B. H. A. A. van den Brule

A network theory for the thermal conductivity of an amorphous polymeric material

A model to relate the thermal conductivity tensor to the deformation of an amorphous polymeric material above the glass transition temperature is presented. The basis of the model is formed by the transient network theory for polymer melts. With this theory it is possible to calculate the average orientation of the macromolecular segments as a function of the history of the deformation. Combined with an expression which relates the thermal conductivity to the orientation of the molecules, this provides us with the information needed to calculate the heat conduction tensor. Despite the fact that the simplest possible network model is chosen, there is good agreement with the sparse, experimental results.

Modeling of concentrated suspensions

The constitutive equation of a concentrated suspension of spherical particles in a Newtonian medium is derived. To this end the method of local volume averaging is employed. To calculate the contribution of the particles to the stress tensor it is assumed that the stress generated in the interstitial holes between the particles is negligible compared to the stress generated in !he narrow gaps separating the particles. The use of the resulting expression is demonstrated with two examples on a cubical arrangement of particles: pure shear and simple shear. Furthermore, the validity of the lubrication approximation employed in this work is checked against the results derived by Nunan and Keller for periodic suspensions.

A mathematical model for the cleansing of silicon substrates by fluid immersion

Abstract The importance of cleanliness for the efficient manufacture of integrated circuits is well known in the microprocessor industry. The efficiency of traditional cleansing methods is known to decrease dramatically for dirt particles smaller than about 1 μm in radius. Experimentally it has been shown that the passage of a liquid-gas phase boundary along a substrate can be exploited to effect particle removal. A model is derived here which explains the success of this process, illustrates the dependency of the method on the speed of immersion, and further shows that it is theoretically independent of particle size.

Anisotropic conduction of heat caused by molecular orientation in a flowing polymeric liquid

To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.

The non-isothermal elastic dumbbell : a model for the thermal conductivity of a polymer solution

In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.

Anisotropic conduction of heat in a flowing polymeric material

In this paper a theory is presented which relates the thermal conductivity tensor of an amorphous polymeric material to the history of deformation of the material. The basis of the theory is formed by the network theory for polymeric materials. It will be shown that the results obtained here are in good agreement with experimental results on rubber. The effect of anisotropic heat conduction on the flow of a polymeric material will be demonstrated by the simple example of viscous heating in shear flow.

A simple constant-stress rheometer

Abstract A description is given of a simple constant-stress rheometer. The basic idea of the rheometer is to use a coaxial cylinder geometry to convert a constant angular velocity into a constant driving torque. It will be shown that in this way it is possible to build a very sensitive constant-stress rheometer. The lowest torques which can be generated in this way are limited by the quality of the air bearing and by the unbalance of the rotating part of the instrument. Since these problems are likely to occur also in other controlled-stress rheometers, a detailed discussion of the most important imperfections is given.

An oven design for torsional rheometers

A newly designed oven for rheological characterisation of polymer melts is presented which relies upon conduction and radiation rather than convection to heat the polymer. The design involves three concentric heating elements, all controlled independently to ensure a stable thermal atmosphere. The overshoot on heating is minimal (10 K, and this was due to opening the oven for sample trimming; the overshoot is 3 K if the oven is not opened) and the results of a typical dynamic shear test show that rheological properties attain their equilibrium values very rapidly (25 min after start-up of the oven fro room temperature, and 15 min after the sample was placed in the rheometer). The temperature of the sample was maintained at ±0.5 K, thus, a stable thermal environment was successfully attained.

Rheometry of viscoplastic dispersions

Phenomenological models for viscoplastic materials are constructed. The response to an oscillatory shear experiment is derived and found to agree with experimental results.

Anisotropic Conduction of Heat in a Polymeric Material

A model to relate the thermal conductivity tensor to the deformation of an amorphous material is presented. The basis of the theory is formed by the network theory for polymer melts and rubbers. With this model the average orientation of the molecular segments can be calculated. Combined with an expression to relate the molecular orientation to the heat flux this enables us to calculate the thermal conductivity tensor. The practical importance of these results is illustrated by a calculation of the temperature rise caused by viscous dissipation in a flowing polymer melt.