Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement
A general unified solution of the plane Couette–Poiseuille–Stokes–Womersley incompressible linear fluid flow in a slit in the presence of oscillatory pressure gradients with periodic synchronous vibrating boundaries is presented. Oscillatory flow remains stable and laminar with no-slip boundary cond...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/757 |
| _version_ | 1797434239472369664 |
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| author | Nihad E. Daidzic |
| author_facet | Nihad E. Daidzic |
| author_sort | Nihad E. Daidzic |
| collection | DOAJ |
| description | A general unified solution of the plane Couette–Poiseuille–Stokes–Womersley incompressible linear fluid flow in a slit in the presence of oscillatory pressure gradients with periodic synchronous vibrating boundaries is presented. Oscillatory flow remains stable and laminar with no-slip boundary conditions applied. Eigenfunction expansion method is used to obtain the exact analytical solution of the general linear inhomogeneous boundary value problem. Fourier expansion of arbitrary harmonic pressure gradient and non-harmonic wall oscillations was used to calculate arbitrary driving of the fluid. In-house developed optimized computational fluid dynamics marching-in-time finite-volume method was used to test and verify all analytical results. A number of particular transients, steady-state and combined flows were obtained from the general analytical result. Generalized Stokes and Womersley flows were solved using the analytical computations and numerical experiments. The combined effects of periodic non-harmonic wall movements with oscillatory pressure gradients offers rich and interesting flow patterns even for a linear Newtonian fluid and may be particularly interesting for pumping-assist microfluidic devices. The main motivation for developing a unified solution of the unsteady laminar planar Couette–Stokes–Poiseuille–Womersley flow originates in a need for, but is not limited to, in-depth exploration of flow patterns in hemodynamic and microfluidic pumping applications. |
| first_indexed | 2024-03-09T10:28:25Z |
| format | Article |
| id | doaj.art-a6d3881982a6480d8cb2b36ef60a9d93 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T10:28:25Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a6d3881982a6480d8cb2b36ef60a9d932023-12-01T21:28:39ZengMDPI AGSymmetry2073-89942022-04-0114475710.3390/sym14040757Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary MovementNihad E. Daidzic0Department of Aviation, Minnesota State University, Mankato, MN 56001, USAA general unified solution of the plane Couette–Poiseuille–Stokes–Womersley incompressible linear fluid flow in a slit in the presence of oscillatory pressure gradients with periodic synchronous vibrating boundaries is presented. Oscillatory flow remains stable and laminar with no-slip boundary conditions applied. Eigenfunction expansion method is used to obtain the exact analytical solution of the general linear inhomogeneous boundary value problem. Fourier expansion of arbitrary harmonic pressure gradient and non-harmonic wall oscillations was used to calculate arbitrary driving of the fluid. In-house developed optimized computational fluid dynamics marching-in-time finite-volume method was used to test and verify all analytical results. A number of particular transients, steady-state and combined flows were obtained from the general analytical result. Generalized Stokes and Womersley flows were solved using the analytical computations and numerical experiments. The combined effects of periodic non-harmonic wall movements with oscillatory pressure gradients offers rich and interesting flow patterns even for a linear Newtonian fluid and may be particularly interesting for pumping-assist microfluidic devices. The main motivation for developing a unified solution of the unsteady laminar planar Couette–Stokes–Poiseuille–Womersley flow originates in a need for, but is not limited to, in-depth exploration of flow patterns in hemodynamic and microfluidic pumping applications.https://www.mdpi.com/2073-8994/14/4/757Couette flowPoiseuille flowStokes’ 1st and 2nd problemWomersley floweigenfunction expansioncomplex Fourier series |
| spellingShingle | Nihad E. Daidzic Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement Symmetry Couette flow Poiseuille flow Stokes’ 1st and 2nd problem Womersley flow eigenfunction expansion complex Fourier series |
| title | Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement |
| title_full | Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement |
| title_fullStr | Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement |
| title_full_unstemmed | Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement |
| title_short | Unified Theory of Unsteady Planar Laminar Flow in the Presence of Arbitrary Pressure Gradients and Boundary Movement |
| title_sort | unified theory of unsteady planar laminar flow in the presence of arbitrary pressure gradients and boundary movement |
| topic | Couette flow Poiseuille flow Stokes’ 1st and 2nd problem Womersley flow eigenfunction expansion complex Fourier series |
| url | https://www.mdpi.com/2073-8994/14/4/757 |
| work_keys_str_mv | AT nihadedaidzic unifiedtheoryofunsteadyplanarlaminarflowinthepresenceofarbitrarypressuregradientsandboundarymovement |