Criterion for Fingering Instabilities in Colloidal Gels

Abstract

We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: (i) stable flows during which the gel undergoes a tensile deformation without yielding, and (ii) unstable flows characterized by the radial growth of air fingers into the gel. We show that the unstable regime occurs beyond a critical energy input, independent of the gel's macroscopic yield stress. This implies a local fluidization of the gel at the tip of the growing fingers and results in the most unstable wavelength of the patterns exhibiting the characteristic scalings of the classical viscous fingering instability. Our work provides a quantitative criterion for the onset of fingering in colloidal gels based on a local shear-induced yielding in agreement with the delayed failure framework.

Fingering instability in adhesion fronts

“…This instability occurs when a viscous fluid is pushed away by a fluid of lower viscosity in a confined environment such as porous media or parallel plates (Hele-Shaw cell). The morphology of such patterns relies on confinement geometry (Rauseo, Barnes & Maher 1987;Al-Housseiny, Tsai & Stone 2012), fluid rheology (Bonn & Meunier 1997;Lindner, Coussot & Bonn 2000;Divoux et al 2020) or surface anisotropy (Ben-Jacob et al 1985). A closely related phenomenon is known as the printer's instability, which consists in the formation of ribbing patterns at the exit of the thin gap between two contra-rotating † Email address for correspondence: jose.bico@espci.fr cylinders coated with a thin liquid film (Pearson 1960;Pitts & Greiller 1961;Rabaud, Couder & Michalland 1991;Rabaud 1994).…”

“…The morphology of such patterns relies on confinement geometry (Rauseo, Barnes & Maher 1987; Al-Housseiny, Tsai & Stone 2012), fluid rheology (Bonn & Meunier 1997; Lindner, Coussot & Bonn 2000; Divoux et al. 2020) or surface anisotropy (Ben-Jacob et al. 1985).…”

Slip in adhesion tests of a Kaolin clay

“…In contrast at the highest concentration there is almost no clay adhered to the surface in this region. The central region of deposition which is conical and relatively symmetric at low concentrations becomes quite unstable and asymmetric with something a bit like a fracture surface at the highest concentrations [17]; however we do not observe the fractal-like structures that have been observed in other yield stress fluids [15,[19][20][21]. This is perhaps due to the higher yield stress of our paste, a property which can suppress fingering [19] One feature immediately apparent from videos of the different concentration experiments is that the initial stages, for both low and high concentrations, look qualitatively different, in each case exhibiting significant slip.…”

“…5 ). Divoux et al [ 21 ] studying a particle gel, also observed a change in the power law exponent during an adhesion test to a value . The transition to the second stage occurred at a critical gap at which the final deposit diameter remained constant.…”

“…Firstly, there has been interest in the deposited patterns left behind on either plate. These patterns can be conical deposits, rough multi-peaked fracture surfaces [18] or viscous-fingering induced tree-like structures [19][20][21][22]. Secondly, a number of studies have focussed on understanding how the measured force (F ) scales with plate separation (h) [15,19,23].…”