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Almqvist, A., Burtseva, E., Ràfols, F. P. & Wall, P. (2019). New insights on lubrication theory for compressible fluids. International Journal of Engineering Science, 145, Article ID 103170.
Open this publication in new window or tab >>New insights on lubrication theory for compressible fluids
2019 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, article id 103170Article in journal (Refereed) Published
Abstract [en]

The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Thin film approximation, Reynold’s equation, Compressible flow, Navier–Stokes equations, Dimension reduction, Asymptotic analysis
National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
Research subject
Machine Elements; Mathematics
Identifiers
urn:nbn:se:ltu:diva-76138 (URN)10.1016/j.ijengsci.2019.103170 (DOI)2-s2.0-85072601607 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-09-27 (johcin)

Available from: 2019-09-27 Created: 2019-09-27 Last updated: 2019-10-02Bibliographically approved
Fabricius, J., Miroshnikova, E., Tsandzana, A. & Wall, P. (2019). Pressure-driven flow in thin domains. Asymptotic Analysis
Open this publication in new window or tab >>Pressure-driven flow in thin domains
2019 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576Article in journal (Refereed) Epub ahead of print
Abstract [en]

We study the asymptotic behavior of pressure-driven Stokes flow in a thin domain. By letting the thickness of the domain tend to zero we derive a generalized form of the classical Reynolds–Poiseuille law, i.e. the limit velocity field is a linear function of the pressure gradient. By prescribing the external pressure as a normal stress condition, we recover a Dirichlet condition for the limit pressure. In contrast, a Dirichlet condition for the velocity yields a Neumann condition for the limit pressure.

Place, publisher, year, edition, pages
IOS Press, 2019
Keywords
Stokes equation, pressure boundary condition, two-scale convergence, thin domain, Bogovskii operator, Korn inequality
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-75853 (URN)10.3233/ASY-191535 (DOI)
Available from: 2019-09-05 Created: 2019-09-05 Last updated: 2019-09-05
Persson, L.-E., Tephnadze, G. & Wall, P. (2018). On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces. Annals of Functional Analysis, 9(1), 137-150
Open this publication in new window or tab >>On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces
2018 (English)In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 9, no 1, p. 137-150Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient. 

Place, publisher, year, edition, pages
Duke University Press, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-63509 (URN)10.1215/20088752-2017-0032 (DOI)000432617900012 ()2-s2.0-85041646355 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-02-19 (svasva)

Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2018-06-08Bibliographically approved
Persson, L.-E., Tephnadze, G. & Wall, P. (2018). On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space H1. Acta Mathematica Hungarica, 154(2), 289-301
Open this publication in new window or tab >>On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space H1
2018 (English)In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 154, no 2, p. 289-301Article in journal (Refereed) Published
Abstract [en]

We prove and discuss a new divergence result of Nörlund logarithmic means with respect to Vilenkin system in Hardy space H1.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Vilenkin system, Nörlund logarithmic mean, partial sum, modulus of continuity, Hardy space
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-66424 (URN)10.1007/s10474-017-0773-8 (DOI)000427375600003 ()
Note

Validerad;2018;Nivå 2;2018-03-14 (rokbeg)

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-04-03Bibliographically approved
Fabricius, J., Tsandzana, A. F., Pérez-Ràfols, F. & Wall, P. (2017). A Comparison of the Roughness Regimes in Hydrodynamic Lubrication. Journal of tribology, 139(5), Article ID 051702.
Open this publication in new window or tab >>A Comparison of the Roughness Regimes in Hydrodynamic Lubrication
2017 (English)In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 139, no 5, article id 051702Article in journal (Refereed) Published
Abstract [en]

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength l, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/l, denoted as k, three different lubrication regimes exist: Reynolds roughness (k-0), Stokes roughness (0<γ<1), and high-frequency roughness (γ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on k. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter k. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

Place, publisher, year, edition, pages
The American Society of Mechanical Engineers (ASME), 2017
National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
Research subject
Mathematics; Machine Elements
Identifiers
urn:nbn:se:ltu:diva-64734 (URN)10.1115/1.4035868 (DOI)000406397500016 ()2-s2.0-85020933899 (Scopus ID)
Note

Validerad;2017;Nivå 2;2017-07-03 (andbra)

Available from: 2017-07-03 Created: 2017-07-03 Last updated: 2018-11-27Bibliographically approved
Abylayeva, A., Baiarystanov, A., Persson, L.-E. & Wall, P. (2017). Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels. Journal of Mathematical Inequalities, 11(3), 683-694
Open this publication in new window or tab >>Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels
2017 (English)In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, no 3, p. 683-694Article in journal (Refereed) Published
Abstract [en]

Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

Place, publisher, year, edition, pages
Ele-Math, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-60850 (URN)10.7153/jmi-2017-11-54 (DOI)000411883200006 ()2-s2.0-85029774121 (Scopus ID)
Note

Validerad;2017;Nivå 2;2017-09-08 (andbra)

Available from: 2016-12-01 Created: 2016-12-01 Last updated: 2017-11-24Bibliographically approved
Almqvist, A., Fabricius, J., Lundström, S. & Wall, P. (2017). Flow in thin domains with a microstructure: Lubrication and thin porous media. Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4-8 July 2016. AIP Conference Proceedings, 1798, Article ID 020172.
Open this publication in new window or tab >>Flow in thin domains with a microstructure: Lubrication and thin porous media
2017 (English)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020172Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.

Place, publisher, year, edition, pages
AIP Publishing, 2017
National Category
Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Fluid Mechanics and Acoustics
Research subject
Machine Elements; Mathematics; Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-62224 (URN)10.1063/1.4972764 (DOI)000399203000171 ()2-s2.0-85013665597 (Scopus ID)
Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4-8 July 2016
Note

2017-03-03 (andbra);Konferensartikel i tidskrift

Available from: 2017-03-01 Created: 2017-03-01 Last updated: 2018-11-20Bibliographically approved
Fabricius, J., Miroshnikova, E. & Wall, P. (2017). Homogenization of the Stokes equation with mixed boundary condition in a porous medium. Cogent Mathamatics, 4(1), Article ID 1327502.
Open this publication in new window or tab >>Homogenization of the Stokes equation with mixed boundary condition in a porous medium
2017 (English)In: Cogent Mathamatics, E-ISSN 2331-1835, Vol. 4, no 1, article id 1327502Article in journal (Refereed) Published
Abstract [en]

We homogenize stationary incompressible Stokes flow in a periodic porous medium. The fluid is assumed to satisfy a no-slip condition on the boundary of solid inclusions and a normal stress (traction) condition on the global boundary. Under these assumptions, the homogenized equation becomes the classical Darcy law with a Dirichlet condition for the pressure.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-64001 (URN)10.1080/23311835.2017.1327502 (DOI)000403291100001 ()
Note

Validerad;2017;Nivå 2;2017-07-06 (rokbeg)

Available from: 2017-06-14 Created: 2017-06-14 Last updated: 2018-07-10Bibliographically approved
Rafols, F. P., Larsson, R., Lundström, S., Wall, P. & Almqvist, A. (2016). A stochastic two-scale model for pressure-driven flow between rough surfaces (ed.). Paper presented at . Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, 472(2190), Article ID 20160069.
Open this publication in new window or tab >>A stochastic two-scale model for pressure-driven flow between rough surfaces
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2016 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 472, no 2190, article id 20160069Article in journal (Refereed) Published
Abstract [en]

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.

National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Fluid Mechanics and Acoustics Mathematical Analysis
Research subject
Machine Elements; Fluid Mechanics; Mathematics
Identifiers
urn:nbn:se:ltu:diva-14714 (URN)10.1098/rspa.2016.0069 (DOI)000379726800016 ()2-s2.0-84978388150 (Scopus ID)e22df646-269f-4f4e-80d7-43e89b5a630a (Local ID)e22df646-269f-4f4e-80d7-43e89b5a630a (Archive number)e22df646-269f-4f4e-80d7-43e89b5a630a (OAI)
Note
Validerad; 2016; Nivå 2; 20160816 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Persson, L.-E., Samko, N. & Wall, P. (2016). Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces (ed.). Paper presented at . Journal of Fourier Analysis and Applications, 22(2), 413-426
Open this publication in new window or tab >>Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces
2016 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, no 2, p. 413-426Article in journal (Refereed) Published
Abstract [en]

We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces L p,φ (R n ,w), defined by a function φ(x,r) and radial type weight w(|x−x 0 |),x 0 ∈R n . These conditions are given in terms of inclusion into L p,φ (R n ,w), of a certain integral constructions defined by φ and w. In the case of φ=φ(r) we also provide easy to check sufficient conditions for that in terms of indices of φ and w.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-10724 (URN)10.1007/s00041-015-9418-x (DOI)000376247200006 ()2-s2.0-84932141263 (Scopus ID)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (Local ID)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (Archive number)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (OAI)
Note
Validerad; 2016; Nivå 2; 20150624 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-8211-3671

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