Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe

2014 ◽  
Vol 740 ◽  
pp. 196-213 ◽  
Author(s):  
Zi Wu ◽  
G. Q. Chen
Keyword(s):  
Time Scale ◽  
Concentration Distribution ◽  
Scale Up ◽  
Straight Pipe ◽  
Concentration Difference ◽  
Molecular Diffusivity ◽  
Initial Stage ◽  
The Mean ◽  
Mean Concentration ◽  
Transverse Variation

AbstractAssociated with Taylor’s classical analysis of scalar solute dispersion in the laminar flow of a solvent in a straight pipe, this work explores the approach towards transverse uniformity of concentration distribution. Mei’s homogenization technique is extended to find solutions for the concentration transport. Chatwin’s result for the approach to longitudinal normality is recovered in terms of the mean concentration over the cross-section. The asymmetrical structure of the concentration cloud and the transverse variation of the concentration distribution are concretely illustrated for the initial stage. The rate of approach to uniformity is shown to be much slower than that to normality. When the longitudinal normality of mean concentration is well established, the maximum transverse concentration difference remains near one-half of the centroid concentration of the cloud. A time scale up to$10 R^2/D$($R$is the radius of the pipe and$D$is the molecular diffusivity) is suggested to characterize the transition to transverse uniformity, in contrast to the time scale of$0.1 R^2/D$estimated by Taylor for the initial stage of dispersion, and that of$1.0 R^2/D$by Chatwin for longitudinal normality.

scholarly journals An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: a multi-scale approach

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Nanda Poddar ◽  
Subham Dhar ◽  
Bijoy Singha Mazumder ◽  
Kajal Kumar Mondal
Keyword(s):  
Magnetic Field ◽  
Concentration Distribution ◽  
Order Approximation ◽  
Transverse Magnetic ◽  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Molecular Diffusivity ◽  
The Magnetic Field ◽  
Mean Concentration ◽  
Transverse Variation

The present paper explores an analytical solution to study the two-dimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei’s homogenization technique is used to acquire the mean concentration distributions up to the second-order approximation and the transverse concentration distributions up to third order. An uneven form of the concentration cloud and the transverse variation of the concentration distribution in a hydromagnetic flow are illustrated for the initial stage. The rate of progress towards uniformity of a solute cloud seems much slower than that of normality. It is observed that the peak of the transverse mean concentration and transverse variation of the concentration distribution of the solute significantly decrease with the increase in the magnetic field for small dispersion times. This is because, with an increase in the magnetic field, the velocity profiles flatten at the central core region between the parallel plates. The research proposes a time scale of 10 δ 2 / D (where δ is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

Iodine in California Farm Milk: 1985–19861

1987 ◽  
Vol 50 (9) ◽  
pp. 765-768 ◽  
Author(s):  
JOHN C. BRUHN ◽  
ANTOINE A. FRANKE ◽  
T. WYATT SMITH
Keyword(s):  
Dairy Farms ◽  
Iodine Concentration ◽  
The Other ◽  
Daily Production ◽  
Concentration Difference ◽  
Milk Samples ◽  
Health Agencies ◽  
The Mean ◽  
Mean Concentration ◽  
Maximum Limit

Iodine has been measured in 1572 California farm milk samples, representing 2,725,000 gallons of milk, or about 54% of daily production. The mean iodine concentration in the analyzed samples was 173.3 μg/kg milk, with a standard deviation of 115.8 μg/kg- The volume-corrected mean iodine concentration for all samples was 188.3 μg/kg. Of the farms examined, 13% used neither an iodine teat-dip or backflush; the milk iodine concentration on these dairy farms averaged 147.8 ± 90.2 μg/kg. Of the farms examined, 73% used iodine teat-dip only; milk iodine concentrations averaged 166.7±109.4 μg/kg. Less than 1% of the farms used iodine only in their backflush systems; their milk iodine concentrations averaged 202.3±107.2 μg/kg. Thirteen percent of the farms used both iodine teat-dip and iodine in their backflush systems; their milk iodine concentrations averaged 251.3±153.9 μg/kg. While the concentration difference between farms using iodine in both the teat-dip and backflush system and farms in the other three groups was statistically significant, the mean concentration was still well below the maximum limit of 500 μg/kg imposed by health agencies in some countries. Overall, 30.7% of samples measured has less than 100 μg iodine/kg; 70.1% had less than 200 μg/kg; 88.8% had less than 300 μg/kg; 94.4% had less than 400 μg/kg; and 98.1% had less than 500 μg/kg.

scholarly journals A Study on Solute Dispersion in a Three Layer Blood-like Liquid Flowing through a Rigid Artery

