Multi-Zone Drying Schemes for Lowering the Residual Solvent Content during Multi-Component Drying of Semicrystalline Polymers

The development of a glassy skin in multicomponent semicrystalline polymer systems limits the diffusion of solvents out of the system and increases residual solvent levels. Based on the results of a mathematical model that we had previously developed, we have proposed a multi-zone drying scheme aimed at lowering the residual solvent levels by taking into account the effect of interactions between the various solvents as predicted by the model. This article focuses on the application of this model to develop optimal drying schemes and to verify the effectiveness of these predictions using experimental techniques. The mathematical model developed previously to study the diffusion of multiple solvents and changes in the crystallinity of semicrystalline polymer systems during drying incorporates many features including Vrentas-Duda diffusion theory, solvent-induced crystallization kinetics, as well as glass transition effects and skinning of the film. The multi-zone drying system was developed by varying the drying temperature in each zone as well as changing the partial pressure of individual solvents during the drying process. The effectiveness of the multi-zone drying schemes predicted by the model was validated experimentally using thermogravimetric methods. The polymer-solvent system chosen was a poly(vinyl alcohol)-water-methanol system. Our experimental data suggested that the multi-zone drying schemes were superior to a single-zone drying system through direct comparison. Further examination of the mathematical model yielded individual solvent profiles and these data reaffirmed our conclusions that a multi-zone drying scheme has the ability to reduce the effect of solvent trapping and thus lower the overall residual solvent content.     

Drying of semicrystalline polymers: mathematical modeling and experimental characterization of poly(vinyl alcohol) films

A mathematical model was developed to predict the drying mechanism of semicrystalline polymers involving multiple solvents. Since drying of semicrystalline polymers can be accompanied by changes in polymer degree of crystallinity, the model integrates crystallization kinetics and the Vrentas-Duda diffusion model to provide a better understanding of the mechanism. The model considers the effect of external conditions such as temperature, film shrinkage and diffusion and evaporation of multiple solvents during drying. Poly(vinyl alcohol) (PVA)/water/methanol was chosen as a test system. The drying kinetics of PVA films swollen in water and methanol were investigated using gravimetric techniques. The model predicts that higher temperatures, lower film thicknesses and lower methanol to water ratios increase the drying rate. The model predictions were compared with experimental data and showed good agreement.     

反相气相色谱法测定小分子溶剂在聚乙烯粒子中的无限稀释扩散系数

基于经典线性非平衡色谱过程的矩分析理论,用反相气相色谱法测定了323.15～358.15 K温度范围内二氯甲烷、三氯甲烷、四氯甲烷3种不同相对分子量的同系物小分子及正己烷在聚乙烯粒子中的无限稀释扩散系数。采用聚合物粒子直接填充的色谱柱,考察了温度、同系物小分子分子量及聚乙烯结晶度对扩散系数的影响。实验结果表明,对同一种小分子溶剂/聚乙烯体系,扩散系数均随温度升高而增大。不同相对分子量的同系物小分子在同一种聚乙烯中扩散系数随分子量增加而减小,聚乙烯结晶度增加也会导致扩散系数减小。采用文献中所报道的Krevelen扩散系数预测模型的计算值与实验测量值较为吻合,表明本文所采用的以聚合物粒子直接填充色谱柱的反相气相色谱扩散分析具有一定的可靠性。     

Drying of a system of multiple solvents: Modeling by the reaction engineering approach

Drying is a very important industrial operation in society. In drying, solute may dissolve in an aqueous solvent, a nonaqueous solvent or a mixture of solvents. Many mathematical models have been published previously to model drying of solute in water. The reaction engineering approach (REA) is known to be an easy‐to‐use approach. It can describe well many drying cases of water removal. Currently, no simple lumped model has been attempted to describe drying of porous materials containing a mixture of solvents. In this study, for the first time, REA is constructively implemented to model drying in a mixture of one aqueous and one nonaqueous solvent. The REA is applied here to model the drying of polyvinyl alcohol/methanol/water under constant and time‐varying environmental conditions. Similar to the relative activation energy of water, that of methanol is generated through one accurate drying run. For modeling the time‐varying drying, the relative activation energies are the same as those for modeling convective drying under constant ambient conditions but combined with the equilibrium activation energies at the corresponding humidity, methanol concentration, and temperature for each drying period. The REA is accurate to model drying of a solute in nonaqueous solvent as well as in a mixture of noninteracting solvents. In the future, spatially distributed REA for nonaqueous or mixtures of both aqueous and nonaqueous solvent will be explored for fundamental understanding and for practical application. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2144–2153, 2016     

Prediction of diffusion in a ternary solvent–solvent–polymer blend by means of binary diffusion data: Comparison of experimental data and simulative results

Multicomponent diffusion of solvents in polymeric systems is not completely understood, despite many scientific contributions to the topic. Literature scarcely offers measurement data on diffusion for model validation in such systems. In this work, the ternary systems consisting of poly(vinyl acetate) and the solvents toluene and methanol was investigated experimentally and numerically. By means of inverse micro Raman spectroscopy (IMRS) concentration gradients in drying thin films have been measured. Initial composition of the samples has been varied systematically in order to detect mutual influence of the solvents' diffusive behavior. It was shown that the mobility of the different species is increased in the presence of other solvents as predicted by theory. This experimental data is provided for model validation. A new expression to calculate the diffusion coefficients in ternary mixtures is proposed which only requires binary data. This expression is tested by means of a model‐based simulation to predict the drying of ternary polymer solutions in terms of concentration profiles and residual solvent content. The results are in very good agreement with the experiments. Cross terms diffusion coefficients and thermodynamic factors were not found to be necessary for a satisfying prediction. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43899.     

Mechanism of bubble formation in the drying of polymer films

A common problem in making thin polymer films by solution processing is the undesirable formation of bubbles during the drying process. These bubbles appear well below the boiling point of the solvent. Experience indicates, however, that the degassing of the polymer solutions reduces bubble formation, indicating a relationship with the presence of air. This work is based on a hypothesis that if the solubility of air in the polymer solution increases with solvent concentration, then the solution can become supersaturated with air as the concentration of the solvent is reduced during the drying process. To test this hypothesis the system poly(vinyl acetate)‐toluene‐nitrogen was chosen. Previously published data on the solubility and diffusion of nitrogen in the polymer‐solvent system were used. Different diffusion models based on the friction coefficients and free‐volume model were then used to correlate the diffusivity data so that the diffusion behavior of the ternary system can be predicted over a broad range of conditions. Finally, the thermodynamic and diffusivity correlations were incorporated into a multicomponent drying model which included main and cross‐diffusion terms to predict saturation behavior in the polymer solution during the drying process. The model without the cross‐diffusion terms represents the ideal system in which the diffusion of one component does not affect the diffusion of others. The drying model did not predict supersaturation of nitrogen when cross‐diffusion terms were neglected. Supersaturation of nitrogen was predicted, however, when the cross‐diffusion terms are included. Therefore, the cross‐diffusion terms in the mass transfer model are essential for the development of nitrogen supersaturation. Also different diffusion models based on the friction coefficients led to qualitatively similar predictions for the supersaturation of nitrogen. The simulation's results supported our experimental observations regarding bubble formation. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Microwave-Vacuum Drying of Pharmaceutical Powders

Due to their temperature sensitive nature, many pharmaceutical products are dried under vacuum to facilitate solvent evaporation at reduced temperatures. However, this necessitates long drying times and represents a processing bottleneck. Microwave heating of such materials at reduced pressures offers a more rapid method of moisture removal, without the risk of product damage. Within this study, the effect of vacuum on the rate of solvent evaporation was investigated, using a range of powders (pharmaceutical actives Paracetamol and Aspirin, and a range of bulk excipients) and solvents including water, ethanol, methanol, and acetone. In general, drying rate increased as system pressure decreased, however, the magnitude and duration was system specific. As expected, the diffusion coefficient decreased from the first to the second falling rate period, with the diffusivity in each drying period increasing with increased vacuum. The findings in this research have significant implications for drying operations in the pharmaceutical industry.     

Microwave-Vacuum Drying of Pharmaceutical Powders

Abstract

Due to their temperature sensitive nature, many pharmaceutical products are dried under vacuum to facilitate solvent evaporation at reduced temperatures. However, this necessitates long drying times and represents a processing bottleneck. Microwave heating of such materials at reduced pressures offers a more rapid method of moisture removal, without the risk of product damage. Within this study, the effect of vacuum on the rate of solvent evaporation was investigated, using a range of powders (pharmaceutical actives Paracetamol and Aspirin, and a range of bulk excipients) and solvents including water, ethanol, methanol, and acetone. In general, drying rate increased as system pressure decreased, however, the magnitude and duration was system specific. As expected, the diffusion coefficient decreased from the first to the second falling rate period, with the diffusivity in each drying period increasing with increased vacuum. The findings in this research have significant implications for drying operations in the pharmaceutical industry.     

