(168v) Smoluchowski Theory of Microstructure for Concentrated Sheared Colloidal Suspensions

This work seeks
to develop a theory for predicting microstructure of colloidal suspensions as a
function of dimensionless quantities: Pe =6¹ηγ^.a³/k_bT and particle volume fraction, ϕ,
where γ^. is the shear rate, a is the particle radius, η is the viscosity of the fluid
matrix and k_bT
is the thermal energy. This problem was pursued by conditionally averaging
probability distribution function conservation equation (Smoluchowski equation)
for two particles. Many-body effects in the averaged hydrodynamic and
thermodynamic coefficients of the conservation equation were then formulated
self-consistently through probabilistic third-particle integrals.  The resulting differential-integral
conservation equation was solved using an iterative method. Comparison between
the theory predictions and simulation results showed that the theory was able
to predict the well-known near equilibrium (Pe << 1) and dilute suspensions (ϕ
<<1) results. In addition this theory was
capable of predicting the details of microstructure at Pe >1 and concentrated regime, which differentiates it from the
previous theoretical works in the field. The important rheological quantities
such as shear stress, τ, first
and second normal stress differences, N₁
and N₂ were calculated
based on the obtained microstructure and were compared
with simulation results. The results of this work suggest that the proposed
self-consistent approach is able to capture the many-body hydrodynamic
interactions in colloidal suspensions.