22,079 research outputs found
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
The Economics of Organic Versus Conventional Cow-calf Production
Costs, returns, and profitability of cow-calf farms that are organic or transitioning to organic are compared with those of cow-calf farms that are non-organic. A method of matching samples is used for the comparison. Results suggest higher cost of organic production due to higher unpaid labor, taxes and insurance, and overhead costs.Matching Samples, Profit, Costs, Farm Management, Production Economics,
A constitutive model for simple shear of dense frictional suspensions
Discrete particle simulations are used to study the shear rheology of dense,
stabilized, frictional particulate suspensions in a viscous liquid, toward
development of a constitutive model for steady shear flows at arbitrary stress.
These suspensions undergo increasingly strong continuous shear thickening (CST)
as solid volume fraction increases above a critical volume fraction, and
discontinuous shear thickening (DST) is observed for a range of . When
studied at controlled stress, the DST behavior is associated with non-monotonic
flow curves of the steady-state stress as a function of shear rate. Recent
studies have related shear thickening to a transition between mostly lubricated
to predominantly frictional contacts with the increase in stress. In this
study, the behavior is simulated over a wide range of the dimensionless
parameters , and , with the dimensionless shear stress and the coefficient of
interparticle friction: the dimensional stress is , and , where is the magnitude of repulsive force at contact
and is the particle radius. The data have been used to populate the model
of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev.
Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity
divergences or \textquotedblleft jamming\textquotedblright\ points at volume
fraction (random close packing) for the
low-stress lubricated state, and at for
any nonzero in the frictional state; a generalization provides the normal
stress response as well as the shear stress. A flow state map of this material
is developed based on the simulation results.Comment: 12 pages, 10 figure
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