2017 ◽  
Vol 61 (3) ◽  
pp. 173 ◽  
Author(s):  
Sudip Debnath ◽  
Apu Kumar Saha ◽  
Ashis Kumar Roy
Keyword(s):  
Yield Stress ◽  
Concentration Distribution ◽  
Dispersion Coefficient ◽  
Absorption Increase ◽  
Peripheral Layer ◽  
Significant Decrement ◽  
Small Absorption ◽  
The Mean ◽  
Dispersion Technique ◽  
Mean Concentration

The unsteady dispersion of a solute has been discussed by the method of generalized dispersion technique in a blood-like liquid flowing through a pipe under the combined effects of finite yield stress and irreversible absorption into the wall.The solvent is enacted as a three-layered liquid by considering the center liquid as a Casson liquid (a core of red blood cell suspension) and a peripheral layer of plasma as a Newtonian liquid. An asymptotic representation for the convection and dispersion coefficients has been shown only for large values of time, which will not hamper the study of physical behavior of the system. The objective of the present study is to examine the nature of exchange coefficient, convective coefficient and in particular, dispersion coefficient together with mean concentration distribution under the effect of absorption parameter (​β)​, yield stress (​​τ​y​​​) (equivalently the plug radius (​​Rp​​​)) and peripheral layer variation (i.e., ratio of central core radius to normal artery radius (​​Ro​​​)). It is found that the presence of peripheral layer makes some important increment in dispersion coefficient compared to single phase Casson liquid for small absorption. Increase in both diffusivity (D*​​) and Peclet number (Pe) make a significant decrement in the magnitude of dispersion coefficient with respect to absorption rate. The decrease in peak of the mean concentration distribution with the increase in reaction rate is found irrespective of the nature of reaction.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

Instant 99mTc-Labelled Glucoheptonate Kit for Kidney Imaging

1983 ◽  
Vol 22 (05) ◽  
pp. 246-250 ◽  
Author(s):  
M. Al-Hilli ◽  
H. M. A. Karim ◽  
M. H. S. Al-Hissoni ◽  
M. N. Jassim ◽  
N. H. Agha
Keyword(s):  
Sodium Hydroxide Solution ◽  
Normal Subjects ◽  
Organ Distribution ◽  
Stable Complex ◽  
Scintillation Camera ◽  
Ph Adjustment ◽  
The Mean ◽  
The Stability ◽  
Kidney Imaging ◽  
Mean Concentration

Gelchromatography column scanning has been used to study the fractions of reduced hydrolyzed 99mTc, 99mTc-pertechnetate and 99mTc-chelate in a 99mTc-glucoheptonate (GH) preparation. A stable high labelling yield of 99mTc-GH complex in the radiopharmaceutical has been obtained with a concentration of 40-50 mg of glucoheptonic acid-calcium salt and not less than 0.45 mg of SnCl2 2 H2O at an optimal pH between 6.5 and 7.0. The stability of the complex has been found significantly affected when sodium hydroxide solution was used for the pH adjustment. However, an alternative procedure for final pH adjustment of the preparation has been investigated providing a stable complex for the usual period of time prior to the injection. The organ distribution and the blood clearance data of 99mTc-GH in rabbits were relatively similar to those reported earlier. The mean concentration of the radiopharmaceutical in both kidneys has been studied in normal subjects for one hour with a scintillation camera and the results were satisfactory.

PROGESTERONE IN THE HUMAN PERIPHERAL BLOOD IN THE PREOVULATORY PERIOD OF THE MENSTRUAL CYCLE

1967 ◽  
Vol 55 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Benno Runnebaum ◽  
Josef Zander
Keyword(s):  
Menstrual Cycle ◽  
Corpus Luteum ◽  
Peripheral Blood ◽  
Human Peripheral Blood ◽  
Progesterone Concentration ◽  
Plasma Progesterone ◽  
Progesterone Secretion ◽  
Graafian Follicle ◽  
The Mean ◽  
Mean Concentration

ABSTRACT Progesterone was determined and identified in human peripheral blood during the preovulatory period of the menstrual cycle, by combined isotope derivative and recrystallization analysis. The mean concentration of progesterone in 1.095 ml of plasma obtained 9 days before ovulation was 0.084 μg/100 ml. However, the mean concentration of progesterone in 1.122 ml of plasma obtained 4 days before ovulation was 0.279 μg/100 ml. These data demonstrate a source of progesterone secretion other than the corpus luteum. The higher plasma-progesterone concentration 4 days before ovulation may indicate progesterone secretion of the ripening Graafian follicle of the ovary.

scholarly journals Trends and Clinico-Epidemiological Features of Human Rabies Cases in Bangladesh, 2006–2018

2020 ◽  
Vol 41 (S1) ◽  
pp. s416-s416
Author(s):  
Sumon Ghosh ◽  
Md. Sohel Rana ◽  
Sukanta Chowdhury
Keyword(s):  
Effective Means ◽  
Scale Up ◽  
Traditional Healers ◽  
Human Rabies ◽  
Epidemiological Analysis ◽  
Increasing Trend ◽  
The Mean ◽  
Death Cases ◽  
Death Data

