J. S. Vrentas

Predictive methods for self-diffusion and mutual diffusion coefficients in polymer-solvent systems

Abstract Methods are presented for the prediction of solvent self-diffusion coefficients and mutual diffusion coefficients in polymer–solvent systems for the complete concentration range and over wide temperature ranges. Procedures are developed for both rubbery and glassy polymer–solvent systems.

Fluid mechanics of laminar liquid jets

Abstract The flow behavior of Newtonian jets is analyzed by the use of a coordinate system which reduces the problems associated with free boundaries. The resulting general equations are simplified by a boundary-layer type analysis and numerical as well as approximate analytical solutions are presented. These solutions predict the velocity distributions and the shape of jets under the influence of surface and body forces. Measurements of jet shape confirm the accuracy of the calculations. The methods developed in this study can in principle be useful in the analysis of a wide class of free-boundary problems.

Analysis of Two-Dimensional Diffusion-Controlled Moving Boundary Problems

This paper presents a technique for the analysis of unsteady, two-dimensional diffusive heat- or mass-transfer problems characterized by moving irregular boundaries. The technique includes an immobilization transformation and a numerical scheme for the solution of the transformed equations. Specifically, the immobilization consists of transforming the governing partial differential equations into a coordinate system where the phase boundaries correspond to fixed coordinate surfaces. An example problem involving the solidification or melting of a finite cylinder is analyzed, and results for a range of conditions are presented.

Heat or mass transfer-controlled dissolution of an isolated sphere

Abstract A comprehensive set of finite-difference solutions describing the heat or mass transfer-controlled dissolution of isolated spheres is presented. The analysis is based on a generalized formulation which includes three specific classes of dissolution problems. A coordinate transformation which immobilizes the moving boundary and maps the infinite region of interest into a finite region is used to minimize the difficulties associated with a numerical analysis of this problem. Radius-time and particle lifetime results are reported for ranges of parameters which include the majority of physically important dissolution processes. In addition, the results of this investigation are used to determine the accuracy and range of applicability of various approximate analytical solutions.

Flow of a newtonian fluid through a sudden contraction

The full Navier-Stokes equations describing flow through a sudden contraction are solved by an explicit finite-difference method. Streamlines, vorticity distributions, velocity profiles, excess pressure drops, and entrance lengths are calculated as functions of Reynolds number and radius ratio. The results are compared with existing experimental data and the limited theoretical work available.

Steady flow in the region of closed streamlines in a cylindrical cavity

An analytical solution is developed to describe the steady, closed streamline velocity field within a cylindrical cavity with a uniformly translating wall at low Reynolds numbers. The solution has application for the case of two-phase flow in a tube where regions of fluid are segmented by a moving train of bubbles or plugs, such as in the pulmonary and peripheral capillaries of the body where segments of plasma are trapped between red blood cells. The mathematical approach presented in this study can in principle be useful in the analysis of a wide class of closed-streamline creeping-flow problems.

Free surface convection in a bounded cylindrical geometry

Abstract Surface tension-driven convection and buoyancy-driven convection in a bounded cylindrical geometry with a free surface are studied for a range of aspect ratios and Nusselt numbers. Linear theory and some aspects of a nonlinear analysis are utilized to determine the critical Marangoni and Rayleigh numbers, the structure of the convective motion, the direction of flow, and the nature of the bifurcation branching. The analysis is based on a somewhat different method for treating free convection problems, the use of Greens functions to reduce the problem to the solution of an integral equation.

Step strain deformations for viscoelastic fluids : experiment

Shear stress and normal stress relaxation data were collected for a range of shear strains for a polystyrene–dibutyl phthalate solution. Data from single‐step shear strain experiments were used to test time–strain factorability and to check on the applicability of the Lodge–Meissner rule. Significant departures from time–strain factorability were found, but the shear and normal stress data were in excellent agreement with the Lodge–Meissner prediction. Data from double‐step shear strain experiments were used to check the predictions of the K–BKZ and Doi–Edwards theories. It was found that these theories do not generally provide adequate descriptions of double‐step shear strain deformations.

Entrance Flows of Non‐Newtonian Fluids

The creeping flow of a Powell‐Eyring fluid through a sudden tubular contraction is considered, and finite difference solutions of the vorticity transport and stream function equations are obtained for a range of contraction ratios, fluid properties, and apparent shear rates. Calculated axial velocity profiles, excess pressure drops, and separation effects at the 90° corner of the contraction are compared with theoretical results for Newtonian fluids and with experimental data for polymer solutions and melts. The results indicate a strong influence of nonlinear viscous effects on the magnitude of the excess entrance pressure loss and on the extent of the circulation pattern at the corner of the contraction.

Integral sorption in glassy polymers

A new theory is developed for integral sorption and desorption processes in glassy polymers. The theory can describe both case II diffusion and the classical case of Fickian diffusion. Predictions of the theory are compared with general experimental observations.