Abstract
We apply the boundary layer equations to inertial flow in wall bounded films that might be characterized as ‘thin’, say ɛ ≤ 0.1 where ɛ is the ratio of the characteristic lengths, yet to which the lubrication approximation of Reynolds no longer applies. Two particular flow geometries are investigated, nominally parallel plates and nominally inclined plates, both with and without spatially periodic perturbation of the stationary plate. A Galerkin-B spline formulation of the governing equations is employed, and we rely on parametric continuation to obtain solutions at higher values of the Reynolds number. In particular, we are able to demonstrate that the boundary layer equations yield accurate results for a wide range of Reynolds numbers when the aspect ratio is less than 1/10. We also find that in both nominally parallel and nominally inclined geometries the sign of the inertial force correction is determined by the film contour in the neighborhood of the exit, this result might have implications in the design of MEMS devices.
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References
Reynolds O (1886). On the theory of lubrication and its application to Mr. Tower’s experiments. Philos Trans Roy Soc 177: 157–234
Becker J and Grun G (2005). The thin film equation: recent advances and some new perspectives. J Phys Cond Matter 17: S291–S307
Schwartz L, Roy RV, Elly RR and Princen HM (2004). Surfactant-driven motion and splitting of droplets on a substrate. J Eng Math 50(2-3): 157–175
Alvarez A, Soto R (2005) Dynamics of a suspension confined in a thin cell. Phys Fluids 17(9):Art. No. 093103
Munch A and Wagner B (2005). Contact-line instability of dewetting thin films. Physica D- Nonlin Phenomena 209(1-4): 178–190
Mishra C and Peles Y (2005). Flow visualization of cavitating flows through a rectangular slot micro-orifice ingrained in a micro-channel. Phys Fluids 17(11): 113602
Mukherjee S, Telekunta S and Mukherjee YX (2005). BEM modeling of damping forces on MEMS with thin plates. Eng Anal Boundary Elements 29(11): 1000–1007
Osterle JF, Chou YT and Saibel E (1975). The effect of lubricant inertia in journal bearing lubrication. Trans ASME 79: 494–496
Constantinescu VN (1970). On the influence of inertia forces in turbulent and laminar self-acting films. J Lub Tech 92: 473–481
Constantinescu VN and Galetuse S (1982). Operating characteristics of journal bearing in turbulent inertial flow. J Lub Tech 104: 173–179
Launder BE and Leschziner M (1978). Flow in finite-width, thrust bearings including inertial effects, I and I. J Lub Tech 100: 330–345
Pozzi A and Tognaccini R (2005). Influence of the Prandtl number on the unsteady thermo-fluid dynamic field around a thick plate. Meccanica 40: 251–266
DiPrima RC and Stuart JT (1972). Non-local effects in the stability of flow between eccentric rotating cylinders. J Fluid Mech 54: 393–415
Malvano R, Vatta F and Vigliani A (1999). Lubricated plane slider bearing: analytic and numerical approach. Meccanica 34: 237–250
San Andres A and Szeri AZ (1985). Flow between eccentric rotating cylinders. J Appl Mech 51: 869–878
Schlichting H (1968) Boundary layer theory, 4th edn. Mc-Graw-Hill
Szeri AZ (1998) Fluid film bearings: theory and design. Cambridge University Press
Dowson D (1998). Modeling of elastohydrodynamic lubrication of real solids by real liquids. Meccanica 33: 47–57
de Boor C (1978) A practical guide to splines. Springer-Verlag
Rajagopal KR and Szeri AZ (2003). On an inconsistency in the derivation of the equations of elastohydrodynamic lubrication. Proc R Soc Lond A 459: 2771–2786
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Szeri, A.Z., Snyder, V. Convective inertia effects in wall-bounded thin film flows. Meccanica 41, 473–482 (2006). https://doi.org/10.1007/s11012-006-0006-7
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DOI: https://doi.org/10.1007/s11012-006-0006-7