NORMAL STRESSES IN COLLOIDAL DISPERSIONS

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 0(Pe2), where Pe = ya2lD. Here, y is the characteristic shear rate, a is the particle size, and z)q is the bare-particle diffusivity. The next term in the perturbation of the microstructure is shown to be 0{Pe5/2). The bulk stress (nondimensionalized by 77% where 77 is the viscosity of the suspending fluid) for a dilute suspension in a general linear flow is determined to 0(<f? Pe). For simple shear flow the theory predicts normal stress differences of Ni/rjy = 0.8992Pe and Nlrfy = — 0.788<£2Pe; there is no correction to the shear viscosity at 0(Pe), however. A scaling theory is also presented for concentrated suspensions using the corrected time scale a2/Do(<£), where D(0) is the short-time self-diffusivity at the volume fraction <f>. The appropriate Peclet number is now Pe = ya2iD(<f>), The scaling theory predicts that the dominant contribution to the stress comes from Brownian motion and scales as Peg(2; <£)/Do(<£X where g (2;0) is the equilibrium radial-distribution function at contact and/>§(<£) = dq(<£)/dq. as maximum packing is approached, <pm, the normal stress differences are predicted to diverge as (1 — <£/<£m)-2Pe, Pe -<< 1. In the presence of interparticle forces there is an additional contribution to the stress analogous to the Brownian contribution. When the length scale of the interparticle force is comparable to the particle size, there is no qualitative change for the divergence of the normal stress differences near maximum packing. For a strongly repulsive interparticle force characterized by a length scale b(> a), the theory predicts that the appropriate Peclet number is now Pe = yb2/D0and that near maximum packing based on the thermodynamic volume fraction <f>b — 4trnb3/3 the normal stress differences diverge as (1 — <f>bf tpbm)~xTPtb, Pe.<.< 1. © 1995, The Society of Rheology. All rights reserved.