Structure factor distortion for hard-sphere dispersions subjected to weak shear flow: Small-angle neutron scattering in the flow–vorticity plane

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Abstract
Small angle neutron scattering (SANS) was used as a probe of the structure factor distortion for concentrated hard-sphere dispersions subjected to steady shear flow. The dispersions consisted of stearically stabilized silica spheres of 40 nm radius suspended in cyclohexane, with volume fractions 0.36<φ<0.52. We subjected the dispersions to weak shear flow (Peclet number Pe<1) in a Couette flow cell, and collected intensity measurements in the flow–vorticity plane. We conducted the experiments using the D11 spectrometer at the Institut Laue-Langevin in Grenoble, France. The data permit a thorough evaluation of the existing theories for the shear-induced distortion of the structure factor. We find that the theories as they stand severely underpredict the distortion at low wave vectors (‖k‖<0.1 nm−1), but the theories can be made to qualitatively agree with the data by adjusting Pe in the equations to a higher value. The theories are based on a perturbation expansion that is linear in small Pe, but such an expansion is inadequate for describing our data. We show that the nonequilibrium contribution to the structure factor is proportional to fractional powers of Pe, with the exponent depending on volume fraction φ. The failure of the theories is probably due to their neglect of hydrodynamic interactions, which are important in concentrated dispersions. The distortion of the structure factor is greatest around its first maximum, with significant distortion being exhibited in both the flow and vorticity directions. The peak in the structure factor broadens, indicating that weak shear flow produces a more disordered structure relative to the equilibrium structure. The data reveal that the shear flow results in a decreased concentration of particles in the flow direction. The concentration of particles in the vorticity direction increases when shear flow is applied, and the formation of temporal clusters is probable.

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