Sheared Suspensions II - Depletion Aggregation
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SHEARED SUSPENSIONS II - DEPLETION AGGREGATION.
J. R. MELROSE DEPARTMENT OF CHEMISTRY, GU2 5XH, UNITED KINGDOM
UNIVERSITY OF SURREY,
GUILDFORD
ABSTRACT A Brownian dynamics algorithm described in the companion paper [1] is used to simulate sheared suspensions The shear of particles interacting via a depletion potential. and interaction forces interplay to give a complex non-equilibrium phase diagram: a variety of shear induced agglomerates form at low shear rate, but, for shear rates above a non-equilibrium phase boundary the agglomerates develop interfaces predominantly orientated parallel to the plane of shear gradient and flow.
INTRODUCTION. In the context of aggregating particles forming weak flocs the effect of shear on the structure of the aggregates and relation between structure and rheology is not understood [2]. This question will be answered here for an idealised model. An attractive depletion interaction arises between large particles suspended in mixture with smaller particles: the large particles exclude volume from the small particles, but, the free volume of the small particles is increased if the large particles are pushed closer together than the diameter of the small particles. Recent experiments on this system have considered latex particles in the presence of added polymer (2,3]. In ref. (3] a simulation model was proposed, in this model only the large particles (henceforth particles) are explicitly included, the small particles (henceforth polymers) are represented as the Aaskura-Oosawa (4] approximation to the depletion interaction. In addition to the depletion potential, the particles are given a steep power law repulsive core, this gives them an isotropic well potential U(r)of fixed range:
Mat. Res. Soc. Symp. Proc. Vol. 248. 01992 Materials Research Society
282
U(r)
=
kT (r/a)-n + Q kT ( L 2 (r/cr)
-
(r/a) 3 /
3 - A
)
H(L,r)
(1) where L = 1 + cc/ and A = -2L 3/3,
a is
the diameter of the
polymer present at a volume fraction 0s and a- is the diameter of the large particles present at volume fraction 0; r is the separation between the particles, H(L,r) = 1(0), r < o+c (r > a+-). The interaction strength, Q depends on 0s and ac/: (2)
Q = 3s /2(c/r) 3).
Note that for Os = 0.4,0.7,1.0, Q = 798.5,1397.5,1996.5 and the potential has minimum values of -10,-24,-40 kT. The earlier study (3] revealed a n = 12 soft core to be inappropriate for the depletion potential, in the present work n = 36 is used and the anomalies of the earlier work (3] are avoided. To correspond to a recent experiment [3) the volume fraction of the large particles, • , is set at 0.3 and t/c is set at 1/11; 0 will be varied. The system is simulated with the algorithm describe in (l], and the shear rate will be quoted in terms of the Peclet number Pe also defined in (1]. Simple shear is applied with Y the direction of the shear gradient, X the direction of the imposed flow and Z the vorticity direction. In equilibrium the particle system possesses liquid and solid phases and a region of phase separation with
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