An Approximate Method for Predicting the Friction Factor of Viscoplastic Shear-Thinning Fluids in Non-Circular Channels of Regular Cross-Sections.

The objective of this study is to provide a straightforward generalized simple and quick method for the prediction of the friction factor for fully developed laminar flow of viscoplastic shear-thinning fluids in non-circular channels of regular cross-sections. The most frequently represented substances processed under these conditions are polymers in the processing and plastics industry. A generalized approximate method was proposed to express the relationship between the friction factor and the Reynolds number for the Herschel-Bulkley rheological model. This method uses the generalized Reynolds number for power-law fluids. Moreover, an additional simplified method for rapid engineering calculations was obtained as well. The suggested method was verified by comparing experimental data for concentric annulus found in the literature and results from simulations for concentric annulus, rectangular, square duct with a central cylindrical core and elliptical cross-sections. The results showed that the suggested methods enable us to estimate the friction factor with high accuracy for the investigated geometries.

Effects of Extrusion and Irradiation on the Mechanical Properties of a Water-Collagen Solution.

This article describes 1D extension tests on bovine collagen samples (8% collagen in water). At such a high collagen concentration, the mechanical properties of semi-solid samples can be approximated by hyperelastic models (two-parametric HGO and Misof models were used), or simply by Hooke's law and the modulus of elasticity E. The experiments confirm a significant increase in the E-modulus of the samples irradiated with high-energy electrons. The modulus E ~ 9 kPa of non-irradiated samples increases monotonically up to E ~ 250 kPa for samples absorbing an e-beam dose of ~3300 Gy. This amplification is attributed to the formation of cross-links by irradiation. However, E-modulus can be increased not only by irradiation but also by exposure to a high strain rate. For example, soft isotropic collagen extruded through a 200 mm long capillary increases the modulus of elasticity from 9 kPa to 30 kPa, and the increase is almost isotropic. This stiffening occurs when the corrugated collagen fibers are straightened and are aligned in the flow direction. It seems that the permanent structural changes caused by extrusion mitigate the effects of the ex post applied irradiation. Irradiation of extruded samples by 3300 Gy increases the modulus of E-elasticity only three times (from 30 kPa to approximately 90 kPa). Extruded and ex post irradiated samples show slight anisotropy (the stiffness in the longitudinal direction is on an average greater than the transverse stiffness).

Age-related distribution of longitudinal pre-strain in abdominal aorta with emphasis on forensic application.

It is a well-known fact that the length of an artery in situ and the length of an excised artery differs. Retraction of blood vessels is usually observed. This pre-tension plays crucial role in arterial biomechanics. It augments an artery wall load-bearing capacity. This paper presents the longitudinal pre-strain of the human aorta as an index of human age. The length of abdominal aortas was measured during autopsies before and after segment resection. The longitudinal pre-strain was calculated in 130 donors; 100 male and 30 female bodies. The pre-strain was defined as the ratio between in situ length and the length after the excision. The mean pre-strain was found to be 1.18±0.10 for male and 1.14±0.10 for female sample (mean±standard deviation). The age in the male group was 41.6±15.9 years; and 47.7±17.7 years in the female group. Statistical analysis revealed the correlation coefficient between age and pre-strain r=-0.821 and r=-0.839 in male and female group, respectively. The analysis also confirmed close correlation between aortic circumference and age; and between circumference and pre-strain. Linear and power law regression equations were employed and prediction intervals were computed. The power law estimates the age more accurately than linear one model. Nevertheless, especially for small values of the pre-strain (aged individuals) the linear model can be advantageous.

Age estimation based on a combined arteriosclerotic index.

This study introduces a new quantity, the combined arteriosclerotic index (CAI), which is defined as the ratio between the diameter and the longitudinal prestrain of an artery. The longitudinal prestrain has been adopted as the ratio between the in situ length and the excised length of the abdominal aorta, and is a measure of arterial elasticity. During ageing, arteriosclerosis is manifested by the loss of pretension and by enlargement of the diameter of the artery. CAI combines these two effects. A sample of 61 female and 194 male autopsy measurements of human abdominal aortas shows that CAI correlates significantly with chronological age (R = 0.916/0.921; female/male). The sample had the following parameters: age 53 ± 19/48 ± 16 years; diameter of the abdominal aorta 12.4 ± 2.2/13.4 ± 2.1 mm; and longitudinal prestrain 1.13 ± 0.10/1.15 ± 0.10 (mean ± sample standard deviation; female/male). The resulting CAI was 11.2 ± 2.7/11.9 ± 2.6 mm. The classical linear regression model was employed for age estimation by CAI. The model gave a residual standard deviation of 7.6/6.3 years and a 95% prediction interval range of ± 15.4/12.5 years (female/male). A two-sample t-test confirmed that there are significant differences between the female and male population during ageing, reflected by CAI, unlike longitudinal prestrain. It was concluded that CAI is a suitable predictor of age at time of death and is easily obtainable in the autopsy room.

Correlations between age, prestrain, diameter and atherosclerosis in the male abdominal aorta.

The longitudinal prestrain of arteries facilitates their physiological function. Remodeling, adaptation and aging result in an age-dependent magnitude of the pretension. Although the phenomenon is known, detailed statistics, especially for human arteries, are lacking. This study was designed to propose the regression model capable of estimating the prestrain of the human abdominal aorta. The length of the abdominal aorta before, l, and after excision from the body, L, the diameter, heart weight, thickness of left ventricle and degree of atherosclerosis were collected in autopsies of 156 male cadavers of known age. Longitudinal prestrain was quantified by means of the stretch ratio λ=l/L. Statistical analysis revealed significant dependence between age, prestrain, diameter and atherosclerosis, which were best fitted to the power law equation. Longitudinal prestretch reduced with age significantly; λmean=1.30±0.07 for age<30 (n=29), whereas λmean=1.06±0.03 for age>59 (n=31) with p-value<0.0001. Raw data gave linear correlation coefficients as follows: λ-age (R=-0.842); l-age (R=0.023); L-age (R=0.476); (l-L)-age (R=-0.811). It was concluded that longitudinal prestrain decreases nonlinearly with age and both age and diameter are suitable predictors of the prestrain. Data suggests that unloaded length elongates with age in contrast to the elastic retraction.