JOURNAL OF COLLOID AND INTERFACE SCIENCE 182, 172–178 (1996) ARTICLE NO. 0448 Shear Thickening and Time-Dependent Rheological Behavior in Aqueous Polyacrylic Ester Dispersions J. XU,* A. M. JAMIESON,² S. Q. W ANG,² ,1 AND S. QUTUBUDDIN * , ² ,1 Departments of *Chemical Engineering and ² Macromolecular Science, Case Western Reserve University, Cleveland, Ohio 44106 Received November 6, 1995; accepted March 20, 1996 and light diffraction (6). Dynamic simulations have repro- We have observed, in a commercial aqueous polyacrylic ester duced many of the essential features of the shear thickening dispersion, a shear thickening phenomenon that exhibits time- rheology ( 7 – 10 ) . In sterically- or electrostatically-stabilized dependent rheological behavior. The critical shearrate g g c for the dispersions of uniform spherical particles, shear flow pro- shear thickening transition varies with volume fraction, tempera- duces an ordered two-dimensional layered structure. At suf- ture, pH, and particle size distribution, in a manner which indi- ficiently high shear rates, hydrodynamic forces overcome cates that the phenomenon is associated with a reversible shear- the interparticle repulsion forces so that the ordered state is induced colloidal order–disorder transition. However, we find broken up, resulting in a disordered state with an apparent that, in the shear thickening region, the rheology may also evolve geometrical jamming leading to a sudden rise in viscosity. with time. Our observations suggest that the time-dependence is caused by the temporary formation of particle clusters at high The disordered state may involve the transitory formation shear rates.  1996 Academic Press, Inc. of large particle aggregates (11, 10) or a random three- Key Words: shear thickening; order–disorder transition; flow- dimensional network (2). Although there is no general induced clusters. agreement about the exact structural changes that take place, there appears to be consensus on the transition from a free- flowing ordered structure to a less regular, more dissipative INTRODUCTION state (13). Boersma et al. (12) recently presented a simple analysis, Flow instabilities are sometimes observed in coating ap- based on a balance between shear forces and interparticle plications of certain aqueous polymer emulsions. Such ef- forces, which is able to predict the dependence of the criti- fects may be associated with shear thickening behavior, cal shear rate on the particle volume fraction (interparticle which is commonly observed in concentrated colloidal dis- distance), the magnitude of the stabilizing force, the dis- persions of uniform particle size. This type of shear thick- persion medium viscosity, and the particle radius. An ex- ening is characterized by an abrupt, sometimes discontinu- pression was derived for the dependence of the critical ous, rise in viscosity above a critical shear rate with no shear rate g g c (12), apparent particle aggregation. The sudden viscosity increase is generally believed to be due to a shear-induced order– disorder transition. Among the first to describe the phenome- g h c Å e 0 e r c 2 0 kh 6ha 2 , [1] non was Hoffman (1, 2), whose early work established the basis for modeling such flow instabilities in terms of torque balance and energy balance, and who produced a mecha- where e 0 is the permittivity of vacuum, e r is the relative nism, based on light scattering evidence, that a transition dielectric constant of the solvent, c 0 is the surface potential, takes place from a two-dimensional ordered state to a three- h is the solvent viscosity, a is the particle radius, h is the dimensional disordered state. The transition occurs when the average interparticle separation, and k is the reciprocal De- hydrodynamic forces on the particles destabilize the layered bye length. This model predicts behavior that is qualitatively structure. similar to the earlier, more elaborate analysis of Hoffman Further studies were subsequently carried out to character- (2) but exhibits significant quantitative differences. For ex- ize the ordered or layered flow region, and supporting evi- ample, as noted by Boersma et al. (12), the analysis of dence for the order–disorder transition was obtained from Hoffman (2) includes van der Waals forces which lead to small angle neutron scattering ( 3, 4 ) , light scattering ( 1, 5 ) , a decrease in g g c for smaller particles. Support for Eq. [1] has been obtained from dynamic simulations (10). 1 To whom correspondence should be addressed. In a review paper, Barnes (13) discussed the importance 172 0021-9797/96 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved.