Richard A. Cairncross

A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Computational fluid mechanics techniques for examining free surface problems in two-dimensional form are now well established. Extending these methods to three dimensions requires a reconsideration of some of the difficult issues from two-dimensional problems as well as developing new formulations to handle added geometric complexity. This paper presents a new finite element formulation for handling three-dimensional free surface problems with a boundary-fitted mesh and full Newton iteration, which solves for velocity, pressure, and mesh variables simultaneously. A boundary-fitted, pseudo-solid approach is used for moving the mesh, which treats the interior of the mesh as a fictitious elastic solid that deforms in response to boundary motion. To minimize mesh distortion near free boundary under large deformations, the mesh motion equations are rotated into normal and tangential components prior to applying boundary conditions. The Navier–Stokes equations are discretized using a Galerkin–least square/pressure stabilization formulation, which provides good convergence properties with iterative solvers. The result is a method that can track large deformations and rotations of free surface boundaries in three dimensions. The method is applied to two sample problems: solid body rotation of a fluid and extrusion from a nozzle with a rectangular cross-section. The extrusion example exhibits a variety of free surface shapes that arise from changing processing conditions. Copyright

Optimization of single-zone drying of polymer solution coatings using mathematical modeling

Optimal conditions for drying polymer–solvent coatings result from a trade-off between minimizing the residual solvent level and creating defects. This article describes an application of automated constrained optimization with a detailed mathematical drying model to find the optimal drying conditions for a prototypical coating in a single-zone oven. The optimization process seeks oven conditions that minimize the residual solvent level for a fixed oven residence time without boiling the solvent within the coating. The optimal oven conditions include the air temperature and coating-side and substrate-side heat-transfer coefficients. The conditions are constrained to physically reasonable values. According to our results, the optimal coating-side heat-transfer coefficient is always equal to or greater than the optimal substrate-side heat-transfer coefficient.

Moisture Sorption, Transport, and Hydrolytic Degradation in Polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.

COMPETING DRYING AND REACTION MECHANISMS IN THE FORMATION OF SOL-TO-GEL FILMS, FIBERS, AND SPHERES

ABSTRACT Drying of films, fibers, and spheres undergoing sol-to-gel transformation is greatly affected by the strong dependence of the diffusion coefficients on composition, molecular weight, and temperature. This dependence is probed by solving the equations of mass and heat transfer by diffusion or conduction and associated convection, along with chemical reaction. A one-dimensional analysis is used that encompasses the planar, cylindrical, and spherical configurations. The solutions are obtained by Galerkins method with finite element basis functions and entail large-scale computation. Skinning and solidification phenomena in silica sol-to-gel systems are greatly affected not only by falling diffusion coefficients, but also by the competition between drying and reaction. The kinetics of silica reactions are modeled with the statistical scheme of Kay and Assink (1988). Gelation is predicted by the recursive technique of Bailey et al. (1990). Results show that at intermediate reaction rates, high molecu...

Anomalous behavior during leveling of thin coating layers with surfactant

Our recently‐published linear analysis [Schwartz et al., Langmuir 11, 3690 (1995)] demonstrated that an initially rippled thin layer of Newtonian liquid with uniformly distributed surfactant may level in unexpected ways. While the presence of surfactant will, in general, slow the rate of leveling compared to that of a perfectly clean system, there was shown to exist a realistic parameter range where increasing, rather than reducing, the amount of surfactant present will hasten leveling. Here, for the two‐dimensional problem, we investigate the importance of nonlinearity though numerical solution of (i) the unsteady lubrication form of the evolution equations with surfactant, and (ii) finite‐element solution of the exact governing equations for slow viscous flow. Confirmation of the linear results is demonstrated and quantitative discrepancy only appears for large‐amplitude and short‐wavelength ripples. Surface tension gradient driven flow explains the anomalies; for moderate surfactants, the surface quick...

