Sheared Suspensions I - Electrorheology and Depletion Aggregation
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SHEARED SUSPENSIONS I - ELECTRORHEOLOGY AND DEPLETION AGGREGATION. J.
R. MELROSE
DEPARTMENT OF CHEMISTRY, GU2 5XH, UNITED KINGDOM
UNIVERSITY OF SURREY,
GUILDFORD
ABSTRACT Idealised models of sheared suspensions are studied by In this and the companion paper [1], computer simulation. non-equilibrium phase diagrams are evaluated for two models: one for electrorheology (this paper), the other for Distinct aggregation due to depletion (companion paper (1]). structural phases and their associated rheology are reported.
INTRODUCTION The theory of sheared suspensions is problematic due to the Although elegant complexity of many body hydrodynamics (MBH). techniques for approximating MBH in computer simulations exist [2), they are O(N 3) algorithms and dynamic simulations of large numbers of particles in 3d are at present prohibitive. The possibility exists that strongly interacting sheared suspensions may show shear induced structure along all three spatial directions and monolayer studies are unsatisfactory in this regard. To make some predictions and to motivate the development of non-equilibrium phase diagrams for sheared suspensions of. we turn to the zeroth order strongly interacting particles, model, idealised models and algorithms (3) which ignore (MBH):
- 1st order, position space algorithm (Smoluchowski level); - isolated particle hydrodynamics (free draining); - uncorrelated Brownian forces; - homogeneous shear applied with sliding boundaries.
Mat. Res. Soc. Symp. Proc. Vol. 248. 01992 Materials Research Society
276
ALGORITHM The update algorithm over a time step h, for the qth coordinate of the ith particle position is (in dimensionless units) riq (t+h) = r iq(t) + (Q Fiq + Giq ) f 2 /2
+ Xiqf
+ 4 Pe (r iy-S/2) f2
qx
G)
where f2 = 2D0h l 2, with a the particle diameter, D0 the Stokes-Einstein diffusion constant: Do = kT/(37n 5s1) and qs the. viscosity of the suspending fluid. Q is the dimensionless magnitude of the particle interactions: Q Fi is the interaction force on particle i and Gi represents repulsive core interactions. The Brownian force is given by Xiq f, where Xiq is a random variable of r.m.s unity. The final term in (1) adds shear to the displacement of the particle in the X (flow) direction with a shear gradient in the Y direction, the computational box side length is So. Figure 1 illustrates the computational geometry. The dimensionless shear rate is the Peclet number, defined from the shear rate • by Pe
=
zr
where zr = 8 D0/T
2
The Peclet number sets the ratio of the shear to Brownian forces, at low Peclet the Brownian forces are larger at high Peclet the shear forces are larger. In the present paper the interaction potential will be taken as that of point dipoles permanently aligned by a strong The interaction field parallel to the shear gradient. strength Q is Q = g2/(kT4nc0Cc03 ) where u and cs are respectively the dipole moment of the particle and the relative dielectric constant of the base fluid. The particles also have either a power law or exponential core replusion.
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