Transition between Condensing and Air Flow Drying of Thin-Film Coatings

The transport characteristics were investigated in the bench-top condenser dryer, which is a new and air-free drying system for advanced coating applications. The measured solvent drying rate agrees with the one-dimensional diffusion theory in the early drying stages, showing the validity of the previously proposed diffusion models in a quantitative sense. The combination of the condenser dryer with the air flow system revealed a characteristic transition in the diffusion kinetics between the convection-drying and the condensing-drying regimes. The drying of immiscible ternary solution coatings showed a transition in the phase-separated morphologies from the isolated droplets to the elongated stripe patterns.     

Transition between Condensing and Air Flow Drying of Thin-Film Coatings

The transport characteristics were investigated in the bench-top condenser dryer, which is a new and air-free drying system for advanced coating applications. The measured solvent drying rate agrees with the one-dimensional diffusion theory in the early drying stages, showing the validity of the previously proposed diffusion models in a quantitative sense. The combination of the condenser dryer with the air flow system revealed a characteristic transition in the diffusion kinetics between the convection-drying and the condensing-drying regimes. The drying of immiscible ternary solution coatings showed a transition in the phase-separated morphologies from the isolated droplets to the elongated stripe patterns.     

A Thermo-Hydro-Mechanics Bidirectional Coupling Mathematical Model for Drying of Biological Porous Medium

Based on Fickian diffusion theory, Fourier's law of heat conduction and thermoelasticity mechanics, a thermo-hydro-mechanics bidirectional coupling mathematical model has been developed to simulate the hot air convective drying of biological porous media. The transient model, composed of a system of partial differential equations, was solved by finite difference methods. The numerical results were compared with available experimental data obtained during the drying of potatoes. The numerical results obtained using the mathematical model were in good agreement with the experimental data. Numerical simulations of the drying curve variations and the spatio-temporal distributions of moisture, temperature, and drying stresses and strains were evaluated.     

Three-Layer Model for Drying of Coating Applied on Silicone-Coated Paper

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate.     

Drying of glassy polymer varnishes: A quartz resonator study

We report on desorption measurements on polymeric thin films coated onto quartz crystal resonators. Due to the high sensitivity of quartz crystal microbalances, the experiments can be performed on very thin films, which have small diffusion time constants even in the glassy state. When drying is performed slowly enough, diffusion equilibrium can be maintained through the whole process of desorption, including the glassy domain. From these quasi-stationary pressure ramps, we derived the solvent chemical potential as a function of polymer volume fraction μ(ϕ). The results fit well to a model recently proposed by Leibler and Sekimoto.¹ In addition, we have derived the mutual diffusion coefficient D(ϕ) from pressure step experiments. We observe a strong decrease of D(ϕ) for high polymer concentrations typical of hypodiffusive systems like polymers. We investigated the drying of an industrial varnish that is a blend of 2 copolymers as well as the drying of its components separately. Both the solvent chemical potential μ(ϕ) and the mutual diffusion coefficient D(ϕ) of the blend interpolate between the respective quantities of the components. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 2235–2246, 1998     

Three-Layer Model for Drying of Coating Applied on Silicone-Coated Paper

Abstract

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate.     

Mechanistic investigation of drying regimes during solvent removal from poly(vinyl alcohol) films

The mechanism of removal of solvents such as water and methanol from semicrystalline poly(vinyl alcohol) films was investigated using various thermal analysis techniques to obtain a mechanistic understanding of the drying process. Various drying regimes were identified, which correspond to different rate‐controlling steps, and characterized by differences in drying rates and mechanisms. The kinetics of solvent removal was measured gravimetrically using thermogravimetric analysis (TGA). The drying kinetics studies yielded four distinct drying regimes hypothesized to be due to (1) removal of free solvent, (2) elimination of bound solvent, (3) solvent removal during the rubbery‐glassy transition, and (4) drying when the polymer is in the glassy state. The amounts of free and bound water present in the polymer were measured using differential scanning calorimetry and compared with the TGA results, and they were found to verify the proposed hypothesis. The rubbery‐glassy transition observed in TGA results was confirmed using dynamic mechanical analysis. The thickness of the films was also measured as a function of drying time using thermomechanical analysis. The drying rate plots were found to be qualitatively similar to the plots of changes in film thicknesses as functions of drying time. The results of these various techniques were analyzed to propose a comprehensive mechanism of solvent removal from poly(vinyl alcohol) films. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 1913–1920, 1999     

