Analyse du flux de Poiseuille bidimensionnel via l'équation de Boltzmann

2004 ◽  
Vol 82 (3) ◽  
pp. 213-225
Author(s):  
M Sabbane ◽  
M Tij
Keyword(s):  
Kinetic Theory ◽  
Poiseuille Flow ◽  
Perturbation Parameter ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Theoretical Predictions ◽  
Method Of Solution ◽  
The Difference ◽  
Physical Quantities ◽  
Small Knudsen Numbers

The two-dimensional Poiseuille flow induced by an external force is analysed in the framework of Boltzmann–Maxwell kinetic theory. In the limit of small Knudsen numbers (Kn [Formula: see text] 0.1), Boltzmann's nonlinear equation, written in terms of moments, is solved using perturbation theory. In our results, the hydrodynamic variable profiles are determined up to the fourth order in the perturbation parameter. Nonetheless, the method of solution remains valid to obtain all physical quantities of a gas undergoing Poiseuille flow. The major conclusion of our analysis has two elements. First, the profiles of hydrodynamic variables in two dimensions differ quantitatively (and sometimes qualitatively) from those in plane geometry. Thus, the Poiseuille flow representation in a cylindrical pipe is more accurate than in a canal between two parallel planes. Second, a critical comparaison between the theoretical predictions of the kinetic theory and those of Navier–Stokes shows that the two theories agree only up to the first order of perturbation. Starting at the second order, the difference between the two increases. Thus, within the limit of validity of the present study, the description by Navier–Stokes remains insufficient to predict the correct profiles for the hydrodynamic variables in the Poisseuille flow. [Journal translation]

Analysis of a rotating flow at small Reynolds number

1964 ◽  
Vol 18 (4) ◽  
pp. 499-512 ◽  
Author(s):  
Michael Bentwich
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Solid Cylinder ◽  
Navier Stokes Equations ◽  
Linear Partial Differential Equations ◽  
Method Of Solution ◽  
Steady Rotation ◽  
Physical Quantities

A solution of the Navier-Stokes equations is obtained for the flow resulting from the steady rotation of a semi-infinite right circular (solid) cylinder about its vertical axis. Incompressible viscous fluid is assumed to fill the space outside the cylinder on one side of a horizontal solid plane. In the proposed method of solution the pertinent physical quantities are expressed as series in positive powers of the Reynolds numberRewith space-dependent coefficients. It is shown that the coefficients of (Re)Mcan be obtained by solving linear partial differential equations which depend on the coefficients of (Re)i, wherei<M. A truncated solution, which holds for smallRe, is obtained by solving for the first two coefficients. These results indicate that at the flat end of the cylinder the pressure distribution is nearly constant, yet along the adjacent bounding plane it rises with the radial direction.

Analytic Solution for Microscale Poiseuille Flow Based on Super-Burnett Equations

2013 ◽  
Vol 705 ◽  
pp. 609-615
Author(s):  
Cheng Qian Song ◽  
Xie Yuan Yin ◽  
Feng Hua Qin
Keyword(s):  
Poiseuille Flow ◽  
Constitutive Relations ◽  
Slip Boundary Condition ◽  
Continuous Model ◽  
Analytic Solutions ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
The Difference

The previous studies show that the transverse distribution of pressure and temperature in microscale Poiseuille flow cannot be predicted by Navier-Stokes equation with the slip boundary condition. In this paper, we analyzed the planar microchannel force-driven Poiseuille flow by high order continuum model. The super-Burnett constitutive relations were used and the nonlinear ordinary differential Equations of higher-orders were obtained by the hypothesis of parallel flow. With a perturbations theory, we linearized the equations and obtained the analytic solutions. The results show that the solutions can capture the temperature dip which is the same as the DSMC result. However, we also find that the temperature profile near the wall does always not match with the DSMC result. Especially, the difference in the qualitative exists when the Knudsen number is large enough. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model such as super-Burnett one.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

Quality of life in Hungarian polio survivors

2021 ◽  
Author(s):  
Erika Viktória Miszory ◽  
Melinda Járomi ◽  
Annamária Pakai
Keyword(s):  
Quality Of Life ◽  
Mental Health ◽  
Sample Selection ◽  
Cross Sectional Study ◽  
Two Dimensions ◽  
Cross Sectional ◽  
Emotional Role ◽  
The Difference ◽  
Polio Survivors

Abstract Aim The number of Hungarian polio patients can be estimated at approximately 3000. Polio infection is currently affecting people 56–65 years of age. The aim of the study was to reveal the quality of life of patients living with polio virus in Hungary. Subject and methods The quantitative cross-sectional study was conducted in January–April 2017 among polyomyelitis patients living in Hungary. In the non-random, targeted, expert sample selection, the target group was composed of patients infected with poliovirus (N = 268). We have excluded those who refused to sign the consent statement. Our data collection method was an SF-36 questionnaire. Using the IBM SPSS Statistics Version 22 program, descriptive and mathematical statistics (χ2-test) were calculated (p < 0.05). Results The mean age of the members of the examined population is 63.5 years; 68.1% were women and 31.90% were men. The majority of the respondents were infected by the polyovirus in 1956 (11.9%), 1957 (24.3%), and 1959 (19.5%). Polio patients, with the exception of two dimensions (mental health, social operation), on the scale of 100 do not reach the “average” quality of life (physical functioning 23 points, functional role 36 points, emotional role 47 points, body pain 48 points, general health 42 points, vitality 50 points, health change 31 points). Conclusion The quality of life of polio patients is far below the dimensions of physical function, while the difference in mental health compared to healthy people is minimal. It would be important to educate health professionals about the existing disease, to develop an effective rehabilitation method.

scholarly journals Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Alice Hodson
Keyword(s):  
Fourth Order ◽  
Perturbation Parameter ◽  
Two Dimensions ◽  
Optimal Error Estimates ◽  
Projection Operators ◽  
Varying Coefficients ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
Perturbation Problems ◽  
Fourth Order Problems

Abstract We present a class of nonconforming virtual element methods for general fourth-order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth-order problems with varying coefficients. We also discuss fourth-order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth-order problems.

