An analytical solution for the velocity and shear rate distribution of non-ideal Bingham fluids in concentric cylinder viscometers

An analytical solution is presented for the calculation of the flow field in a concentric cylinder viscometer of non-ideal Bingham-fluids, described by the Worrall-Tuliani rheological model. The obtained shear rate distribution is a function of the a priori unknown rheological parameters. It is shown that by applying an iterative procedure experimental data can be processed in order to obtain the proper shear rate correction and the four rheological parameters of the Worrall-Tuliani model as well as the yield surface radius. A comparison with Krieger's correction method is made. Rheometrical data for dense cohesive sediment suspensions have been reviewed in the light of this new method. For these suspensions velocity profiles over the gap are computed and the shear layer thicknesses were found to be comparable to visual observations. It can be concluded that at low rotation speeds the actually sheared layer is too narrow to fullfill the gap width requirement for granular suspensions and slip appears to be unavoidable, even when the material is sheared within itself. The only way to obtain meaningfull measurements in a concentric cylinder viscometer at low shear rates seems to be by increasing the radii of the viscometer. Some dimensioning criteria are presented.Notation A, B Integration constants - C Dimensionless rotation speed = µ/_y - c = 2µ - d = ₀ ²–2c_y - f() = (–₀)²+2c(–_y) - r Radius - r _b Bob radius - r _c Cup radius - r _y Yield radius - r ₀ Stationary surface radius - r Rotating Stationary radius - Y ₀ Shear rate parameter = /µ Greek letters Shear rate - = (r _y /r _b )²– 1 - µ Bingham viscosity - µ₀ Initial differential viscosity - µ µ₀-µ - Rotation speed - Angular velocity - Shear stress - _b Bob shear stress - _B Bingham stress - _y (True) yield stress - ₀ Stress parameter = _B +µ Y ₀ - _B - _y      

The effect of temperature gradients on the sharkskin surface instability in polymer extrusion through a slit die

The sharkskin surface instability is commonly observed in the extrusion of polymer melts. We present a series of experiments in which a specifically designed rectangular slit die with insulated and independently heated sides and is used to induce precise temperature gradients across a flowing polyethylene melt. Our previous experiments demonstrated that the character of the surface distortions produced by the sharkskin instability was a function of the die wall temperature and therefore the extrudate had viscoelastic properties at the surface. In this paper, we explore the role of temperature and viscoelastic property gradients near the capillary wall. The amplitude of the sharkskin instability is quantified and plotted against apparent shear and extension rates. Analysis of the data demonstrates that the amplitude and frequency of the instability is independent of bulk temperature and temperature gradient and is dependent only on wall temperature. The data are normalized using a dimensionless Weissenberg number based on the extension rate to collapse the data collected over all temperatures and gradients onto a single master curve. We conclude with an example of a rectangular extrudate exhibiting varying surface roughness due to differential die heating and discuss the implications of our observations on the sharkskin surface instability mechanism and on commercial applications.     

Multiscale Modeling of the Active Site of [Fe] Hydrogenase: The H2 Binding Site in Open and Closed Protein Conformations

A series of QM/MM optimizations of the full protein of [Fe] hydrogenase were performed. The FeGP cofactor has been optimized in the water‐bound resting state ( 1 ), with a side‐on bound dihydrogen ( 2 ), or as a hydride intermediate ( 3 ). For inclusion of H₄ MPT in the closed structure, advanced multiscale modeling appears to be necessary, especially to obtain reliable distances between CH‐H₄MPT⁺ and the dihydrogen (H₂) or hydride (H^?) ligand in the FeGP cofactor. Inclusion of the full protein is further important for the relative energies of the two intermediates 2 and 3 . We finally find that hydride transfer from 3 has a significantly higher barrier than found in previous studies neglecting the full protein environment.     

Pushing the speed limit in enantioselective supercritical fluid chromatography

Chromatographic enantioseparations on the order of a few seconds can be achieved by supercritical fluid chromatography using short columns packed with chiral stationary phases. The evolution of ‘world record’ speeds for the chromatographic separation of enantiomers has steadily dropped from an industry standard of 20–40 min just two decades ago, to a current ability to perform many enantioseparations in well under a minute. Improvements in instrument and column technologies enabled this revolution, but the ability to predict optimal separation time from an initial method development screening assay using the t_{min cc} predictor greatly simplifies the development and optimization of high‐speed chiral chromatographic separations. In this study, we illustrate how the use of this simple tool in combination with the workhorse technique of supercritical fluid chromatography on customized short chiral columns (1–2 cm length) allows us to achieve ultrafast enantioseparations of pharmaceutically relevant compounds on the 5–20 s scale, bringing the technique of high‐throughput enantiopurity analysis out of the specialist realm and into the laboratories of most researchers.     

Measurement of the flexibility of wet cellulose fibres using atomic force microscopy

Flexibility and modulus of elasticity data for two types of wet cellulose fibres using a direct force–displacement method by means of AFM are reported for never dried wet fibres immersed in water. The flexibilities for the bleached softwood kraft pulp (BSW) fibres are in the range of 4–38 × 10¹² N^?1 m^?2 while the flexibilities for the thermomechanical pulp (TMP) fibres are about one order of magnitude lower. For BSW the modulus of elasticity ranges from 1 to 12 MPa and for TMP between 15–190 MPa. These data are lower than most other available pulp fibre data and comparable to a soft rubber band. Reasons for the difference can be that our measurements with a direct method were performed using never dried fibres immersed in water while other groups have employed indirect methods using pulp with different treatments.