Liquid water transport in polylactide homo and graft copolymers

The successful design of new biodegradable, renewable resource plastics as replacements to commodity barrier plastics would benefit from an accurate measurement of sorption and diffusion of liquids. In this study, the diffusion of liquid water in amorphous polylactide [PLA] and a PLA graft copolymer, poly(1,5-cyclooctadiene-co-5-norbornene-2-methanol-graft-dl-lactide) [PCNL], was examined with time-resolved Fourier transform infrared attenuated total reflectance (FTIR-ATR) spectroscopy. Non-Fickian behavior was observed for all experiments, indicated by a slow approach to steady state due to diffusion and polymer relaxation occurring on similar time scales. This non-Fickian behavior highlights the variability of the sorption isotherms reported in the literature, where others have collected nonequilibrium sorption behavior (instead of true steady-state equilibrium sorption) at different time points and film thicknesses. The dynamic infrared data provided direct evidence for both water diffusion and water-induced polymer relaxation, where both were quantified and regressed to a diffusion-relaxation model to determine the diffusion coefficient and the polymer relaxation time constant. In addition to the successful measurement and modeling of the diffusion-relaxation phenomena for diffusion of a liquid in a nonequilibrium state glassy polymer, this study also determined that the diffusivity of water in the PLA graft copolymer (with only 5 wt % rubber) was 3-fold lower than in the PLA homopolymer.

Sol—gel derived ceramic films — fundamentals and applications

Sol-gel processing begins with a colloidal dispersion, or sol, of particles or polymers in a liquid. Through subsequent chemical cross-linking, electrostatic destabilization, evaporation or some combination thereof, the fluid sol may be transformed into a rigid gel, which is a substance containing a continuous solid skeleton enclosing a continuous liquid phase. This sol-to-gel transition allows the solid phase to be shaped into films, fibers, microspheres or monoliths. Of these various forms, amorphous (or partially crystalline) thin films represent the earliest commercial application of sol-gel technology [1]. Thin films (normally less than 1 μm in thickness) use little in the way of raw materials and may be processed without cracking, overcoming the major disadvantage of sol-gel processing of bulk materials. Early applications of sol-gel coatings as optical films were reviewed by Schroeder [2]. Since then, many new uses of sol-gel films have appeared in electronic, protective, membrane and sensor applications [3–15]. Most often the as-deposited films are amorphous, but depending on composition and thermal history, they may subsequently crystallize: ferroelectric PLZT (lead lanthanum zirconate titanate) and nonlinear optic LiNbO3 are excellent examples of crystalline films derived from amorphous precursors [16–18].

Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results

Many practically relevant polymers undergoing desorption change from the rubbery (saturated) to the glassy (nearly dry) state. The dynamics of such systems cannot be described by the simple Fickian diffusion equation due to viscoelastic effects. The mathematical model solved numerically is a set of two coupled PDEs for concentration and stress. Asymptotic solutions are presented for a moving boundary-value problem for the two states in the short-time limit. The solutions exhibit desorption overshoot, where the penetrant concentration in the interior is less than that on the surface. In addition, it is shown that if the underlying time scale of the equations is ignored when postulating boundary conditions, nonphysical solutions can result.

Life-Cycle Assessment of Biodiesel Produced from Grease Trap Waste

Grease trap waste (GTW) is a low-quality waste material with variable lipid content that is an untapped resource for producing biodiesel. Compared to conventional biodiesel feedstocks, GTW requires different and additional processing steps for biodiesel production due to its heterogeneous composition, high acidity, and high sulfur content. Life-cycle assessment (LCA) is used to quantify greenhouse gas emissions, fossil energy demand, and criteria air pollutant emissions for the GTW-biodiesel process, in which the sensitivity to lipid concentration in GTW is analyzed using Monte Carlo simulation. The life-cycle environmental performance of GTW-biodiesel is compared to that of current GTW disposal, the soybean-biodiesel process, and low-sulfur diesel (LSD). The disposal of the water and solid wastes produced from separating lipids from GTW has a high contribution to the environmental impacts; however, the impacts of these processed wastes are part of the current disposal practice for GTW and could be excluded with consequential LCA system boundaries. At lipid concentrations greater than 10%, most of the environmental metrics studied are lower than those of LSD and comparable to soybean biodiesel.

OPTIMIZATION OF SINGLE-ZONE DRYING OF POLYMER SOLUTION COATINGS TO AVOID BLISTER DEFECTS

ABSTRACT The optimal conditions for drying polymer-solvent coatings result from a trade-off between minimizing the residual solvent level and creating defects. Blistering defects can be caused by boiling the solvent within the coating. In this paper, we use a detailed drying model with automated constrained optimization to find optimal drying conditions for prototypical coatings that minimize the residual solvent without blistering the coating. The drying oven is assumed to have a single zone with fixed residence time. The optimal drying conditions include the oven air temperature and substrate-side and coating-side heat transfer coefficients The latter are constrained to physically reasonable values. According to our results, the optimal coating-side heat transfer coefficient is always equal to or greater than the optimal substrate-side heat transfer coefficient.