Non-linear dynamics, chaos, complexity and enclaves in granitoid magmas

1996 ◽  
Vol 87 (1-2) ◽  
pp. 217-223 ◽  
Author(s):  
James Flinders ◽  
John D. Clemens
Keyword(s):  
Deterministic Chaos ◽  
Interfacial Area ◽  
Two Dimensions ◽  
Mixing Processes ◽  
Nd Isotope ◽  
Natural Systems ◽  
Non Linear ◽  
The Difference ◽  
Magma System ◽  
Isotope Systematics

ABSTRACT:Most natural systems display non-linear dynamic behaviour. This should be true for magma mingling and mixing processes, which may be chaotic. The equations that most nearly represent how a chaotic natural system behaves are insoluble, so modelling involves linearisation. The difference between the solution of the linearised and ‘true’ equation is assumed to be small because the discarded terms are assumed to be unimportant. This may be very misleading because the importance of such terms is both unknown and unknowable. Linearised equations are generally poor descriptors of nature and are incapable of either predicting or retrodicting the evolution of most natural systems. Viewed in two dimensions, the mixing of two or more visually contrasting fluids produces patterns by folding and stretching. This increases the interfacial area and reduces striation thickness. This provides visual analogues of the deterministic chaos within a dynamic magma system, in which an enclave magma is mingling and mixing with a host magma. Here, two initially adjacent enclave blobs may be driven arbitrarily and exponentially far apart, while undergoing independent (and possibly dissimilar) changes in their composition. Examples are given of the wildly different morphologies, chemical characteristics and Nd isotope systematics of microgranitoid enclaves within individual felsic magmas, and it is concluded that these contrasts represent different stages in the temporal evolution of a complex magma system driven by nonlinear dynamics. If this is true, there are major implications for the interpretation of the parts played by enclaves in the genesis and evolution of granitoid magmas.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

Low P50 in deer mice native to high altitude

1985 ◽  
Vol 58 (1) ◽  
pp. 193-199 ◽  
Author(s):  
L. R. Snyder
Keyword(s):  
High Altitude ◽  
Significant Negative Correlation ◽  
Deer Mice ◽  
Hypoxic Stress ◽  
Hemoglobin Saturation ◽  
Partial Pressures ◽  
Theoretical Predictions ◽  
Low Altitude ◽  
The Difference

Whereas it is widely believed that animals native to high altitude show lower O2 partial pressures at 50% hemoglobin saturation (P50) than do related animals native to low altitude, that “fact” has not been well documented. Consequently, P50 at pH 7.4, PCO2(7.4), the CO2 Bohr effect, and the buffer slope (delta log PCO2/delta pH) were determined via the mixing technique in Peromyscus maniculatus native to a range of altitudes but acclimated to 340 or 3,800 m. PCO2(7.4) and buffer slope were substantially lower at high altitude. The change in P50(7.4) between acclimation altitudes was minimal (0.8% increase at 3,800 m), because of counterbalancing changes in PCO2, 2,3-diphospho-D-glycerate concentration, and perhaps other factors. At both acclimation altitudes there was a highly significant negative correlation between P50(7.4) and native altitude. Since pH in vivo probably increases slightly at high altitude, the data on P50 corrected to pH 7.4 are probably underestimates of the difference in in vivo P50 at low vs. high altitude. Hence these results corroborate theoretical predictions that low P50 is advantageous under severe hypoxic stress.

scholarly journals Tunable Adhesion of a Bio-Inspired Micropillar Arrayed Surface Actuated by a Magnetic Field

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Xingji Li ◽  
Zhilong Peng ◽  
Yazheng Yang ◽  
Shaohua Chen
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Magnetic Particles ◽  
Rotation Angle ◽  
Adhesion Force ◽  
Practical Applications ◽  
Section Shape ◽  
Theoretical Predictions ◽  
Large Elastic Deformation ◽  
The Difference

Bio-inspired functional surfaces attract many research interests due to the promising applications. In this paper, tunable adhesion of a bio-inspired micropillar arrayed surface actuated by a magnetic field is investigated theoretically in order to disclose the mechanical mechanism of changeable adhesion and the influencing factors. Each polydimethylsiloxane (PDMS) micropillar reinforced by uniformly distributed magnetic particles is assumed to be a cantilever beam. The beam's large elastic deformation is obtained under an externally magnetic field. Specially, the rotation angle of the pillar's end is predicted, which shows an essential effect on the changeable adhesion of the micropillar arrayed surface. The larger the strength of the applied magnetic field, the larger the rotation angle of the pillar's end will be, yielding a decreasing adhesion force of the micropillar arrayed surface. The difference of adhesion force tuned by the applied magnetic field can be a few orders of magnitude, which leads to controllable adhesion of such a micropillar arrayed surface. Influences of each pillar's cross section shape, size, intervals between neighboring pillars, and the distribution pattern on the adhesion force are further analyzed. The theoretical predictions are qualitatively well consistent with the experimental measurements. The present theoretical results should be helpful not only for the understanding of mechanical mechanism of tunable adhesion of micropillar arrayed surface under a magnetic field but also for further precise and optimal design of such an adhesion-controllable bio-inspired surface in future practical applications.

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