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Coupling between long ranged repulsions and short ranged attractions in a colloidal model of zero shear rate viscosity

In this work, we analyzed an isotropic colloidal model incorporating both short-range sticky attractions and long-range electrostatic repulsions. We computed the zero-shear viscosity and second virial coefficient for a dilute colloidal suspension (i.e., pair interactions only) as a function of the strength of attractions and repulsions. We also developed an analytical approximation that allows us to better understand the coupling of the two types of interactions. The attractions and repulsions contribute to the zero-shear viscosity and second virial coefficient in different ways, leading to cases with the same second virial coefficient but different zero-shear viscosity. The analytical approximation shows that the mechanism of the coupling of interactions is that long-range repulsions can weaken the influence of short-range attractions. This effect alters how repulsions change the zero-shear viscosity. Acting independently, both attractions and repulsions increase the viscosity coefficient of the system. However, when both type of interactions are considered together, repulsions can screen the effect of attractive interactions thereby reducing the viscosity.