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Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Menzel A. G., Daivis P. J., Todd B. D.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 3

219--231

EN

The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier’s Law and Fick’s Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux.We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 104 reduced time units for relaxation to the steady state and averaging over very long runs of order 105 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.

2

Algorytm MEB wyznaczania pola temperatury w przepływie Poiseuille’a w przewodach prostoosiowych o stałej temperaturze ścianki

Teleszewski T. J., Werner-Jaszczuk A.

Symulacja w Badaniach i Rozwoju

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2012

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Vol. 3, nr 4

233--241

PL

W publikacji przedstawiono algorytm metody elementów brzegowych wyznaczania pola temperatury przepływu Poiseuille’a w przewodach prostoosiowych o dowolnym przekroju poprzecznym, w którym ścianka utrzymywana jest w stałej temperaturze. Weryfikacja metody elementów brzegowych została wykonana poprzez porównanie rezultatów obliczeń MEB ze znanym rozwiązaniem analitycznym. Wyprowadzony algorytm może być stosowany w przepływach cieczy lepkich o znacznych lepkościach np. olejów. W prezentowanej publikacji przedstawiono graficzne rezultaty obliczeń dla wybranych przykładów, dla których nie są znane rozwiązania analityczne.

EN

The paper presents the numerical application Boundary Element Method to calculate the temperature distribution in a fluid moving in Poiseuille flow in a pipe with arbitrary cross-section at constant temperature in wall. The efficiency and the credibility of proposed algorithm were verified by numerical tests. This algorithm can be used to calculate temperature distribution in system pipe with liquid where the viscosity is large. Numerical examples are presented. The computer program Viscous Dissipation 1D was written in Fortran programming languages.

3

Effects of hematocrit level on the oscillatory flow characteristic of blood in a stenosed artery

Poria S., De K. N., Mazumdar H. P.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 4

1103-1115

EN

In this paper, a simple model for the oscillatory flow of blood through a stenosed artery is considered. Blood is considered throughout the whole tube (arterial) to be a suspension mainly of red ceIls. A standard distribution of the red celIs is assumed which is based on the idea that the concentration of the red celIs and hence viscosity of blood is higher towards the center of the tube. In effect, viscosity as assumed to vary radialIy. Analytical expressions for the axial velocity, the volumetric flow rate, resistive impedance and phase lag are derived. Effects of hematocrit level on these flow characteristics are discussed.

4

A note on the flows of inhomogeneous fluids with shear-dependent viscosities

Anand M., Rajagopal K. R.

Archives of Mechanics

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2005

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Vol. 57, nr 5

417--428

EN

Inhomogenous fluids have not been studied with the intensity that they deserve. In fact, many studies that are supposedly concerned with the response of inhomogeneous fluids are not directed at inhomogeneous fluids, and this stems from not recognizing the fact that the properties of a fluid varying in its current configuration does not mean that the fluid is inhomogeneous. Here, we show that mild variations in the properties of the fluid which might warrant it being approximated as a homogeneous fluid with average properties could lead to significant errors in the computation of both global and local quantities, associated with the flow.

5

Microchannels flow modelling with the micropolar fluid theory

Kucaba-Piętal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2004

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Vol. 52, nr 3

209-214

EN

The aim of this paper is to study the applicability of the theory of micropolar fluids to modelling and calculating flows in microchannels depending on the geometrical dimension of the flow field. First, it will be shown that if the characteristic linear dimension of the flow becomes appropriately large, the equations describing the micropolar fluid flow can be transformed into Navier-Stokes equations. Next, Poiseuille flows in a microchannel is studied in detail. In particular, the maximal cross-sectional size of the channel for which the micropolar effects of the fluid flow become important will be established. The experimentally determined values of rheological constants of the fluid have been used in calculations.

6

On the unsteady unidirectional flows due to sudden application of a pressure gradient

Erdogan M. E.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 2

345-368

EN

Some properties of unsteady unidirectional flows of viscous fluids are discussed for flows impulsively started from rest by a constant pressure gradient in the direction of the flow. Three illustrative examples are given. The first example is the unsteady Poiseuille flow, the second is the unsteady generalized Couette flow and the third is the unsteady flow in a circular pipe. It is found that the expressions of the quantities such as velocity, flux and skin friction are in series forms which may be rapidly convergent for large values of the dimensionless time but slowly convergent for small values of the dimensionless time or vice versa. It is shown that if their expressions can be found for one of large values of the dimensionless time or small values of the dimensionless time, these expressions can also be used for the other.

7

Flow parameters of some micropolar fluids

Kucaba-Pietal A.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1998

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z. 6

199-203

EN

The aim of the paper is to present the profiles of velocities and microrotations for some micropolar fluids used in technological processes - in defectoscopy. The experimental data needed to perform the calculation were obtained by Migun [4]. The Poiseuille flow is considered. Results show similarity of obtained distributions, but difference in max. values for microrotation is about 17%. Calculation were carried out using MATHCAD 6+.

PL

W pracy przedstawiono obliczone, w oparciu o dane eksperymentalne, rozkłady prędkości i mikrorotacji dla płynów mikropolarnych używanych w defektoskopii. Rozpatrywano przepływ Poiseuillea. Wyniki pokazują jakościowe podobieństwo profili rozważanych cieczy, jednakże różnica w max wartości mikrorotacji wynosi ok 17%. Obliczenia wykonano za pomocą MATHCAD 6+.