Suspensions are of wide interest and form the basis for many smart fluids [1][2][3][4][5][6][7]. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior [8, 9]. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro-or magnetorheological response.Shear thickening is presumed to be due to general mechanisms such as hydrodynamics [9, 10] or dilation [11][12][13], and thus all suspensions are expected to exhibit shear thickening under the right conditions [8]. So far, however, the exact conditions have not been determined. One condition is apparently set by attractive particle interactions. It has long been known that attractions, observed as flocculation in suspensions, can prevent shear thickening. This has been shown by modifying the chemistry, for example by adding flocculating agents to observe the transition from shear thickening to thinning (for a review, see [8]). In other cases, crossing the gel transition was shown to eliminate shear thickening [14,15]. A key problem, therefore, is to understand how interparticle attractions interfere with shear thickening. We demonstrate here that a simple and direct criterion for the existence of an observable shear thickening regime in dense, non-Brownian suspensions can be developed by comparing the yield stress produced by attractions with the inherent shear thickening stresses. We then generalize this condition to show how a yield stress from any source modifies the shear thickening phase diagram.Our experiments used an Anton Paar rheometer to * Electronic address: embrown@uchicago.edu •: viscosity curve of the same system at the same φ with added surfactant. The shear thickening regime is the region of positive slope in the curves of viscosity η versus applied stress τ . Shear thinning is characterized by a negative slope and Newtonian fluids, such as water, exhibit constant η. b, Images show clustering due to interparticle attractions (top) and no clustering when surfactant is added (bottom). Scale bar is 200 µm. All images (including subsequent figures) were taken at rest under an optical microscope in a dilute quasi two-dimensional layer. In this dilute case, attractions can be observed by the high number of particle contacts in the form of clusters or chains.measure the shear stress τ an...

We investigated the effects of particle shape on shear thickening in densely packed suspensions. Rods of different aspect ratios and nonconvex hooked rods were fabricated. Viscosity curves and normal stresses were measured using a rheometer for a wide range of packing fractions for each shape. Suspensions of each shape exhibit qualitatively similar discontinuous shear thickening. The logarithmic slope of the stress vs shear rate increases dramatically with packing fraction and diverges at a critical packing fraction φ(c) which depends on particle shape. The packing fraction dependence of the viscosity curves for different convex shapes can be collapsed when the packing fraction is normalized by φ(c). Intriguingly, viscosity curves for nonconvex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. The value of φ(c) is found to coincide with the onset of a yield stress at the jamming transition, suggesting the jamming transition also controls shear thickening. The yield stress is found to correspond with trapped air in the suspensions, and the scale of the stress can be attributed to interfacial tension forces which dramatically increase above φ(c) due to the geometric constraints of jamming. Using this connection we show that the jamming transition can be identified by simply looking at the surface of suspensions. The relationship between shear and normal stresses is found to be linear in both the shear thickening and jammed regimes, indicating that the shear stresses come from friction. In the limit of zero shear rate, normal stresses pull the rheometer plates together due to the surface tension of the liquid below φ(c), but push the rheometer plates apart due to jamming above φ(c).

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Solid polymer electrolyte blends were prepared with POSS-PEO(n=4)8 (3K), poly(ethylene oxide) (PEO(600K)), and LiClO4 at different salt concentrations (O/Li = 8/1, 12/1, and 16/1). POSS-PEO(n=4)8/LiClO4 is amorphous at all O/Li investigated, whereas PEO(600K) is amorphous only for O/Li = 8/1 and semicrystalline for O/Li = 12/1 and 16/1. The tendency of PEO(600K) to crystallize limited the amount of POSS-PEO(n=4)(8) that could be incorporated into the blends, so that the greatest incorporation of POSS-PEO(n=4)(8) occurred for O/Li = 8/1. Blends of POSS-PEO(n=4)(8)/PEO(600K)/LiClO4 (O/Li = 8/1 and 12/1) microphase separated into two amorphous phases, a low T(g) phase of composition 85% POSS-PEO(n=4)(8)/15% PEO(600K) and a high T(g) phase of composition 29% POSS-PEO(n=4)(8)/71% PEO(600K). For O/Li = 16/1, the blends contained crystalline (pure PEO(600K)), and two amorphous phases, one rich in POSS-PEO(n=4)(8) and one rich in PEO(600K). Microphase, rather than macrophase separation was believed to occur as a result of Li(+)/ether oxygen cross-link sites. The conductivity of the blends depended on their composition. As expected, crystallinity decreased the conductivity of the blends. For the amorphous blends, when the low T(g) (80/20) phase was the continuous phase, the conductivity was intermediate between that of pure PEO(600K) and POSS-PEO(n=4)(8). When the high T(g) (70/30, 50/50, 30/70, and 20/80) phase was the continuous phase, the conductivity of the blend and PEO(600K) were identical, and lower than that for the POSS-PEO(n=4)(8) over the whole temperature range (10-90 degrees C). This suggests that the motions of the POSS-PEO(n=4)(8) were slowed down by the dynamics of the long chain PEO(600K) and that the minor, low Tg phase was not interconnected and thus did not contribute to enhanced conductivity. At temperatures above T(m) of PEO(600K), addition of the POSS-PEO(n=4)(8) did not result in conductivity improvement. The highest RT conductivity, 8 x 10(-6) S/cm, was obtained for a 60% POSS-PEO(n=4)(8)/40% PEO(600K)/LiClO4 (O/Li = 12/1) blend.

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

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We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored. A. Chen ( )

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