publication . Preprint . 2019

The effect of a wall on the interaction of two spheres in shear flow: Batchelor-Green theory revisited

Fouxon, Itzhak; Rubinstein, Boris; Ge, Zhouyang; Brandt, Luca; Leshansky, Alexander;
Open Access English
  • Published: 27 Aug 2019
Abstract
The seminal Batchelor-Green's (BG) theory on the hydrodynamic interaction of two spherical particles of radii a suspended in a viscous shear flow neglects the effect of the boundaries. In the present paper we study how a plane wall modifies this interaction. Using an integral equation for the surface traction we derive the expression for the particles' relative velocity as a sum of the BG's velocity and the term due to the presence of a wall at finite distance, z_0. Our calculation is not the perturbation theory of the BG solution, so the contribution due to the wall is not necessarily small. The distance at which the wall significantly alters the particles inte...
Subjects
free text keywords: Physics - Fluid Dynamics
Related Organizations
Funded by
EC| Microflusa
Project
Microflusa
Fabricating colloidal materials with microfluidics
  • Funder: European Commission (EC)
  • Project Code: 664823
  • Funding stream: H2020 | RIA
Communities
FET H2020FET OPEN: FET-Open research projects
FET H2020FET OPEN: Fabricating colloidal materials with microfluidics
Download from
27 references, page 1 of 2

[1] J. Happel and H. Brenner, Low Reynolds number hydrodynamics: with special applications to particulate media, (Springer Science and Business Media, 2012).

[2] S. Kim and S. J. Karrila, Microhydrodynamics: principles and selected applications, (Courier Corporation , 2013).

[3] E. M. Purcell and D. J. Morin, Electricity and magnetism, (Cambridge University Press, 2013).

[4] G. K. Batchelor and J. T. Green, The hydrodynamic interaction of two small freely-moving spheres in a linear ow eld, J. Fluid Mech. 56, 375 (1972).

[5] P. A. Arp and S. G. Mason, The kinetics of owing dispersions: VIII. Doublets of rigid spheres (theoretical), J. Coll. Inter. Sc. 61, 21 (1977).

[6] C. J. Lin, K. J. Lee, and N. F. Sather, Slow motion of two spheres in a shear eld, J. Fluid Mech. 43, 35 (1970). [OpenAIRE]

[7] M. Zurita-Gotor, J. Blawzdziewicz, and E. Wajnryb, Swapping trajectories: a new wall-induced cross-streamline particle migration mechanism in a dilute suspension of spheres, J. Fluid Mech. 592, 447 (2007).

[8] B. Shen, M. Leman, M. Reyssat, and P. Tabeling, Dynamics of a small number of droplets in micro uidic HeleShaw cells, Exp. in Fluids 55, 1728 (2014). [OpenAIRE]

[9] B. Shen, J. Ricouvier, F. Malloggi, and P. Tabeling, Designing colloidal molecules with micro uidics, Adv. Sci. 3, 1600012 (2016).

[10] Z. Ge, O. Tammisola, and L. Brandt, Flow-assisted droplet assembly in a 3D micro uidic channel, Soft Matter 15, 3451 (2019).

[11] N. Liron and S. Mochon, Stokes ow for a stokeslet between two parallel at plates, J. Eng. Math. 10, 287 (1976). [OpenAIRE]

[12] I. Fouxon, Z. Ge, L. Brandt, and A. Leshansky, Integral representation of channel ow with interacting particles, Phys. Rev. E, 96, 063110 (2017). [OpenAIRE]

[13] S. Haber and H. Brenner, Hydrodynamic interactions of spherical particles in quadratic Stokes ows, Int. J. Mult. Flow 25, 1009 (1999).

[14] H. Brenner and M. E. O'Neill, On the Stokes resistance of multiparticle systems in a linear shear eld, Chem. Eng. Sc. 27, 1421 (1972).

[15] G. K. Batchelor and J. T. Green, The determination of the bulk stress in a suspension of spherical particles to order c2, J. Fluid Mech. 56, 401 (1972).

27 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue