Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.

Measuring and predicting the dynamics of linear monodisperse entangled polymers in rapid flow through an abrupt contraction. A small angle neutron scattering study

Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Slip flows of Newtonian and viscoelastic fluids in a 4:1 contraction

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.

The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Characteristics of the deep ocean carbon system during the past 150,000 years: ΣCO2 distributions, deep water flow patterns, and abrupt climate change

Studies of carbon isotopes and cadmium in bottom-dwelling foraminifera from ocean sediment cores have advanced our knowledge of ocean chemical distributions during the late Pleistocene. Last Glacial Maximum data are consistent with a persistent high-ΣCO2 state for eastern Pacific deep water. Both tracers indicate that the mid-depth North and tropical Atlantic Ocean almost always has lower ΣCO2 levels than those in the Pacific. Upper waters of the Last Glacial Maximum Atlantic are more ΣCO2-depleted and deep waters are ΣCO2-enriched compared with the waters of the present. In the northern Indian Ocean, δ13C and Cd data are consistent with upper water ΣCO2 depletion relative to the present. There is no evident proximate source of this ΣCO2-depleted water, so I suggest that ΣCO2-depleted North Atlantic intermediate/deep water turns northward around the southern tip of Africa and moves toward the equator as a western boundary current. At long periods (>15,000 years), Milankovitch cycle variability is evident in paleochemical time series. But rapid millennial-scale variability can be seen in cores from high accumulation rate series. Atlantic deep water chemical properties are seen to change in as little as a few hundred years or less. An extraordinary new 52.7-m-long core from the Bermuda Rise contains a faithful record of climate variability with century-scale resolution. Sediment composition can be linked in detail with the isotope stage 3 interstadials recorded in Greenland ice cores. This new record shows at least 12 major climate fluctuations within marine isotope stage 5 (about 70,000–130,000 years before the present).

Eddy Formation in the Tropical Atlantic Induced by Abrupt Changes in the Meridional Overturning Circulation

The variability of the meridional overturning circulation (MOC) in the upper tropical Atlantic basin is investigated using a reduced-gravity model in a simplified domain. Four sets of idealized numerical experiments are performed: (i) switch-on of the MOC until a fixed value when a constant northward flow is applied along the western boundary; (ii) MOC with a variable flow; (iii) MOC in a quasi-steady flow; and (iv) shutdown of the MOC in the Northern Hemisphere. Results from experiments (i) show that eddies are generated at the equatorial region by shear instability and detached northward; eddies are responsible for an enhancement of the mean flow and the variability of the MOC. Results from experiments (ii) show a transitional behavior of the MOC related to the eddy generation in interannual-decadal time scales as the Reynolds number varies due to the variations in the MOC. In experiments (iii), a critical Reynolds number Re(c) around 30 is found, above which eddies are generated. Experiments (iv) demonstrate that even after the collapse of MOC in the Northern Hemisphere, eddies can still be generated and carry energy across the equator into the Northern Hemisphere; these eddies act to attenuate the impact of the MOC shutdown on short time scales. The results described here may be particularly pertinent to ocean general circulation models in which the Reynolds number lies close to the bifurcation point separating the laminar and turbulent regimes.

Peptidergic control of gastrointestinal blood flow in the estuarine crocodile, Crocodylus porosus

