The non-Newtonian rheology of dilute colloidal suspensions

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions

Force on a sphere via the generalized reciprocal theorem

An approach based on the generalized reciprocal theorem is presented to derive the well-known result for the drag force exerted on a rigid sphere translating in a viscous fluid in an arbitrary manner. The use of generalized reciprocal theorem allows one to bypass the calculation of stress distribution over the particle surface in order to compute the force

Classical Robustness of Quantum Unravellings

We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction the level of robustness depends on the measurement strategy, or unravelling, and that no single strategy is maximally robust in all ways.Comment: 8 Pages, 2 figures, Version 2. Minor changes to wording for clarification and some references added. Accepted for publication in Europhysics Letter

The effects of recent mortgage refinancing

Rising home prices and generally falling interest rates in recent years, together with a desire to convert the accumulated equity in their homes into spendable funds, have prompted many homeowners to refinance their mortgages. In the spring of 1999, the Federal Reserve surveyed consumers to determine the extent of refinancing, the extent to which refinancing homeowners "cashed-out" some of their equity when they refinanced, how much equity they took out, and how they spent the funds. Survey results suggest that cash-out refinancings in 1998 and early 1999 likely boosted consumption spending a bit, may have had a larger effect on home improvement spending, and may have moderated the growth of consumer credit during that period.Mortgages ; Housing - Finance ; Interest rates

Yielding of Hard-Sphere Glasses during Start-Up Shear

Concentrated hard-sphere suspensions and glasses are investigated with rheometry, confocal microscopy, and Brownian dynamics simulations during start-up shear, providing a link between microstructure, dynamics, and rheology. The microstructural anisotropy is manifested in the extension axis where the maximum of the pair-distribution function exhibits a minimum at the stress overshoot. The interplay between Brownian relaxation and shear advection as well as the available free volume determine the structural anisotropy and the magnitude of the stress overshoot. Shear-induced cage deformation induces local constriction, reducing in-cage diffusion. Finally, a superdiffusive response at the steady state, with a minimum of the time-dependent effective diffusivity, reflects a continuous cage breakup and reformation

Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection

Reply to the comment from Ikeda, Berthier, and Sollich (IBS)

We thank IBS for their comments which question our interpretation of the universal viscosity divergence near the flow-arrest transition in constant stress and pressure rheology of hard-sphere colloidal suspensions [2]. IBS introduced two Péclet numbers: Pe_0 = ẏ_ɑ^2=d0 and Pe = ẏ_ɑ^2/d(φ), with ẏ the strain rate, ɑ the particle size, d0 the isolated single-particle diffusivity and d_0 the long- time at-rest self-diffusivity, and considered three regimes: (i) Pe_0 < Pe ≪ 1, (ii) Pe_0 ≪ 1 ≪ Pe, and (iii) 1 ≪ Pe_0 < Pe

Wang and Brady Reply

We thank Ikeda, Berthier, and Sollich (IBS) [1] for their comments which question our interpretation of the universal viscosity divergence near the flow-arrest transition in constant stress and pressure rheology of hard-sphere colloidal suspensions [2]. IBS introduced two Péclet numbers: Pe_0 = γa^2/d^0 and Pe = γa^2/d(ϕ), with γ the strain rate, a the particle size, d_0 the isolated single-particle diffusivity, and d(ϕ) the long-time at-rest self-diffusivity. And they considered three regimes: (i) Pe_0 < Pe ≪ 1, (ii) Pe_0 ≪ 1 ≪ Pe, and (iii) 1 ≪ Pe_0 < Pe

Evaluation of liquid methane storage and transfer problems in supersonic aircraft

Evaluation of liquid methane storage and transfer problems for future supersonic aircraft cryogenic fuel requirement