Three Equation Model for A Thin Layer Fluid Flowing Down An Inclined Plane

2007 ◽  
Author(s):  
Hamid Ait Abderrahmane ◽  
Georgios Vatistas
Keyword(s):  
Thin Layer ◽  
Equation Model ◽  
Inclined Plane

Improved two-equation model for thin layer fluid flowing down an inclined plane problem

2007 ◽  
Vol 19 (9) ◽  
pp. 098106 ◽  
Author(s):  
H. Ait Abderrahmane ◽  
G. H. Vatistas
Keyword(s):  
Thin Layer ◽  
Plane Problem ◽  
Equation Model ◽  
Inclined Plane

An Accurate Low Dimension Model for the Waves on Thin Layer Fluid Flowing Down an Inclined Plane

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
H. Ait Abderrahmane ◽  
G. H. Vatistas
Keyword(s):  
Film Flow ◽  
Equation Model ◽  
Surface Velocity ◽  
Inclined Plane ◽  
Linear Pulse ◽  
Pulse Structure ◽  
The Waves ◽  
Theoretical Results ◽  
Primary Instability ◽  
Good Agreement

This technical brief deals with the surface instability mode of a liquid film flowing down an inclined plane. A four-equation model that describes the development of the film depth, the flow rate, the free-surface velocity, and the wall shear stress is proposed. The obtained results were found to be in very good agreement with experimental and theoretical results of Liu et al. (1993, “Measurements of the Primary Instability of Film Flow,” J. Fluid Mech., 250, pp. 69–101) and Brevdo et al. (1999, “Linear Pulse Structure and Signalling in Film Flow on an Inclined Plane,” J. Fluid Mech., 396, pp. 37–71).

scholarly journals Study of the drying kinetics and calculation of mass transfer properties in hot air drying of Cynara cardunculus

2020 ◽  
Vol 5 (1) ◽  
pp. 740-750
Author(s):  
Raquel P. F. Guiné ◽  
Maria João Lima
Keyword(s):  
Mass Transfer ◽  
Thin Layer ◽  
Transfer Coefficient ◽  
Mass Transfer Coefficient ◽  
Moisture Diffusion ◽  
Equation Model ◽  
Convective Drying ◽  
Cynara Cardunculus ◽  
Thin Layer Drying ◽  
Transfer Properties

AbstractIn the present work, mass transfer properties of thistle flower (Cynara cardunculus L.) were evaluated for the convective drying carried out at temperatures between 35 and 65°C, with an air flow of 0.5 m/s. The calculations followed two different algorithms, based on mathematical models derived from the thin layer drying equation and Fick’s second law of diffusion. The results obtained indicated that different methodologies resulted in different values of mass transfer properties, which is an alert that care must be taken when choosing which calculation method might be more appropriate in a specific practical application. In all cases, the values of moisture diffusion and mass transfer coefficient were found to increase with increasing operating temperature. The values of diffusivity increased from 2.7866 × 10−9 to 1.4027 × 10−8 m2/s for the thin layer model-based algorithm and from 1.9256 × 10−10 to 1.2033 × 10−9 m2/s for Fick’s equation model. The values of the mass transfer coefficient increased from 8.4335 × 10−8 to 8.4400 × 10−7 m/s and from 5.8277 × 10−9 to 7.2398 × 10−8 m/s, respectively, for the thin layer and Fick’s law-based models.

A three-equation model for thin films down an inclined plane

2016 ◽  
Vol 804 ◽  
pp. 162-200 ◽  
Author(s):  
G. L. Richard ◽  
C. Ruyer-Quil ◽  
J. P. Vila
Keyword(s):  
Stokes Equations ◽  
Random Noise ◽  
Mathematical Structure ◽  
Liquid Films ◽  
Equation Model ◽  
Navier Stokes ◽  
Neutral Stability ◽  
Inclined Plane ◽  
Navier Stokes Equations ◽  
Wave Limit

We derive a new model for thin viscous liquid films down an inclined plane. With an asymptotic expansion in the long-wave limit, the Navier–Stokes equations and the work–energy theorem are averaged over the fluid depth. This gives three equations for the mass, momentum and energy balance which have the mathematical structure of the Euler equations of compressible fluids with relaxation source terms, diffusive and capillary terms. The three variables of the model are the fluid depth, the average velocity and a third variable called enstrophy, related to the variance of the velocity. The equations are numerically solved by classical schemes which are known to be reliable and robust. The model gives satisfactory results both for the neutral stability curves and for the depth profiles of wavy films produced by a periodical forcing or by a random noise perturbation. The numerical calculations agree fairly well with experimental measurements of Liu & Gollub (Phys. Fluids, vol. 6, 1994, pp. 1702–1712). The calculation of the wall shear stress below the waves indicates a flow reversal at the first depth minimum downstream of the main hump, in agreement with experiments of Tihon et al. (Exp. Fluids, vol. 41, 2006, pp. 79–89).

