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In the vicinity of their glass transition, dense colloidal suspensionsacquire elastic properties over experimental timescales. We investigate thepossibility of a visco-elastic flow instability in curved geometry for suchmaterials. To this end, we first present a general strategy extending afirst-principles approach based on projections onto slow variables (so farrestricted to strictly homogeneous flow) in order to handle inhomogeneities. Inparticular, we separate the advection of the microstructure by the flow, at theorigin of a fluctuation advection term, from the intrinsic dynamics. On accountof the complexity of the involved equations, we then opt for a drasticsimplification of the theory, in order to establish its potential to describeinstabilities. These very strong approximations lead to a constitutive equationof the White-Metzner class, whose parameters are fitted with experimentalmeasurements of the macroscopic rheology of a glass-forming colloidaldispersion. The model properly accounts for the shear-thinning properties ofthe dispersions, but, owing to the approximations, the description is not fullyquantitative. Finally, we perform a linear stability analysis of the flow inthe experimentally relevant cylindrical (Taylor-Couette) geometry and provideevidence that shear-thinning strongly stabilises the flow, which can explainwhy visco-elastic instabilities are not observed in dense colloidalsuspensions.

Shear-thinning in dense colloidal suspensions and its effect on elastic  instabilities: from the microscopic equations of motion to an approximation  of the macroscopic rheology