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

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


Nazockdast, E. - Presenter, Benjamin Levich Institute and Department of Chemical Engineering
Morris, J. F. - Presenter, Benjamin Levich Institute, City College of CUNY

This work seeks
to develop a theory for predicting microstructure of colloidal suspensions as a
function of dimensionless quantities: Pe =6¹ηγ.a3/kbT 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 kbT
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.