Normal stresses in colloidal dispersions

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Abstract
Normal stresses in colloidal dispersions at low shear rates are determined theoretically for both dilute and concentrated suspensions of Brownian hard spheres. An evolution equation for the pair‐distribution function is developed and the perturbation to the microstructure in a general linear flow is shown to be regular to O(Pe2), where Pe=γ̇a2/D0. Here, γ̇ is the characteristic shear rate, a is the particle size, and D0 is the bare‐particle diffusivity. The next term in the perturbation of the microstructure is shown to be O(Pe5/2). The bulk stress (nondimensionalized by ηγ̇, where η is the viscosity of the suspending fluid) for a dilute suspension in a general linear flow is determined to O(φ2Pe). For simple shear flow the theory predicts normal stress differences of N1/ηγ̇=0.899φ2Pe and N2/ηγ̇=−0.788φ2Pe; there is no correction to the shear viscosity at O(Pe), however. A scaling theory is also presented for concentrated suspensions using the corrected time scale a2/Ds0(φ), where Ds0(φ) is the short‐time...

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