Step-strain deformations for viscoelastic fluids: Formulation of a strain-coupling constitutive equation

An integral constitutive equation which includes strain-coupling effects is proposed. The constitutive equation is more general than the K-BKZ equation, and it is shown that this equation can explain various important aspects of double-step stress-relaxation data.     

Mechanical energy balances for a capillary viscometer

The entrance and exit flow processes for a cylindrical geometry are analyzed by writing macroscopic mechanical energy balances for a capillary viscometer. These equations can be used to compute the entrance and exit excess dissipation integrals from measured pressure differences if viscometric normal stress data are available for the material of interest. Upper and lower bounds are derived for these integrals for cases when high shear rate normal stress data are not available. The utilization of macroscopic mechanical energy balances in the interpretation of capillary viscometer results is illustrated using numerical solutions for a Maxwell fluid and experimental pressure drop data for high density polythylene.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Strain-coupling effects in start-up experiments

A strain-coupling integral constitutive equation is used to analyze a start-up shear flow experiment. The theory is used to examine the effect of strain-coupling on the strain at the maximum in the shear stress-time curve. The analysis shows that there is a significant dependence of this strain on the shear rate even when a factorable strain-coupling model is used.     

Evaluation of theories for diffusion in polymer–solvent systems

A method is proposed for examining differences in the predictive capabilities of three versions of the free-volume theory of polymer—solvent diffusion using only a small amount of diffusivity data. The utility of the method is illustrated using a limited diffusivity data set for the methanol-poly(vinyl acetate) system.