Peptidergic mechanisms influencing the resistance of the gastrointestinal vascular bed of the estuarine crocodile, Crocodylus porosus, were investigated. The gut was perfused in situ via the mesenteric and the celiac arteries, and the effects of different neuropeptides were tested using bolus injections. Effects on vascular resistance were recorded as changes in inflow pressures. Peptides found in sensory neurons [substance P, neurokinin A, and calcitonin gene-related peptide (CGRP)] all caused significant relaxation of the celiac vascular bed, as did vasoactive intestinal polypeptide (VIP), another well-known vasodilator. Except for VIP, the peptides also induced transitory gut contractions. Somatostatin and neuropeptide Y (NPY), which coexist in adrenergic neurons of the C. porosus, induced vasoconstriction in the celiac vascular bed without affecting the gut motility. Galanin caused vasoconstriction and occasionally activated the gut wall. To elucidate direct effects on individual vessels, the different peptides were tested on isolated ring preparations of the mesenteric and celiac arteries. Only CGRP and VIP relaxed the epinephrine-precontracted celiac artery, whereas the effects on the mesenteric artery were variable. Somatostatin and NPY did not affect the resting tonus of these vessels, but somatostatin potentiated the epinephrine-induced contraction of the celiac artery. Immunohistochemistry revealed the existence and localization of the above-mentioned peptides in nerve fibers innervating vessels of different sizes in the gut region. These data support the hypothesis of an important role for neuropeptides in the control of the vascular bed of the gastrointestinal tract in C. porosus.

Ductus venosus Doppler and postnatal outcomes in fetuses with absent or reversed end-diastolic flow in the umbilical arteries

Objective: To evaluate the relationship between ductus venosus Doppler findings on the day of delivery and postnatal outcomes in pregnancies with absent or reversed end-diastolic (ARED) flow in the umbilical arteries. Study design: Postnatal outcomes of 103 newborns of pregnancies with a diagnosis of ARED flow on Doppler velocimetry of the umbilical arteries were analyzed retrospectively between January 1997 and December 2004. Single pregnancies and fetuses without malformations were included. The cases were divided into two groups according to the flow during atrial contraction (a-wave) in the ductus venosus on the day of delivery: group A, 20 cases with absent or reversed flow in the ductus venosus and group B, 83 cases with positive flow. The results were analyzed statistically using the chi-square test, Fisher`s exact test and the Mann-Whitney U test with the level of significance set at 5%. Results: All newborns were delivered by cesarean section. Gestational age was similar in the two groups (group A: 30 weeks and group B: 30.9 weeks, P = 0.23). Absent or reversed ductus venosus flow was associated with the following adverse postnatal outcomes: lower birthweight (P < 0.001), lower Apgar scores in the first (P = 0.001) and fifth minute (P = 0.001), a higher frequency of orotracheal intubation (P = 0.001) and pH at birth less than 7.20 (P < 0.001), pulmonary hemorrhage (P = 0.03), thrombocytopenia (P = 0.02), hypoglycemia (P = 0.01), intracranial hemorrhage (P = 0.02), and postnatal death (P = 0.007). Conclusion: The study of ductus venosus flow may provide additional information regarding the best time for interruption of pregnancies with ARED flow in the umbilical arteries characterized by extreme prematurity. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Endothelin-1 Induces Contraction of Female Rat Internal Pudendal and Clitoral Arteries through ET(A) Receptor and Rho-Kinase Activation

