Polymer-Induced Drag Reduction in Dilute Newtonian and Semi-Dilute Non-Newtonian Fluids: An Assessment of the Double-Gap Concentric Cylinder Method.

Polymer-induced drag reduction (DR) in fluids was studied using a rotational rheometer with double-gap concentric cylinder geometry. Although both polymers (polyacrylamide (PAM) and 2-acrylamido-2-methylpropane sulfonic acid (SPAM)) had molecular weights of several MDa, the contrasting polymer charge, nonionic and anionic, led to different polymer overlap concentrations (c*), PAM ≫ SPAM, and fluid rheology, with PAM fluids mostly Newtonian and SPAM fluids non-Newtonian (shear-thinning). Based on these differences, it was important to account for the infinite shear viscosity and normalize the polymer concentration by the intrinsic concentration (c int) so that the DR performance of the two polymer fluids could be accurately compared. Both polymers induced DR, and the maximum DR by SPAM (DR% = 28) was slightly higher than that by PAM (DR% = 22) when Re p ∼ 1700. For PAM, the loss of DR with time diminished at higher polymer concentrations (≥100 ppm, at Re p = 3149) but was found to be sensitive to high Re p, with polymer chain scission the likely cause of the reduced performance. For the semi-dilute SPAM fluids, the shear stability contrasted that of PAM, showing negligible dependence on the polymer concentration and Re p. The apparent rapid loss of DR was predominantly attributed to a time-dependent effect and not polymer degradation. In pipe flow, the maximum DR for SPAM was higher than that measured by rheometry and was attributed to differences in the flow conditions. However, changes in the normalized DR/c with polymer concentration were found to be consistent between the two flow geometries. Furthermore, the high fluid stresses in pipe flow (at high Re p) led to drag reduction losses consistent with PAM, as the time-dependent effect was not seen.

Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy.

Fluorescence recovery after photobleaching (FRAP) is a widely used technique for studying diffusion in biological tissues. Most of the existing approaches for the analysis of FRAP experiments assume isotropic diffusion, while only a few account for anisotropic diffusion. In fibrous tissues, such as articular cartilage, tendons and ligaments, diffusion, the main mechanism for molecular transport, is anisotropic and depends on the fibre alignment. In this work, we solve the general diffusion equation governing a FRAP test, assuming an anisotropic diffusivity tensor and using a general initial condition for the case of an elliptical (thereby including the case of a circular) bleaching profile. We introduce a closed-form solution in the spatial coordinates, which can be applied directly to FRAP tests to extract the diffusivity tensor. We validate the approach by measuring the diffusivity tensor of [Formula: see text] FITC-Dextran in porcine medial collateral ligaments. The measured diffusion anisotropy was [Formula: see text] (SE), which is in agreement with that reported in the literature. The limitations of the approach, such as the size of the bleached region and the intensity of the bleaching, are studied using COMSOL simulations.

Enhancing Chromium (VI) removal from synthetic and real tannery effluents by using diatomite-embedded nanopyroxene.

A commercial filter aid material of Diatomite was modified via loading it with a low mass fraction of polyethylenimine-functionalized pyroxene nanoparticles (PEI-PNs) to enhance its adsorption activities. The modified Diatomite was then used for Cr(VI) removal from dichromate solution and from real tannery wastewater. For the synthetic wastewater, batch adsorption experiments were first performed at various pH and Cr(VI) initial concentrations. Then, the obtained kinetic parameters were used to investigate the continuous adsorption inside the fixed-bed column. The continuous removal of the Cr(VI) was performed inside a fixed-bed column under various influent flow rates, Cr(VI) initial concentrations, and bed-heights. In the column experiments, high adsorption of Cr(VI) was observed at low flow rates, high bed heights, and low influent initial concentrations. A dimensionless form of the advection-axial dispersion model, featuring Peclet number as a fitting parameter, was then used to study the breakthrough behavior under various dynamic parameters. Afterward, the modified Diatomite was used to remediate well characterized real tannery wastewater. For the treatment of the tannery wastewater, our modified filter aid, compared with the non-modified one, showed an outstanding performance and a higher removal efficiency.

