Viscoelastic flow around particles using the Oldroyd-B and exp-PTT models
In fluid mechanics we have three fundamental problems for the flow around particles are pure shear and elongational flow imposed far from the particles, and steady translation of the particles with constant velocity. Here we study analytically an elongational flow around a cylindrical particle and a...
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| Main Authors: | , |
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| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/11610/20014 |
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| Summary: | In fluid mechanics we have three fundamental problems for the flow around particles are pure shear and elongational flow imposed far from the particles, and steady translation of the particles with constant velocity. Here we study analytically an elongational flow around a cylindrical particle and a steady translation of a spherical particle. We assume the ambient fluid to be viscoelastic and modelled with Upper Convected Maxwell, Oldroyd-B (UCM) and exponential Phan-Thien and Tanner (exp-PTT) under isothermal and creeping flow conditions. The solution for all the dependent variables is expanded as an asymptotic power series with the small parameter being the Weissenberg number, Wi. The resulting sequence of equations is solved analytically up to fourth order in the Weissenberg number.
In the first chapter we study the effect of steady planar elongational flow past an infinitely long circular cylinder. Here the small parameter is the Weissenberg number which is defined as the product of the single relaxation time of the fluid "λ" times the constant rate of elongation "ε ̇", Wi≡ε ̇λ. In the second chapter we study the effect of Navier type slip on the surface of a spherical particle which translates with constant velocity U in a viscoelastic ambient fluid. Again, the small parameter here is the Weissenberg number which is defined as Wi≡λU⁄R where λ is the single relaxation time of the fluid and R the radius of the particle. Also, for the steady translation we applied techniques to accelerate the convergence of series solutions in order to derive more accurate expressions for the drag force on the particle.
This thesis is part of my work at [E. A. Gryparis, S. D. Gkormpatsis, K. D. Housiadas and R. I. Tanner, “Viscoelastic planar elongational flow past an infinitely long cylinder”, Physics of Fluids 31, 033104, (2019)] and [S. D. Gkormpatsis, E. A. Gryparis, K. D. Housiadas and A. N. Beris, “Steady sphere translation in a viscoelastic fluid with slip on the surface of the sphere”, Journal of Non-Newtonian Fluid Mechanics 275, 104217, (2020)]. |
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