Transport Properties of Polymeric Liquids

Bird, R. B.; Öttinger, Hans Christian

doi:10.1146/annurev.pc.43.100192.002103

Cited by 44 publications

(18 citation statements)

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“…micro-seconds to seconds), atomistic descriptions of the polymer molecule are typically 'coarse-grained' to consider only the longer relaxation times of the polymer. Excellent reviews of the literature on coarse-grained polymer models are provided by Bird et al (1987), Larson (1988) and Bird and Ottinger (1992). The models can be broadly categorized as bead-rod models such as 4 Kramers chain and bead-spring models such as the FENE model.…”

Section: Fenementioning

confidence: 99%

“…The computational demand of three-dimensional DNS of turbulence limits the models for the polymer to a class known as the finitely extensible nonlinear elastic model that invokes the Peterlin (1961) approximation to close the dynamic equations (FENE-P). In this description, the polymer is modeled as two beads connected by a spring with a nonlinear force law that diverges as the separation distance approaches the maximum extension, L max (Beris and Edwards 1994, Bird et al 1987, Larson et al 1999. The model reproduces shear thinning, and yields an extensional viscosity that is substantially larger than the shear viscosity, which appears to be an essential ingredient to capture the qualitative features of turbulent drag reduction in wall-bounded flows.…”

Section: Introductionmentioning

confidence: 99%

“…We discuss the relationships between the individual spring properties and the chain properties in section 2.3. The polymer stress exerted on the fluid is given by (Bird et al 1987) T…”

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confidence: 99%

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Dynamics of dissolved polymer chains in isotropic turbulence

Jin¹,

Collins²

2007

New J. Phys.

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Section: Fenementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of dissolved polymer chains in isotropic turbulence

Jin¹,

Collins²

2007

New J. Phys.

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“…These new variables are then assumed to obey evolution equations of their own. The resulting theories are compared with a relatively large body of experimental work measuring stresses in well controlled flows, and the comparisons have led to increasingly sophisticated theories, such that reasonable quantitative predictions are now possible for stress in flowing complex fluids (4)(5)(6). Experimental progress eventually led to theoretical advance.…”

Section: Transport Phenomena In Complex Fluidsmentioning

confidence: 99%

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Schieber

Venerus

Bush

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

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Almost no experimental data exist to test theories for the nonisothermal flow of complex fluids. To provide quantitative tests for newly proposed theories, we have developed a holographic grating technique to study energy transport in an amorphous polymer melt subject to flow. Polyisobutylene with weight-averaged molecular mass of 85 kDa is sheared at a rate of 10 s ؊1 , and all nonzero components of the thermal conductivity tensor are measured as a function of time, after cessation. Our results are consistent with proposed generalizations to the energy balance for microstructural fluids, including a generalized Fourier's law for anisotropic media. The data are also consistent with a proposed stress-thermal rule for amorphous polymer melts. Confirmation of the universality of these results would allow numerical modelers to make quantitative predictions for the nonisothermal flow of polymer melts.N early all biological and advanced synthetic materials can exhibit molecular order or structure spontaneously, or be induced by flow. For example, rod-like molecules can form liquid crystals or membranes at equilibrium, and surfactants can self-assemble into worm-like shapes (1). These materials with microstructure exhibit nonequilibrium behavior much more complex than what is observed for simple, low-molecular-weight liquids. Upon flow, they may orient, crystallize, and show stresses many orders of magnitude larger than water. What is more, these large stresses relax back to equilibrium on time scales from seconds to minutes when the flow is stopped (2).The governing dynamics of simple (low-molecular-weight) f luids are well understood. Their derivation begins with straightforward balance equations for mass, momentum, and energy (and possibly angular momentum conservation) applied to a continuum (3). Mass conservation leads to an evolution equation for density , the continuity equation. The second and third balances, however, are not closed; we have too many unknowns and not enough equations. For closure we need additional equations called constitutive relations. For the momentum balance, we need an equation to relate stress to velocity in the f luid, and, in the case of the energy balance, we require two additional equations: a relationship between energy and measurable quantities, usually temperature T and velocity v; and a relationship between heat f lux and temperature. For simple f luids, these constitutive relations are well known. For the stress tensor we use the Newtonian constitutive equation, which states that the stress is linearly related to the instantaneous velocity gradient ٌv, through the viscosity. The energy density is a sum of internal energy density u, and kinetic energy density 1͞2 v 2 . The third relation is Fourier's law for the heat f lux q, which is linearly related to the temperature gradient by a scalar thermal conductivity.Using these three relations, we then have a closed set of evolution equations for the density , the velocity field v, and the temperature field T. If material parameters, ...

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“…Hence, from the mathematical point of view, the density profiles obtained from the CD simulations should be the same as those obtained from the FEM solution provided the same boundary conditions (that is, SFDC geometry), operating conditions and sensing mechanisms are used in both cases. [This equivalence is exactly the same as that between Brownian dynamics simulations of kinetic theory models of polymeric molecules at infinite dilution and the corresponding "diffusion equation" solutions for the phase space density (Bird and Ottinger, 1992).] The advantage of the FEM solution to Eq.…”

Section: Cellular Dynamics Simulationsmentioning

confidence: 69%

Analysis of bacterial migration: I. Numerical solution of balance equation

1994

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Chemotaxis describes the ability of motile bacteria to bias their motion in the direction of increasing gradients of chemicals, usually energy sources, known as attractants. In experimental studies of the migration of chemotactic bacteria, I-D phenomenological cell balance equations (River0 et al., 1989) have been used to quantitatively analyze experimental observations . While attractive for their simplicity and the ease of solution, they are limited in the strict mathematical sense to the situation in which individual bacteria are confined to motion in one dimension and respond to attractant gradients in one dimension only. Recently, Ford and Cummings (1992) (Frymier et al., 1993), and experimental data from our laboratory for E. coli responding to a-methylaspartate. We also investigate two aspects of the experimentally derived expression for the tumblingprobability: the effect of different models for the down-gradient swimming behavior of the bacteria and the validity of ignoring the temporal derivative of the attractant concen tra t ion .

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Transport Properties of Polymeric Liquids

Cited by 44 publications

References 0 publications

Dynamics of dissolved polymer chains in isotropic turbulence

Dynamics of dissolved polymer chains in isotropic turbulence

Measurement of anisotropic energy transport in flowing polymers by using a holographic technique

Analysis of bacterial migration: I. Numerical solution of balance equation

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