Anisotropic Diffusivity Tensor in Articular Cartilage: Effective Medium Approach.

Due to the avascular nature of articular cartilage, molecular transport occurs via interstitial fluid flow as well as via diffusion. Diffusion in cartilage has been studied experimentally, but no mathematical models have been developed to interpret the experimental results and the observed isotropy or anisotropy in the different cartilage zones. Here, we propose a model for the determination of the diffusivity tensor of uncharged macromolecules in articular cartilage, accounting for the inhomogeneity and anisotropy arising from fiber arrangement, volumetric fraction, and radius. We study a representative element of volume (REV) comprising a fiber surrounded by fluid-saturated proteoglycan matrix. The REV permeability tensor is evaluated using a previously developed model, while the REV diffusivity tensor is obtained by incorporating the hydrodynamic effect and the steric effect of the fiber-reinforced matrix. Both effects are represented by anisotropic second-order tensors. The overall diffusivity tensor is obtained as the averaging integral of the REV diffusivity, weighted by the probability distribution of fiber orientation. The model's predictions of the trend of the magnitude of the diffusivity of spheroidal macromolecules as a function of molecular radius agree with published experimental results. For large linear macromolecules, the model underestimates the diffusivity magnitude (i.e., the equivalent isotropic diffusivity). The model correctly predicts the anisotropic behavior for linear macromolecules, although it underestimates the numerical value of the diffusivity anisotropy ratio of large linear macromolecules in the superficial zone, and overestimates it in the deep zone. In summary, this model constitutes a first step toward understanding the relation between diffusivity and permeability in articular cartilage.

Effect of structural distortions on articular cartilage permeability under large deformations.

The permeability of articular cartilage has a key role in load support and lubrication in diarthrodial joints. The microstructural rearrangement and consequent alteration in permeability caused by the large deformations undergone by cartilage have been previously modelled with a multi-scale approach. At the microscopic scale, the tissue is regarded as a homogeneous fluid-filled proteoglycan matrix reinforced by collagen fibres. A material point is described by a representative element of volume (REV), comprising a collagen fibre surrounded by a jacket of fluid-saturated proteoglycan matrix. At the macroscopic scale, the statistical orientation of the fibres is accounted for via averaging of the REV over all possible directions. The previous models accounted for volumetric deformation and fibre reorientation, but did not consider the cross-sectional distortion of the REV, which changes the widths of the fluid channels in different directions. We account for REV cross-sectional distortion and demonstrate its effects by simulating confined compression tests for the superficial, middle and deep zones of articular cartilage. The proposed model captures published experimental results that were not reproduced correctly by the previous models, and shows that each factor (volumetric deformation, fibre reorientation, REV cross-sectional distortion) can be dominant, depending on fibre orientation and amount of compression, implying that all three factors should be accounted for when modelling cartilage permeability.

Force measurements during running on different instrumented treadmills.

One method to determine the forces produced during running is to conduct extensive kinematic and kinetic analysis. These analyses can be performed by having an individual perform repeated over-ground running trials or simply run continuously on an instrumented treadmill. The forces produced during over-ground running may not be the same as the forces during treadmill running and these differences could be attributed to a number of factors, including the design of the instrumented treadmill. The purpose of this paper was to determine whether there are differences in force measurements on different instrumented treadmill setups in comparison to over-ground running and to correct for any of these differences using a theoretical model. 11 participants ran on three different treadmills and performed over-ground running at 2.7, 3.6, and 4.5 m/s. Ground reaction forces were measured via force plates and an instrumented pressure insole. We found that the magnitude of the vertical ground reaction force differed between the three treadmills and over-ground running. The difference in ground reaction forces estimated by the pressure insole and the treadmill-force-plate system or instrumented treadmill can be explained by a three degree of freedom mechanical model of a person running on a treadmill and this model could potentially be used to correct for errors in force measurement from instrumented treadmills. The model included a force plate, a treadmill, and a wobbling mass with varying natural frequencies and damping characteristics, and constant masses. These findings provide researchers a method to correct forces from an instrumented treadmill set-up to determine a close approximation of the actual forces experienced by a participant during treadmill running.