Three Dimensional Flow of Colloidal Glasses

Recent experiments performed on a variety of soft glassy materials have demonstrated that any imposed shear flow serves to simultaneously fluidize these systems in all spatial directions [Ovarlez \textit{et al.} (2010)]. When probed with a second shear flow, the viscous response of the experimental system is determined by the rate of the primary, fluidizing flow. Motivated by these findings, we employ a recently developed schematic mode-coupling theory [Brader \textit{et al.} (2009)] to investigate the three dimensional flow of a colloidal glass, subject to a combination of simple shear and uniaxial compression. Despite differences in the specific choice of superposed flow, the flow curves obtained show good qualitative agreement with the experimental findings and recover the observed power law describing the decay of the scaled viscosity as a function of the dominant rate. We then proceed to perform a more formal analysis of our constitutive equation for different kind of `mixed' flows consisting of a dominant primary flow subject to a weaker perturbing flow. Our study provides further evidence that the theory of Brader \textit{et al.} (2009) reliably describes the dynamic arrest and mechanical fluidization of dense particulate suspensions.