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

Abstract

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, ...

Anisotropic thermal transport in a crosslinked polyisoprene rubber subjected to uniaxial elongation

“…Hence, the data shown in Figure 9 provide experimental evidence that supports the validity of the stress‐thermal rule eq 2 expressed as follows: D 11 − D 33 = D eq C t σ. The value of the normalized stress‐thermal coefficient from this figure is C t G N ≅ 0.014 ± 0.003, which is somewhat smaller than that observed for other crosslinked polymers34, 35 and polymer melts 29–33…”

“…Over the past 15 years, we have developed and implemented an FRS setup that allows for measurement of time‐dependent components the thermal diffusivity tensor D = k /ρ ĉ p in polymeric materials. This setup has been used to investigate anisotropic thermal conduction in polymer melts subjected to step and constant rate shear flows,29–33 in crosslinked elastomers subjected to uniaxial elongation,34, 35 and in quenched amorphous polymers 36. In these studies, the state of stress was also measured allowing for examination of the validity of the stress thermal rule.…”

Synchronized molecular-dynamics simulation for the thermal lubrication of a polymeric liquid between parallel plates

“…Note that the thermal conductivity of polymeric liquids is anisotropic under shear flows in general [26,27,28,29], and some experimental studies have reported that the linear stress-thermal relation between the stress tensor and thermal conductivity holds. [30,31,32,33] However, in the present study, we only consider the isotropic thermal conductivity as the first step because the effect of shear thinning of the viscosity is thought to be more crucial to viscous heating under strong shear flows than that of the anisotropy of the thermal conductivity.…”

Synchronized Molecular-Dynamics Simulation via Macroscopic Heat and Momentum Transfer: An Application to Polymer Lubrication

“…(3b). Note that the thermal conductivity of polymeric liquids is anisotropic under shear flows, in general [29][30][31][32], and some experimental studies have reported that the linear stress-thermal relation between the stress tensor and thermal conductivity holds [33][34][35][36]. However, in the present study, we only consider the isotropic thermal conductivity as the first step because the effect of shear thinning of the viscosity is thought to be more crucial to viscous heating under strong shear flows than that of the anisotropy of the thermal conductivity.…”