Lubrication approximation of pressure-driven viscoelastic flow in a hyperbolic channel

被引:13
|
作者
Housiadas, Kostas D. [1 ]
Beris, Antony N. [2 ]
机构
[1] Univ Aegean, Dept Math, Karlovassi 83200, Samos, Greece
[2] Univ Delaware, Dept Chem & Biomol Engn, Newark, DC 19716 USA
关键词
CONSTANT SHEAR-VISCOSITY; AXISYMMETRICAL CONTRACTION; EXTENSIONAL VISCOSITY; CONSTITUTIVE EQUATION; INJECTION FORCES; CONVERGING FLOW; EXPANSION FLOWS; DROP ESTIMATION; BOGER FLUIDS; OLDROYD-B;
D O I
10.1063/5.0183154
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We investigate theoretically the steady incompressible viscoelastic flow in a hyperbolic contracting channel. The fluid viscoelasticity is modeled using the upper convected Maxwell (UCM), Oldroyd-B, Phan-Thien and Tanner (PTT), Giesekus, and the finite elasticity non-linear elastic dumbbell with the Peterlin approximation (FENE-P) models. We first develop the general governing equations for flow within a non-deformable channel whose cross section varies with the distance from the inlet. We then exploit the classic lubrication approximation, assuming a small aspect ratio of the channel to simplify the original governing equations. The final equations, which we formulate in terms of the stream unction, are then solved analytically using a high-order asymptotic scheme in terms of the Deborah number, De, and the formulas for the average pressure drop are derived up to eight orders in De. The accuracy of the original perturbation solution is enhanced and extended over a wide range of parameters by implementing a convergence acceleration method for truncated series. Furthermore, convergence of the transformed solutions for the average pressure drop is demonstrated. The validity and accuracy of the theoretical results is independently confirmed through comparison with numerical results from simulations performed using high-order finite differences and pseudospectral methods. The results reveal the decrease in the average pressure drop with increasing the Deborah number, the polymer viscosity ratio, and the ratio of the inlet to the outlet height. We also show that the fundamental UCM and Oldroyd-B models can predict the major viscoelastic phenomena for this type of internal and confined lubrication flows, while the effect of the rheological parameters of the PTT, Giesekus, and FENE-P models on the results is minor.
引用
收藏
页数:19
相关论文
共 50 条
  • [31] Pressure-driven miscible two-fluid channel flow with density gradients
    Sahu, K. C.
    Ding, H.
    Valluri, P.
    Matar, O. K.
    PHYSICS OF FLUIDS, 2009, 21 (04)
  • [32] Theory to predict particle migration and margination in the pressure-driven channel flow of blood
    Qi, Qin M.
    Shaqfeh, Eric S. G.
    PHYSICAL REVIEW FLUIDS, 2017, 2 (09):
  • [33] Pressure-driven flow through a single nanopore
    Velasco, A. E.
    Friedman, S. G.
    Pevarnik, M.
    Siwy, Z. S.
    Taborek, P.
    PHYSICAL REVIEW E, 2012, 86 (02):
  • [34] Pressure-Driven Suspension Flow near Jamming
    Oh, Sangwon
    Song, Yi-qiao
    Garagash, Dmitry I.
    Lecampion, Brice
    Desroches, Jean
    PHYSICAL REVIEW LETTERS, 2015, 114 (08)
  • [35] Instabilities of a pressure-driven flow of magnetorheological fluids
    Rodriguez-Arco, L.
    Kuzhir, P.
    Lopez-Lopez, M. T.
    Bossis, G.
    Duran, J. D. G.
    JOURNAL OF RHEOLOGY, 2013, 57 (04) : 1121 - 1146
  • [36] Pressure-driven flow in open fluidic channels
    Davey, Nicholas
    Neild, Adrian
    JOURNAL OF COLLOID AND INTERFACE SCIENCE, 2011, 357 (02) : 534 - 540
  • [37] Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel
    Fusi, Lorenzo
    Farina, Angiolo
    INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2011, 46 (08) : 991 - 1000
  • [38] Two-fluid pressure-driven channel flow with wall deposition and ageing effects
    Sileri, D.
    Sahu, K. C.
    Matar, O. K.
    JOURNAL OF ENGINEERING MATHEMATICS, 2011, 71 (01) : 109 - 130
  • [39] Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid
    Sahu, K. C.
    Valluri, P.
    Spelt, P. D. M.
    Matar, O. K.
    PHYSICS OF FLUIDS, 2007, 19 (12)
  • [40] Effective slip in pressure-driven Stokes flow
    Lauga, E
    Stone, HA
    JOURNAL OF FLUID MECHANICS, 2003, 489 : 55 - 77