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Shear-induced collective diffusivity down a concentration gradient in a viscous emulsion of drops

Published online by Cambridge University Press:  03 April 2019

Abhilash Reddy Malipeddi  and
Kausik Sarkar Open the ORCID record for Kausik Sarkar [Opens in a new window]
Abhilash Reddy Malipeddi
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC20052, USA
Kausik Sarkar*
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, DC20052, USA
*
†Email address for correspondence: sarkar@gwu.edu
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Abstract

The shear-induced collective diffusivity down a concentration gradient in a viscous emulsion is computed using direct numerical simulation. A layer of randomly packed drops subjected to a shear flow, shows the layer width to increase with the $1/3$ power of time, consistent with a semi-dilute theory that assumes a diffusivity linear with concentration. This characteristic scaling and the underlying theory are used to compute the collective diffusivity coefficient. This is the first ever computation of this quantity for a system of deformable particles using fully resolved numerical simulation. The results match very well with previous experimental observations. The coefficient of collective diffusivity varies non-monotonically with the capillary number, due to the competing effects of increasing deformation and drop orientation. A phenomenological correlation for the collective diffusivity coefficient as a function of capillary number is presented. We also apply an alternative approach to compute collective diffusivity, developed originally for a statistically homogeneous rigid sphere suspension – computing the dynamic structure factor from the simulated droplet positions and examining its time variation at small wavenumber. We show that the results from this alternative approach qualitatively agree with our computation of collective diffusivity including the prediction of the non-monotonic variation of diffusivity with the capillary number.

JFM classification

Drops and Bubbles: Drops Complex Fluids: Emulsions Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 5 - 25
Copyright
© 2019 Cambridge University Press 

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Malipeddi and Sarkar supplementary movie

A layer of drops diffusing in a shear flow, and the corresponding drop volume fraction as a function of distance along the shear direction evolving with time for Ca=0.05

Download Malipeddi and Sarkar supplementary movie(Video)
Video 4.3 MB