Microstructure of strongly sheared suspensions and its impact on rheology and diffusion

The effects of Brownian motion alone and in combination with an interparticle force of hard-sphere type upon the particle configuration in a strongly sheared suspension are analysed. In the limit Pe[rightward arrow][infty infinity] under the influence of hydrodynamic interactions alone, the pair-distribution function of a dilute suspension of spheres has symmetry properties that yield a Newtonian constitutive behaviour and a zero self-diffusivity. Here, Pe=[gamma][ogonek]a2/2D is the Péclet number with [gamma][ogonek] the shear rate, a the particle radius, and D the diffusivity of an isolated particle. Brownian diffusion at large Pe gives rise to an O(aPe[minus sign]1) thin boundary layer at contact in which the effects of Brownian diffusion and advection balance, and the pair-distribution function is asymmetric within the boundary layer with a contact value of O(Pe0.78) in pure-straining motion; non-Newtonian effects, which scale as the product of the contact value and the O(a3Pe[minus sign]1) layer volume, vanish as Pe[minus sign]0.22 as Pe[rightward arrow][infty infinity]

Self-diffusion in sheared suspensions

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number Pe = ẏa^2/2D, where ẏ is the shear rate, a is the particle radius, and D = k_BT/6πηa is the diffusion coefficient of an isolated particle. Here, k_B is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by k_BT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction ø = 4/3πa^3n and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D_∞^s, is given by the sum of D_0^s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D_0^s and D_∞^s are anisotropic, in general, with the anisotropy of D_0^s due solely to that of the steady microstructure. The influence of flow upon D_∞^s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations. The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(φPe^(3/2)) for Pe « 1 and ø « 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D_0^s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with ẏ. Regardless of whether or not the particles interact hydrodynamically, flow influences D_∞^s at O(øPe) and O(øPe^(3/2)). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe^(3/2)), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe^(3/2)DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor. At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D_∞^s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of Pe = ẏa^2/2D^s_0(φ)$. At small Pe the dependence on Pe is the same as at low ø

Convergence of derivative expansions of the renormalization group

We investigate the convergence of the derivative expansion of the exact renormalization group, by using it to compute the beta function of scalar field theory. We show that the derivative expansion of the Polchinski flow equation converges at one loop for certain fast falling smooth cutoffs. The derivative expansion of the Legendre flow equation trivially converges at one loop, but also at two loops: slowly with sharp cutoff (as a momentum-scale expansion), and rapidly in the case of a smooth exponential cutoff. Finally, we show that the two loop contributions to certain higher derivative operators (not involved in beta) have divergent momentum-scale expansions for sharp cutoff, but the smooth exponential cutoff gives convergent derivative expansions for all such operators with any number of derivatives.Comment: Latex inc axodraw. 20 page

Collective diffusion in sheared colloidal suspensions

Collective diffusivity in a suspension of rigid particles in steady linear viscous flows is evaluated by investigating the dynamics of the time correlation of long-wavelength density fluctuations. In the absence of hydrodynamic interactions between suspended particles in a dilute suspension of identical hard spheres, closed-form asymptotic expressions for the collective diffusivity are derived in the limits of low and high Péclet numbers, where the Péclet number Pe = gamma-dot a^2/D0 with gamma-dot being the shear rate and D0 = kB T/6πη a is the Stokes–Einstein diffusion coefficient of an isolated sphere of radius a in a fluid of viscosity η. The effect of hydrodynamic interactions is studied in the analytically tractable case of weakly sheared (Pe « 1) suspensions. For strongly sheared suspensions, i.e. at high Pe, in the absence of hydrodynamics the collective diffusivity Dc = 6 Ds∞, where Ds∞ is the long-time self-diffusivity and both scale as φ gamma-dot a^2$, where φ is the particle volume fraction. For weakly sheared suspensions it is shown that the leading dependence of collective diffusivity on the imposed flow is proportional to D0 φPe Ê, where Ê is the rate-of-strain tensor scaled by gamma-dot, regardless of whether particles interact hydrodynamically. When hydrodynamic interactions are considered, however, correlations of hydrodynamic velocity fluctuations yield a weakly singular logarithmic dependence of the cross-gradient-diffusivity on k at leading order as ak → 0 with k being the wavenumber of the density fluctuation. The diagonal components of the collective diffusivity tensor, both with and without hydrodynamic interactions, are of O(φPe2), quadratic in the imposed flow, and finite at k = 0. At moderate particle volume fractions, 0.10 ≤ φ ≤ 0.35, Brownian Dynamics (BD) numerical simulations in which there are no hydrodynamic interactions are performed and the transverse collective diffusivity in simple shear flow is determined via time evolution of the dynamic structure factor. The BD simulation results compare well with the derived asymptotic estimates. A comparison of the high-Pe BD simulation results with available experimental data on collective diffusivity in non-Brownian sheared suspensions shows a good qualitative agreement, though hydrodynamic interactions prove to be important at moderate concentrations

