Shear-gradient induced transport and non-local stresses: Non-uniform flow of glasses and gels
July 31-August 4, 2017
Spatial gradients of the shear rate lead to transport of matter from regions of high to low shear rate in many different types of systems (like granular matter, blood [see figure], and macromolecular solutions). Such shear-gradient induced mass transport leads banded flow profiles in systems with a yield stress, provided that the yield stress is a sufficiently pronounced function of concentration. In this presentation, the origin of such shear-induced mass fluxes resulting from direct interactions will be discussed, and an explicit expression for the corresponding transport coefficient is derived. The mechanism through which shear-gradient induced mass transport leads to non- uniform, shear-banded flow profiles in colloidal glasses and gels is discussed. The advection-diffusion equation that includes shear-gradient induced mass transport, together with an appropriate equation of motion for the flow velocity, including non-local stresses, are solved numerically . The resulting stability diagram and shear-banded flow profiles will be compared to experiments on hard-sphere colloidal glasses . In addition, a constitutive theory is presented for non-local stresses, which arise from very large spatial gradients in the flow velocity. These non- local stresses are essential for the understanding of shear-banding phenomena and for flows in micro channals.
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Jan K.G. Dhont, "Shear-gradient induced transport and non-local stresses: Non-uniform flow of glasses and gels" in "Association in Solution IV", Ulf Olsson, Lund University, Sweden Norman Wagner, University of Delaware, USA Anand Yethiraj, Memorial University of Newfoundland, Canada Eds, ECI Symposium Series, (2017). http://dc.engconfintl.org/assoc_solution_iv/20