A. Kralchevsky  & K. Nagayama 2000 Capillary interactions between particles bound to interfaces, liquid films and biomembranes. Adv. Colloid Interface Sci. 85, 145192.

M. Oettel  & S. Dietrich 2008 Colloidal interactions at fluid interfaces. Langmuir 24, 14251441.

M. E. O’Neill , K. B. Ranger  & H. Brenner 1986 Slip at the surface of a translating–rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: removal of the contact-line singularity. Phys. Fluids 29, 913924.

B. J. Park  & E. M. Furst 2011 Attractive interactions between colloids at the oil–water interface. Soft Matt. 7, 76767682.

J. T. Petkov , N. D. Denkov , K. D. Danov , O. D. Velev , R. Aust  & F. Durst 1995 Measurement of the drag coefficient of spherical particles attached to fluid interfaces. J. Colloid Interface Sci. 172, 147154.

O. Pitois  & X. Chateau 2002 Small particle at a fluid interface: effect of contact angle hysteresis on force and work of detachment. Langmuir 18, 97519756.

B. Radoev , M. Nedjalkov  & V. Djakovich 1992 Brownian motion at liquid–gas interfaces. Part 1. Diffusion coefficients of macroparticles at pure interfaces. Langmuir 8, 29622965.

P. Singh  & T. I. Hesla 2004 The interfacial torque on a partially submerged sphere. J. Colloid Interface Sci. 280, 542543.

I. Sriram , R. Walder  & D. K. Schwartz 2012 Stokes–Einstein and desorption-mediated diffusion of protein molecules at the oil–water interface. Soft Matt. 8, 60006003.

N. D. Vassileva , D. van den Ende , F. Mugele  & J. Mellema 2005 Capillary forces between spherical particles floating at a liquid–liquid interface. Langmuir 21, 1119011200.

M. Zabarankin 2007 Asymmetric three-dimensional Stokes flow about two fused equal spheres. Proc. R. Soc. Lond. A 463, 23292349.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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