Applications of Photoelectron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 506-507
Author(s):  
William J. Baxter
Keyword(s):  
Electron Microscopy ◽  
Thermal Decomposition ◽  
Chemical Composition ◽  
Ultraviolet Radiation ◽  
Thin Layer ◽  
Edge Effects ◽  
Electron Optics ◽  
Surface Layers ◽  
Crystalline Orientation ◽  
Fluorescent Screen

In this form of electron microscopy, photoelectrons emitted from a metal by ultraviolet radiation are accelerated and imaged onto a fluorescent screen by conventional electron optics. image contrast is determined by spatial variations in the intensity of the photoemission. The dominant source of contrast is due to changes in the photoelectric work function, between surfaces of different crystalline orientation, or different chemical composition. Topographical variations produce a relatively weak contrast due to shadowing and edge effects.Since the photoelectrons originate from the surface layers (e.g. ∼5-10 nm for metals), photoelectron microscopy is surface sensitive. Thus to see the microstructure of a metal the thin layer (∼3 nm) of surface oxide must be removed, either by ion bombardment or by thermal decomposition in the vacuum of the microscope.

Idiographic Dynamics of Positive Affect in GAD

2020 ◽  
Vol 36 (3) ◽  
pp. 500-509
Author(s):  
Hannah G. Bosley ◽  
Devon B. Sandel ◽  
Aaron J. Fisher
Keyword(s):  
Positive Affect ◽  
Structural Equation ◽  
Alternative Hypothesis ◽  
Equation Model ◽  
Aggregated Data ◽  
Regulatory Strategy ◽  
Constant State ◽  
Automatic Search ◽  
Time Lagged ◽  
Exploratory Procedure

Abstract. Generalized anxiety disorder (GAD) is associated with worry and emotion regulation difficulties. The contrast-avoidance model suggests that individuals with GAD use worry to regulate emotion: by worrying, they maintain a constant state of negative affect (NA), avoiding a feared sudden shift into NA. We tested an extension of this model to positive affect (PA). During a week-long ecological momentary assessment (EMA) period, 96 undergraduates with a GAD analog provided four daily measurements of worry, dampening (i.e., PA suppression), and PA. We hypothesized a time-lagged mediation relationship in which higher worry predicts later dampening, and dampening predicts subsequently lower PA. A lag-2 structural equation model was fit to the group-aggregated data and to each individual time-series to test this hypothesis. Although worry and PA were negatively correlated in 87 participants, our model was not supported at the nomothetic level. However, idiographically, our model was well-fit for about a third (38.5%) of participants. We then used automatic search as an idiographic exploratory procedure to detect other time-lagged relationships between these constructs. While 46 individuals exhibited some cross-lagged relationships, no clear pattern emerged across participants. An alternative hypothesis about the speed of the relationship between variables is discussed using contemporaneous correlations of worry, dampening, and PA. Findings suggest heterogeneity in the function of worry as a regulatory strategy, and the importance of temporal scale for detection of time-lagged effects.

Differential Item Functioning in Brief Instruments of Disordered Eating

2019 ◽  
Vol 35 (6) ◽  
pp. 823-833 ◽  
Author(s):  
Desiree Thielemann ◽  
Felicitas Richter ◽  
Bernd Strauss ◽  
Elmar Braehler ◽  
Uwe Altmann ◽  
...  
Keyword(s):  
Differential Item Functioning ◽  
Disordered Eating ◽  
Structural Equation ◽  
Young Female ◽  
Eating Attitudes ◽  
Equation Model ◽  
German Population ◽  
Test Fairness ◽  
Item Functioning ◽  
Multiple Indicator

Abstract. Most instruments for the assessment of disordered eating were developed and validated in young female samples. However, they are often used in heterogeneous general population samples. Therefore, brief instruments of disordered eating should assess the severity of disordered eating equally well between individuals with different gender, age, body mass index (BMI), and socioeconomic status (SES). Differential item functioning (DIF) of two brief instruments of disordered eating (SCOFF, Eating Attitudes Test [EAT-8]) was modeled in a representative sample of the German population ( N = 2,527) using a multigroup item response theory (IRT) and a multiple-indicator multiple-cause (MIMIC) structural equation model (SEM) approach. No DIF by age was found in both questionnaires. Three items of the EAT-8 showed DIF across gender, indicating that females are more likely to agree than males, given the same severity of disordered eating. One item of the EAT-8 revealed slight DIF by BMI. DIF with respect to the SCOFF seemed to be negligible. Both questionnaires are equally fair across people with different age and SES. The DIF by gender that we found with respect to the EAT-8 as screening instrument may be also reflected in the use of different cutoff values for men and women. In general, both brief instruments assessing disordered eating revealed their strengths and limitations concerning test fairness for different groups.

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