A comparative study of herbage intake, ingestive behaviour and diet selection, and effects of condensed tannins upon body and wool growth in lambs grazing Yorkshire fog (Holcus lanatus) and annual ryegrass (Lolium multiflorum) dominant swards

An experiment was carried out from August to early November 1994 to examine differences in diet selection, herbage intake, grazing behaviour and animal performance between weaned lambs rotationally grazing swards of annual ryegrass (Lolium multiflorum)/white clover (Trifolium repens) and Yorkshire fog (Holcus lanatus)/T. repens with or without Lotus corniculatus. There were four replicate groups of six lambs per treatment. The effects of condensed tannins (CT) on lamb production were assessed by twice-daily oral administration of 10g polyethylene glycol (PEG; molecular weight 4000) to half the lambs on each sward. The Lotus content of all swards was very low, and results are presented here for main sward comparisons meaned over lotus treatments. Overall mean estimates of pre-grazing herbage mass and sward surface height for the annual ryegrass and Yorkshire fog swards respectively, were 5820 v. 4360 +/- 190 kg DM/ha (P , P < 0.01) and liveweight gain (141 v. 120 +/- 4.3 g per lamb per day, P < 0.01), although differences in carcass weight (17.9 v. 18.2 +/- 0.3 kg) and FEC transformed values (9.6 v. 11.0 +/- 06 eggs/g fresh faeces) were not significant. The effects of CT on animal performance were greater in Yorkshire fog swards. CT had no significant effects on diet selection, herbage intake and grazing behaviour patterns

Anatomy of a Community-Level Fiscal Impact Model: FIT-4-NH.

Abstract: This paper describes the development of a fiscal impact tool for New Hampshire communities (HT -4-NH). FIT -4-NH belongs to a family of computergenerated fiscal impact assessment models designed to estimate the impacts to local government revenues and expenditures that result from economic changes. In the past, work in this area has centered on the completion of countylevel models for the midwestern states. FIT-4-NH is unique in that it was designed for rural community-level use in the northern New England region of the country

The digital Sabbath and the digital distraction: Arts-based research methods for new audiences

Despite the known affordances of Arts-Based Research Practice within the international education environment, its use remains relatively uncommon in Western Australia. The reasons for this are likely the contested nature of quality criteria by which Arts-Based Practice is evaluated as well as the challenges as well associated with the dissemination of research findings. Mixed-methods research is increasingly recognised as an appropriate and practical approach for education phenomena, and within this domain, inquiry that combines traditional qualitative and arts-based strategies offers the education researcher advantages that are not readily available through other approaches. As professional artists and researchers we share our experiences in employing our visual arts specialism within a qualitative approach. Our focus for inquiry was a “Digital Sabbath” intervention (a practice of regularly unplugging from all technology/devices with the aim of increasing social connectedness and mitigating stress) with seven early career visual arts teachers whose voices and experience of the digital disruption might otherwise have remained silenced. The importance of the study was both that we trialed a well-being intervention, but also that we innovated our methodological research repertoire by combining traditional and contemporary elements of the Qualitative paradigm