Solvent‐induced crystal formation in polymers: Experimental studies and theoretical modeling of poly(vinyl alcohol) based on free‐volume concepts

A model has been developed to describe the simultaneous diffusion and solvent‐induced crystal formation in polymers based on the idea that crystal formation is governed by polymer chain mobility and a thermodynamic driving force. The polymer chain mobility is described based on solvent and polymer physical characteristics using the free‐volume theory of transport. The semicrystalline polymer‐solvent system is treated as a ternary system consisting of crystalline polymer, amorphous polymer, and solvent. The addition of solvent to the amorphous phase is assumed to increase the local free volume and facilitate movement of polymer chains, thereby enabling crystal formation. Diffusion of the solvent is assumed to occur solely in the amorphous polymer phase. The species continuity equations are formulated in volume‐averaged coordinates and give rise to a convective term due to the density change accompanying transformation of the amorphous polymer to the crystalline polymer. Accurate modeling of this problem requires that a moving boundary be considered. The model was tested using gravimetric sorption data for the poly(vinyl alcohol)‐water system. In the experimental studies, the water was initially absorbed and then a high percentage of it was expelled. The proposed model accurately describes this behavior. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45171.     

Constant and Intermittent Drying Characteristics of Olive Cake

The drying kinetics of olive cake, the solid by-product of the olive oil extraction process, has been experimentally investigated in a small-scale tray dryer using both constant and intermittent (on/off) heating schemes. The parameters investigated include inlet air temperature and intermittency of heat input. The drying kinetics was interpreted through two mathematical models, the Page equation and the Lewis equation. The Page equation was most appropriate in describing the drying behavior of olive cake. A diffusion model was used to describe the moisture transfer and the effective diffusion coefficient at each temperature was determined. The dependence of the effective diffusion coefficient on drying temperature can be adequately explained based on an Arrhenius-type relation. The effective diffusion coefficient varied between 7.6 × 10^-8 and 2.5 × 10^-7 m²/min with an activation energy of 38.55 kJ/mol. Comparison of time evolution of material moisture content due to intermittent and constant drying is also made.     

Migration during Convective Drying. I-Theoretical

A model is proposed which makes possible the mathematical treatment of the movement of solute resulting from the evaporation of solvent from the surface of a capillary network. It is considered useful in predicting the migration of solute in the capillaries of a textile material during the constant–rate period of convective drying. Within the limits of certain simplifying assumptions, the concentration depth profiles are defined as a function of time by the solution to the equation of Fick's second law of diffusion satisfying defined boundary conditions.     

Drying Simulation of a Solid Slab with Three Dimensional Shrinkage

ABSTRACT

A mathematical model is developed to simulate the drying of a hygroscopic porous solid. The model, based on the gradient of moisture concentration per unit volume as driving force, takes into account the migration of water within the solid by diffusion and the evaporation at the interface. A mathematical equation for diffusion in a slab with three dimensional shrinkage has been derived, assuming that the magnitude of shrinkage is equal to the volume of water evaporated. The resulting diffusion equation and the heat balance eauation for infinite thermal conductivitv were solved n;merically with temperature dependent diffusion coefficient and convective boundary conditions. The deDendence of the desorption isotherm with temperature is-also considered. corndination of all these factors in a single model provides a tool that is effective in predictinq dryinq behavior and also useful in exploring and understanding the impact of important variables on the drying process.     

R&D Needs in the Drying of Coatings

The key technologies involved in the drying of coatings are first reviewed and then the factors that influence the drying process are identified, leading to a discussion uf future R&D needs. The drying mechanisms in the constant and falling rate periods are discussed. Present and nticipated estrictions on the use of solvents will result in aqueous systems replacing some solvent systems. and in wider use of high solids coatings and 100% solids coatings. Cross-linking reactions to solidify monomers and low-molecular polymers now become important. Dryers will become chemical reactors. Further development of models of drying, of diffusion, of surface solvent levels, and of solvent vapor pressures will be needed, along with those of dryer defects and drying stresses. To accurately simulate a wide range of coating systems more physical property data is needed. Nan-convection heating and environmental concerns complete the discussion.