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Modelling a hydrodynamic instability in freely settling colloidal gels

Published online by Cambridge University Press:  12 October 2018

Zsigmond Varga Open the ORCID record for Zsigmond Varga [Opens in a new window] ,
Jennifer L. Hofmann  and
James W. Swan
Zsigmond Varga
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Jennifer L. Hofmann
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
James W. Swan*
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: jswan@mit.edu
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Abstract

Attractive colloidal dispersions, suspensions of fine particles which aggregate and frequently form a space-spanning elastic gel are ubiquitous materials in society with a wide range of applications. The colloidal networks in these materials can exist in a mode of free settling when the network weight exceeds its compressive yield stress. An equivalent state occurs when the network is held fixed in place and used as a filter through which the suspending fluid is pumped. In either scenario, hydrodynamic instabilities leading to loss of network integrity occur. Experimental observations have shown that the loss of integrity is associated with the formation of eroded channels, so-called streamers, through which the fluid flows rapidly. However, the dynamics of growth and subsequent mechanism of collapse remain poorly understood. Here, a phenomenological model is presented that describes dynamically the radial growth of a streamer due to erosion of the network by rapid fluid back flow. The model exhibits a finite-time blowup – the onset of catastrophic failure in the gel – due to activated breaking of the inter-colloid bonds. Brownian dynamics simulations of hydrodynamically interacting and settling colloids in dilute gels are employed to examine the initiation and propagation of this instability, which are in good agreement with the theory. The model dynamics is also shown to accurately replicate measurements of streamer growth in two different experimental systems. The predictive capabilities and future improvements of the model are discussed and a stability-state diagram is presented providing insight into engineering strategies for avoiding settling instabilities in networks meant to have long shelf lives.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Low-Reynolds-number flows Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 1014 - 1044
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Copyright
© 2018 Cambridge University Press 

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Varga et al. supplementary movie 1

Movie of settling gel with δ=0.1, ε=0.05, G=0.5 and φ=20% (same as in figure 2). The differently coloured layers are purely for illustrative purposes, indicate initial particle positions in the gel, and are meant to guide the eye through the breakdown of the network during free settling. The dispersion gelled over 500τ_D in the absence of gravity and has a structure characterized by d_f=2.05. At t=0τ_G gravity is turned on in the simulation and the network settles for 2500 τ_G.

Download Varga et al. supplementary movie 1(Video)
Video 13 MB

Varga et al. supplementary movie 2

Movie of settling gel with δ=0.15, ε=0.05, G=0.3 and φ=20%. The differently coloured layers are purely for illustrative purposes, indicate initial particle positions in the gel, and are meant to guide the eye through the breakdown of the network during free settling. The dispersion gelled over 500τ_D in the absence of gravity and has a structure characterized by d_f=2.11. At t=0τ_G gravity is turned on in the simulation and the network settles for 2500 τ_G.

Download Varga et al. supplementary movie 2(Video)
Video 16.3 MB

Varga et al. supplementary movie 3

Movie of settling gel with δ=0.1, ε=0.02, G=0.5 and φ=20%. The differently coloured layers are purely for illustrative purposes, indicate initial particle positions in the gel, and are meant to guide the eye through the breakdown of the network during free settling. The dispersion gelled over 500τ_D in the absence of gravity and has a structure characterized by d_f=1.96. At t=0τ_G gravity is turned on in the simulation and the network settles for 2500 τ_G.

Download Varga et al. supplementary movie 3(Video)
Video 16.4 MB

Varga et al. supplementary movie 4

Movie of settling gel with δ=0.1, ε=0.05, G=0.5 and φ=20%. The differently coloured layers are purely for illustrative purposes, indicate initial particle positions in the gel, and are meant to guide the eye through the breakdown of the network during free settling. The dispersion gelled over 500τ_D in the absence of gravity and has a structure characterized by d_f=2.08. A streamer was seeded in the centre with a radius of R_0=0.8R^* and the gel cross section is shown. At t=0τ_G gravity is turned on in the simulation and the network settles for 2500 τ_G.

Download Varga et al. supplementary movie 4(Video)
Video 9.5 MB