Introduction. Endothelin-1 (ET-1), a potent vasoconstrictor peptide, acts mainly through the Gprotein-coupled ET(A) receptor (ET(A)R). Increased vascular ET-1 production and constrictor sensitivity have been observed in various cardiovascular diseases, including hypertension, as well as erectile dysfunction. The internal pudendal artery (IPA) supplies blood to the vagina and clitoris. Inadequate blood flow through the IPA may lead to insufficient vaginal engorgement and clitoral tumescence. Aim. Characterize the effects of ET-1 on the IPA and clitoral artery (CA). Methods. IPA and CA from female Sprague Dawley rats (225-250 g) were mounted in myograph chambers. Arterial segments were submitted to increasing concentrations of ET-1 (10-10-10-6 M). Segments were incubated with the ET(A)R antagonist, atrasentan (10-8 M) or the Rho-kinase inhibitor, Y-27632 (10-6 M) 30 minutes prior to agonist exposure. All E(max) values are expressed as % KCl-induced maximal contraction. ET(A)R, RhoA, and Rho-kinase expression from IPA was evaluated by Western blot. mRNA of preproET-1, ET(A)R, ET(B)R, RhoA, and Rho-kinase were measured by real time PCR. Main Outcome Measures. ET-1 constrictor sensitivity in IPA and CA, protein expression and messenger RNA levels of ET-1-mediated constriction components. Results. ET-1 concentration-dependently contracted IPA (% Contraction and pD2, respectively: 156 +/- 18, 8.2 +/- 0.1) and CA (163 +/- 12, 8.8 +/- 0.08), while ET(A)R antagonism reduced ET-1-mediated contraction (IPA: 104 +/- 23, 6.4 +/- 0.2; CA: 112 +/- 17, 6.6 +/- 0.08). Pretreatment with Y-27632 significantly shifted ET-1 pD2 in IPA (108 +/- 24, 7.9 +/- 0.1) and CA (147 +/- 58 and 8.0 +/- 0.25). Protein expression of ET(A)R, ET(B)R, RhoA, and Rho-kinase were detected in IPA. IPA and CA contained preproET-1, ET(A)R, ET(B)R, RhoA, and Rho-kinase message. Conclusion. We observed that the IPA and CA are sensitive to ET-1, signaling through the ET(A)R and Rho-kinase pathway. These data indicate that ET-1 may play a role in vaginal and clitoral blood flow and may be important in pathologies where ET-1 levels are elevated. Allahdadi KJ, Hannan JL, Tostes RC, and Webb RC. Endothelin-1 induces contraction of female rat internal pudendal and clitoral arteries through ETA receptor and Rho-kinase activation. J Sex Med 2010;7:2096-2103.

Shear stress and sediment transport calculations for sheet flow under waves

A simple method is provided for calculating transport rates of not too fine (d(50) greater than or equal to 0.20 mm) sand under sheet flow conditions. The method consists of a Meyer-Peter-type transport formula operating on a time-varying Shields parameter, which accounts for both acceleration-asymmetry and boundary layer streaming. While velocity moment formulae, e.g.., = Constant x calibrated against U-tube measurements, fail spectacularly under some real waves (Ribberink, J.S., Dohmen-Janssen, C.M., Hanes, D.M., McLean, S.R., Vincent, C., 2000. Near-bed sand transport mechanisms under waves. Proc. 27th Int. Conf. Coastal Engineering, Sydney, ASCE, New York, pp. 3263-3276, Fig. 12), the new method predicts the real wave observations equally well. The reason that the velocity moment formulae fail under these waves is partly the presence of boundary layer streaming and partly the saw-tooth asymmetry, i.e., the front of the waves being steeper than the back. Waves with saw-tooth asymmetry may generate a net landward sediment transport even if = 0, because of the more abrupt acceleration under the steep front. More abrupt accelerations are associated with thinner boundary layers and greater pressure gradients for a given velocity magnitude. The two real wave effects are incorporated in a model of the form Q(s)(t) = Q(s)[theta(t)] rather than Q(S)(t) = Q(S)[u(infinity)(t)], i.e., by expressing the transport rate in terms of an instantaneous Shields parameter rather than in terms of the free stream velocity, and accounting for both streaming and accelerations in the 0(t) calculations. The instantaneous friction velocities u(*)(t) and subsequently theta(t) are calculated as follows. Firstly, a linear filter incorporating the grain roughness friction factor f(2.5) and a phase angle phi(tau) is applied to u(infinity)(t). This delivers u(*)(t) which is used to calculate an instantaneous grain roughness Shields parameter theta(2.5)(t). Secondly, a constant bed shear stress is added which corresponds to the streaming related bed shear stress -rho ($) over bar((u) over tilde(w) over tilde)(infinity) . The method can be applied to any u(infinity)(t) time series, but further experimental validation is recommended before application to conditions that differ strongly from the ones considered below. The method is not recommended for rippled beds or for sheet flow with typical prototype wave periods and d(50) < 0.20 turn. In such scenarios, time lags related to vertical sediment movement become important, and these are not considered by the present model. (C) 2002 Elsevier Science B.V. All rights reserved.