Background: Vaccinating dogs against rabies is an effective means of reducing human rabies. Methods: We analyzed 1,327 clinically diagnosed human rabies deaths and mass dog vaccination (MDV) data during 2006–2018 to quantify the impacts of MDV on human rabies incidence in Bangladesh and a subset of rabies death data (n = 422) for clinico-epidemiological analysis. Results: We found a positive and increasing trend of dog population vaccination (P = .01 and τ = 0.71) and a negative and declining trend (P < .001 and τ = −0.88) of human rabies cases (correlation coefficient, −0.82). Among 422 human rabies death cases, most victims (78%) sought treatment from traditional healers, and 12% received postexposure prophylaxis (PEP). The mean incubation period of rabies cases with exposure sites on the head and neck (35 days) was shorter than the upper limb (mean, 64 days; P = .02) and lower limb (mean, 89 days; P < .01). MDV is effective for reducing human rabies cases in Bangladesh. Conclusions: Creating awareness among the animal bite victims to stop relying on traditional healers rather seeking PEP, addressing the role of traditional healers through an awareness education program in respect to the treatment of dog bites, ensuring availability of PEP, and continuing to scale up MDV can help prevent human rabies deaths.Funding: NoneDisclosures: None

scholarly journals On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1303
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Kadir Hamasalh
Keyword(s):  
Time Scale ◽  
Initial Value Problems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Forward Difference ◽  
The Mean ◽  
Monotonicity Analysis ◽  
Monotonicity Results

Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and then, we can show that y(z) is υ-increasing on Ma+υh,h, where the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) for each z∈Ma+h,h. Conversely, if y(a+υh) is greater or equal to zero and y(z) is increasing on Ma+υh,h, we show that the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) on Ma,h. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale hZ utilizing the monotonicity results.

scholarly journals The Relationship between Inflammation Markers (CRP, IL-6, sCD40L) and Colorectal Cancer Stage, Grade, Size and Location

Diagnostics ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1382
Author(s):  
Olga Martyna Koper-Lenkiewicz ◽  
Violetta Dymicka-Piekarska ◽  
Anna Justyna Milewska ◽  
Justyna Zińczuk ◽  
Joanna Kamińska
Keyword(s):  
Colorectal Cancer ◽  
Linear Regression ◽  
Tumor Size ◽  
Distal Colon ◽  
Proximal Colon ◽  
Model Parameters ◽  
Grade Group ◽  
Who Grade ◽  
The Mean ◽  
Mean Concentration

The aim of the study was the evaluation whether in primary colorectal cancer (CRC) patients (n = 55): age, sex, TNM classification results, WHO grade, tumor location (proximal colon, distal colon, rectum), tumor size, platelet count (PLT), mean platelet volume (MPV), mean platelet component (MCP), levels of carcinoembryonic antigen (CEA), cancer antigen (CA 19-9), as well as soluble lectin adhesion molecules (L-, E-, and P-selectins) may influence circulating inflammatory biomarkers: IL-6, CRP, and sCD40L. We found that CRP concentration evaluation in routine clinical practice may have an advantage as a prognostic biomarker in CRC patients, as this protein the most comprehensively reflects clinicopathological features of the tumor. Univariate linear regression analysis revealed that in CRC patients: (1) with an increase in PLT by 10 × 103/μL, the mean concentration of CRP increases by 3.4%; (2) with an increase in CA 19-9 of 1 U/mL, the mean concentration of CRP increases by 0.7%; (3) with the WHO 2 grade, the mean CRP concentration increases 3.631 times relative to the WHO 1 grade group; (4) with the WHO 3 grade, the mean CRP concentration increases by 4.916 times relative to the WHO 1 grade group; (5) with metastases (T1-4N+M+) the mean CRP concentration increases 4.183 times compared to non-metastatic patients (T1-4N0M0); (6) with a tumor located in the proximal colon, the mean concentration of CRP increases 2.175 times compared to a tumor located in the distal colon; (7) in patients with tumor size > 3 cm, the CRP concentration is about 2 times higher than in patients with tumor size ≤ 3 cm. In the multivariate linear regression model, the variables that influence the mean CRP value in CRC patients included: WHO grade and tumor localization. R2 for the created model equals 0.50, which indicates that this model explains 50% of the variance in the dependent variable. In CRC subjects: (1) with the WHO 2 grade, the mean CRP concentration rises 3.924 times relative to the WHO 1 grade; (2) with the WHO 3 grade, the mean CRP concentration increases 4.721 times in relation to the WHO 1 grade; (3) with a tumor located in the rectum, the mean CRP concentration rises 2.139 times compared to a tumor located in the distal colon; (4) with a tumor located in the proximal colon, the mean concentration of CRP increases 1.998 times compared to the tumor located in the distal colon; if other model parameters are fixed.

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