Constitutive Equations for Polymeric Liquids

Bird, R. Byron; Wiest, John M.

doi:10.1146/annurev.fl.27.010195.001125

Cited by 232 publications

(107 citation statements)

References 95 publications

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“…This framework also includes the parameters γ = 0, κ 1 = κ 2 = 1, which is an upper convected Maxwell fluid, used to describe a polymer melt [22]. The results below readily, and immediately, generalize to other parameters in the constitutive relation, for example γ = 0, κ 1 = κ 2 = −1, a lower convected Maxwell fluid [23,25]. Finally, note that the three-sphere swimmer kinematics are coupled to the fluid mechanics via no-slip boundary conditions, which are imposed on all sphere surfaces,…”

Section: A Governing Equationsmentioning

confidence: 98%

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Three-sphere swimmer in a nonlinear viscoelastic medium

Curtis

Gaffney

2013

Phys. Rev. E

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A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres.

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Section: A Governing Equationsmentioning

confidence: 98%

“…(15); instead, the boundary conditions contain additional O(δ) terms, as illustrated by equation (25). In order to correct u (α)…”

Section: B Higher-order Corrections In δmentioning

confidence: 99%

Three-sphere swimmer in a nonlinear viscoelastic medium

Curtis

Gaffney

2013

Phys. Rev. E

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“…A non-isothermal version of the Oldroyd-B constitutive model based on the pseudo-time hypothesis [3,12] gives the following equations for the extra stress τ = :…”

Section: Governing Equationsmentioning

confidence: 99%

“…Because of the high viscosities of polymeric fluids, especially polymer melts, a temperature rise due to viscous dissipation may considerably affect the isothermal flow field; as stated in the present work. Moreover, fluid parameters, such as viscosity and relaxation time are very sensitive to temperature changes [12]. In spite of this crucial importance of the temperature dependent flow phenomenon, relatively little attention has been paid to the non-isothermal flow of viscoelastic fluids until the last few years [9,13,14].…”

Section: Introductionmentioning

confidence: 99%

Non-isothermal spherical Couette flow of Oldroyd-B fluid

Hassan

Zidan

Moussa

2008

Z. angew. Math. Phys.

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The present paper is concerned with non-isothermal spherical Couette flow of Oldroyd-B fluid in the annular region between two concentric spheres. The inner sphere rotates with a constant angular velocity while the outer sphere is kept at rest. The viscoelasticity of the fluid is assumed to dominate the inertia such that the latter can be neglected in the momentum and energy equations. An approximate analytical solution is obtained through the expansion of the dynamical variable fields in power series of Nahme number. Non-homogeneous, harmonic for axial-velocity and temperature equations and biharmonic for stream function equations, have been solved up to second order approximation. In comparison of the present work with isothermal case; [1,2], two additional terms; a first order velocity and a second order stream function are stem as a result of the interaction between the fluid viscoelasticity and temperature profile. These contributions prove to be the most important results for rheology in this work.

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“…In contrast, almost all previous thin fluid film modelling use only a power law dependence. Some industrial plastics have a complicated non-monotonic dependence that cannot be represented by a simple power law [9]. Similarly, dense suspensions often have non-monotonic dependence [5].…”

Section: Introductionmentioning

confidence: 99%

The inertial dynamics of thin film flow of non-Newtonian fluids

Roberts

2008

Physics Letters A

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Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case where the viscosity depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a relatively large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible foundation for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids when the flow is not creeping.

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Constitutive Equations for Polymeric Liquids

Cited by 232 publications

References 95 publications

Three-sphere swimmer in a nonlinear viscoelastic medium

Three-sphere swimmer in a nonlinear viscoelastic medium

Non-isothermal spherical Couette flow of Oldroyd-B fluid

The inertial dynamics of thin film flow of non-Newtonian fluids

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