Stress‐induced diffusion of macromolecules

Tirrell, Matthew; Malone, Michael F.

doi:10.1002/pol.1978.180160318

Cited by 7 publications

(11 citation statements)

References 3 publications

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“…Later, Marrucci 22 related the entropy change with the stress level for an Oldroyd-B liquid and Metzner 23 employed this result to analyze polymer retention in flows through porous media. Tirrell and Malone 24 have made similar arguments. However, Aubert, Prager, and Tirrell 25 pointed out that it is not clear that a spatial gradient in intramolecular free energy can result in displacement of the center of mass.…”

Section: Introductionmentioning

confidence: 57%

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

2005

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In this work, a continuum theory is developed for the behavior of flowing dilute polymer solutions near solid surfaces, using a bead-spring dumbbell model of the dissolved polymer chains. Hydrodynamic interactions between the chains and the wall lead to migration away from the wall in shear flow. At steady state, this hydrodynamic effect is balanced by molecular diffusion; an analytical expression for the resulting concentration profile is derived. It is shown that the depletion layer thickness is determined by the normal stresses that develop in flow and can be much larger than the size of the polymer molecule. The transient development of this depletion layer is also studied, as well as the spatial development downstream from an entrance. Numerical and similarity solutions in these cases show that the developing concentration profile generally displays a maximum at an intermediate distance from the wall.

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Section: Introductionmentioning

confidence: 57%

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

2005

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“…Polymer solutions [12] Stress induced migration: thermodynamic theory Migration towards center [13] Stress induced migration: fluid mech. Theory No radial migration [8] Polymer species dissolved in the fluid diffuse away from the wall, which generates a region of low viscosity adjacent to wall and as a result bulk slips Concentration profile develops down stream from the tube entry.…”

Section: Reference Approach Predictionmentioning

confidence: 99%

“…In the case of polymer solutions, apparent wall slip has been attributed to migration of macromolecules away from the wall under a stress gradient [8,12,13]. For melts, the mechanisms of constitutive (bulk) instability [14±16], desorption from the wall [17±19] and chain disentanglement at the wall [20] have been proposed for explaining wall slip.…”

Section: Introductionmentioning

confidence: 99%

Slipping fluids: a unified transient network model

Joshi

Lele

Mashelkar

2000

Journal of Non-Newtonian Fluid Mechanics

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Wall slip in polymer solutions and melts play an important role in fluid flow, heat transfer and mass transfer near solid boundaries. Several different physical mechanisms have been suggested for wall slip in entangled systems. We look at the wall slip phenomenon from the point of view of a transient network model, which is suitable for describing both, entangled solutions and melts. We propose a model, which brings about unification of different mechanisms for slip. We assume that the surface is of very high energy and the dynamics of chain entanglement and disentanglement at the wall is different from those in the bulk. We show that severe disentanglement in the annular wall region of one radius of gyration thickness can give rise to non-monotonic flow curve locally in that region. By proposing suitable functions for the chain dynamics so as to capture the right physics, we show that the model can predict all features of wall slip, such as flow enhancement, diameter-dependent flow curves, discontinuous increase in flow rate at a critical stress, hysteresis in flow curves, the possibility of pressure oscillations in extrusion and a second critical wall shear stress at which another jump in flow rate can occur. #

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“…Similarly, Newton's law of viscosity says that the viscous stress must be linearly proportional to the rate of strain, but the viscosity coefficient can depend non-linearly on the temperature and specific volume or pressure ( [42], pp. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Quasilinear Phenomenological Lawsmentioning

confidence: 99%

“…Then theory is needed to project the information acquired in simple experiments to the complex reality of the process. The need for robust theories is even more pressing when tackling more complex transport phenomena, like coupled flow and heat transfer [17][18][19][20][21][22] or mass transfer [23][24][25][26][27][28][29][30]; experimental evidence on such processes is still limited [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

Pasquali

Scriven

2004

Journal of Non-Newtonian Fluid Mechanics

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A new method is presented for accounting for microstructural features of flowing complex fluids at the level of mesoscopic, or coarse-grained, models by ensuring compatibility with macroscopic and continuum thermodynamics and classical transport phenomena. In this method, the microscopic state of the liquid is described by variables that are local expectation values of microscopic features. The hypothesis of local thermodynamic equilibrium is extended to include information on the microscopic state, i.e., the energy of the liquid is assumed to depend on the entropy, specific volume, and microscopic variables. For compatibility with classical transport phenomena, the microscopic variables are taken to be extensive variables (per unit mass or volume), which obey convection-diffusion-generation equations. Restrictions on the constitutive laws of the diffusive fluxes and generation terms are derived by separating dissipation by transport (caused by gradients in the derivatives of the energy with respect to the state variables) and by relaxation (caused by non-equilibrated microscopic processes like polymer chain stretching and orientation), and by applying isotropy. When applied to unentangled, isothermal, non-diffusing polymer solutions, the equations developed according to the new method recover those developed by the Generalized Bracket [J. Non-Newtonian Fluid Mech. 23 (1987) Rheol. 38 (1994) 769]. Minor differences with published results obtained by the Generalized Bracket are found in the equations describing flow coupled to heat and mass transfer in polymer solutions. The new method is applied to entangled polymer solutions and melts in the general case where the rate of generation of entanglements depends nonlinearly on the rate of strain. A link is drawn between the mesoscopic transport equations of entanglements and conformation and the microscopic equation describing the configurational distribution of polymer segment stretch and orientation. Constraints are derived on the generation terms in the transport equations of entanglements and conformation, and the formula for the elastic stress is generalized to account for reversible formation and destruction of entanglements. A simplified version of the transport equation of conformation is presented which includes many previously published constitutive models, separates flow-induced polymer stretching and orientation, yet is simple enough to be useful for developing large-scale computer codes for modeling coupled fluid flow and transport phenomena in two-and three-dimensional domains with complex shapes and free surfaces.

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Stress‐induced diffusion of macromolecules

Cited by 7 publications

References 3 publications

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

Slipping fluids: a unified transient network model

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

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