Existence Of Two Types Of Drag Reduction In Pipe Flow Of Dilute Polymer Solutions

Drag reduction in the pipe flow of polymer solutions is shown to be of two types which apparently occur by two separate mechanisms. In turbulent flow, drag reduction is probably caused by viscoelastic effects. The critical solvent Reynolds number at the onset of drag reduction is proportional to about the first power of the diameter. Thus, the critical velocity is independent of tube diameter. Polymers dissolved in good solvents show more drag reduction than in poor solvents. The other type of drag reduction occurs when the laminar region is extended to high Reynolds numbers. It is followed by a transition region and a turbulent region in which the drag is not affected. © 1967, American Chemical Society. All rights reserved

Numerical Differentiation Of Equally Spaced And Not Equally Spaced Experimental Data

Procedures are given for smoothing and differentiating experimental data with both equal and nonequal spacing in the independent variable. Selection of the number of points to be included in the movable strip technique and of the degree of the polynomial is discussed. Equations are given to estimate the error by calculating a confidence interval on each slope. A technique for handling certain types of nonrandom errors is presented. © 1967, American Chemical Society. All rights reserved

Intracellular iron uptake is favored in Hfe-KO mouse primary chondrocytes mimicking an osteoarthritis-related phenotype

HFE-hemochromatosis is a disease characterized by a systemic iron overload phenotype mainly associated with mutations in the HFE protein (HFE) gene. Osteoarthritis (OA) has been reported as one of the most prevalent complications in HFE-hemochromatosis patients, but the mechanisms associated with its onset and progression remain incompletely understood. In this study, we have characterized the response to high iron concentrations of a primary culture of articular chondrocytes isolated from newborn Hfe-KO mice and compared the results with that of a similar experiment developed in cells from C57BL/6 wild-type (wt) mice. Our data provide evidence that both wt- and Hfe-KO-derived chondrocytes, when exposed to 50 mu M iron, develop characteristics of an OA-related phenotype, such as an increased expression of metalloproteases, a decreased extracellular matrix production, and a lower expression level of aggrecan. In addition, Hfe-KO cells also showed an increased expression of iron metabolism markers and MMP3, indicating an increased susceptibility to intracellular iron accumulation and higher levels of chondrocyte catabolism. Accordingly, upon treatment with 50 mu M iron, these chondrocytes were found to preferentially differentiate toward hypertrophy with increased expression of collagen I and transferrin and downregulation of SRY (sex-determining region Y)-box containing gene 9 (Sox9). In conclusion, high iron exposure can compromise chondrocyte metabolism, which, when simultaneously affected by an Hfe loss of function, appears to be more susceptible to the establishment of an OA-related phenotype.European Regional Development FundEuropean Union (EU) [EMBRC.PT Alg-01-0145-FEDER-022121, Norte-01-0145-FEDER-000012]Fundacao para a Ciencia e a TecnologiaPortuguese Foundation for Science and Technology [SFRH/BD/77056/2011]Portuguese Foundation for Science and TechnologyPortuguese Foundation for Science and TechnologyPortuguese Science and Technology FoundationPortuguese Foundation for Science and Technologyinfo:eu-repo/semantics/publishedVersio

A molecular approach to predicting the onset of drag reduction in the turbulent flow of dilute polymer solutions

The significant variables in drag reduction have been separated into two classifications, flow variables and solution variables. A theory has been offered which permits prediction of the critical Reynolds number in the turbulent flow of polymer solutions. The theory states that the relaxation time of the polymer molecule in solution equals a characteristic flow time for the tube in question at the point of incipient turbulent suppression. This is equivalent to a Deborah number near unity. Reasonable agreement has been shown between the experimental results of this investigation and predictions of flow rates based on this theory for the presence or absence of drag reduction and for the onset of turbulence suppression. No adjustable parameters were used in the analysis. The theory seems to be applicable at values of C[η] greater than 0·10. The theory leads to the prediction that the wall shear rate at the point of incipient turbulence suppression decreases as the product of reduced viscosity, molecular weight and solvent viscosity increases. Thus for large effects this product should be made as large as possible. Friction factor measurements in both good and poor (Theta) solvents showed that the maximum drag reduction in the poor solvent was only about 40% of that in the good solvent at similar flow rates in the same tube. Thus the effect of an expanded configuration of the polymer molecule in solution is to increase drag reduction. © 1967

Effects Of Molecular Characteristics Of Polymers On Drag Reduction

Turbulent measurements in capillary tubes and in pipes were made on nonpolar solutions of seven polymer species, three at more than one molecular weight, over wide concentration ranges. A critical concentration, Cc, was taken as the minimum concentration for disappearance of the turbulence transition region. Above this concentration, friction factor‐generalized Reynolds number data show only a gradual deviation from extension of the laminar line. Cc increases with tube diameter and decreases with molecular weight. The critical dimensionless volume friction Cc [η] is less dependent on molecular weight. The levels of Cc [η] for different polymer species in a given tube show marked differences which are related to β, the molecular rigidity parameter. Low β values, or high flexibility, are associated with low Cc [η] values. Available data for Cc [η] in good and in poor solvents show little solvency effect. Polymer samples of low m′, the ratio of the polymer molecular weight to the critical tanglement molecular weight of the polymer, give solutions with little or no drag‐reducing capacity, even those with low β values. Samples must have m′ values of 50 or more to show significant drag reduction. This allows prediction of the minimum useful molecular weights for drag reduction for any polymer species. For solutions above Cc, all of these data and literature data (for aqueous and nonaqueous systems with a wide range of n′ values) fit a single f/fpv versus generalized Reynolds number relationship. Copyright © 1971 American Institute of Chemical Engineer