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...

This paper resulted from a conference entitled “Lactation and Milk: Defining and refining the critical questions” held at the University of Colorado School of Medicine from January 18–20, 2012. The mission of the conference was to identify unresolved questions and set future goals for research into human milk composition, mammary development and lactation. We first outline the unanswered questions regarding the composition of human milk (Section I) and the mechanisms by which milk components affect neonatal development, growth and health and recommend models for future research. Emerging questions about how milk components affect cognitive development and behavioral phenotype of the offspring are presented in Section II. In Section III we outline the important unanswered questions about regulation of mammary gland development, the heritability of defects, the effects of maternal nutrition, disease, metabolic status, and therapeutic drugs upon the subsequent lactation. Questions surrounding breastfeeding practice are also highlighted. In Section IV we describe the specific nutritional challenges faced by three different populations, namely preterm infants, infants born to obese mothers who may or may not have gestational diabetes, and infants born to undernourished mothers. The recognition that multidisciplinary training is critical to advancing the field led us to formulate specific training recommendations in Section V. Our recommendations for research emphasis are summarized in Section VI. In sum, we present a roadmap for multidisciplinary research into all aspects of human lactation, milk and its role in infant nutrition for the next decade and beyond.

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).

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.When fluids are confined to thin layers, their flow behavior can differ markedly from the bulk. This is an issue of considerable importance in situations ranging from molecular lubrication films where it can induce increased friction (Braun & Naumovets, 2006) to macroscopic granular materials flowing out of a narrow hopper opening, where the particles can jam into rigid structures. Here we investigate this transition from flowing to jamming for densely packed, non-Brownian suspensions which exhibit shear thickening in the absence of strong interparticle interactions (Barnes, 1989;Brown et al., 2010). Shear thickening fluids are non-Newtonian such that their dynamic viscosity -defined as shear stress divided by shear rate in a steady state -increases over some range of shear rate. In dense suspensions this phenomenon is remarkable because it is characterized by a dramatic increase of stress with shear rate (Metzner & Whitlock, 1958;Hoffmann, 1972;1982;Laun, 1994;Frith et al., 1996;Maranzano & Wagner, 2001;Egres & Wagner, 2005;Lootens et al., 2005;Fall et al., 2008;Brown & Jaeger, 2009) which goes by the name of Discontinuous Shear Thickening, as well as the ability to absorb impacts (Lee et al., 2003). Consequences of jamming can be seen even in bulk rheology in terms of a critical packing fraction φ c corresponding to random loose packing above which the suspension is jammed, i.e. a yield stress is measured. This critical packing fraction controls the shear stress as a function of shear rate such that the slope increases with packing fraction and becomes discontinuous at φ c (Brown & Jaeger, 2009). Prior work on shear thickening fluids ...

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