Drying of Polymeric and Solid Materials : Modelling and Industrial Applications

Drying of Polymeric and Solid Materials shows for the first time how the process of drying can be enhanced by combining mathematical and numerical models with experiments. The main advantages of this method are a significant saving of time and money. Numerical modelling can predict the kinetics of drying and the profiles of liquid concentration through the solid. This helps in the selection of optimal operational conditions. The simulation of the process is also crucial in the assessment of diffusity and the rate of evaporation.

1 Principles and General Equations.- 1.1 Transport of Liquid Through a Solid.- 1.1.1 Polymers.- 1.1.2 Wood Materials.- 1.1.3 Basic Equations of Diffusion (Fick’s Laws).- 1.2 Evaporation of Liquid from the Surface.- 1.2.1 Infinite Rate of Evaporation.- 1.2.2 Finite Rate of Evaporation.- 1.3 Diffusion of Vapour Outside the Solid.- 1.4 Effect of Parameters.- 1.4.1 Dimensions of the Grain.- 1.4.2 Nature of the Solid and Liquid.- 1.4.3 Shape of the Solid.- 1.4.4 Surrounding Atmosphere.- 1.4.5 Temperature.- 1.5 General Equations.- 1.5.1 Operational Conditions.- 1.5.2 Differential Equation of Diffusion.- 1.5.3 Equation of Evaporation.- Symbols.- 2 Thin Plane Sheet.- 2.1 Non-steady State with Infinite Rate of Evaporation.- 2.1.1 Infinite Atmosphere with Uniform Initial Concentration of Liquid.- 2.1.2 Layer of Diffusing Substance Deposited on a Permeable Sheet.- 2.1.3 Layer of Diffusing Substance Located Between Two Permeable Sheets.- 2.1.4 Finite Atmosphere with Constant Diffusivity.- 2.2 Non-steady State with Finite Rate of Evaporation.- 2.3 Membrane Suspended in an Infinite Atmosphere.- 2.3.1 Transient Conditions with Infinite Rate of Evaporation.- 2.3.2 Steady-State Conditions with Infinite Rate of Evaporation.- 2.3.3 Composite Membrane Under Steady-State Conditions with Infinite Rate of Evaporation.- 2.3.4 Steady-State Conditions with Constant Concentration on One Surface and Finite Rate of Evaporation on the Other.- 2.4 Conclusions.- 2.4.1 Edge Effects.- 2.4.2 Constant Diffusivity.- 2.4.3 Effect of the Volume of the Surrounding Atmosphere.- 2.4.4Effect of the Rate of Evaporation.- Appendixes. Methods of Solution of Fick’s Law When the Diffusivity is Constant.- 2. A Separation of Variables.- 2.B Diffusion-Evaporation From a Plane Sheet of Thickness L, with Infinite Rate of Evaporation.- 2.C Half-Life of Desorption Process.- 2.D Reflection and Superposition.- 2.E Error Function.- 2.F Layer of Diffusing Substance on a Permeable Sheet, with Infinite Rate of Evaporation.- 2.G Membrane with Constant Concentration on Each Surface, and Infinite Rate of Evaporation.- Symbols.- 3 Cylinder.- 3.1 Solid Cylinder of Infinite Length, Non-steady State with Constant Diffusivity.- 3.1.1 Infinite Atmosphere with Infinite Rate of Evaporation.- 3.1.2 Finite Atmosphere with Infinite Rate of Evaporation.- 3.1.3 Infinite Atmosphere with Finite Rate of Evaporation.- 3.2 Cylinder of Finite Length, Non-steady State.- 3.2.1 Infinite Atmosphere with Infinite Rate of Evaporation.- 3.2.2 Infinite Atmosphere with Finite Rate of Evaporation.- 3.3 Liquid-Filled Hollow Cylinder of Infinite Length, Steady State.- 3.3.1 Infinite Atmosphere with Infinite Rate of Evaporation.- 3.3.2 Infinite Atmosphere with Finite Rate of Evaporation.- 3.4 Conclusions.- Appendix. Radial Diffusion in a Solid Cylinder of Infinite Length with Infinite Rate of Evaporation.- 4 Sphere.- 4.1 Solid Sphere, Non-steady State with Infinite Rate of Evaporation.- 4.1.1 Infinite Atmosphere.- 4.1.2 Finite Atmosphere.- 4.2 Solid Sphere, Non-steady State with Finite Rate of Evaporation.- 4.3 Liquid-Filled Hollow Sphere.- 4.3.1 Non-steady State with Infinite Rate of Evaporation...- 4.3.2 Steady State with Infinite Rate of Evaporation.- 4.3.3 Steady State with Finite Rate of Evaporation.- 4.4 Conclusions.- Symbols.- 5 Numerical Analysis for a Plane Sheet.- 5.1 Infinite Rate of Evaporation.- 5.1.1 Constant Diffusivity.- 5.1.2 Concentration-Dependent Diffusivity.- 5.2 Finite Rate of Evaporation.- 5.2.1 Constant Diffusivity.- 5.2.2 Concentration-Dependent Diffusivity.- 5.3 Conclusions.- Symbols.- 6 Numerical Analysis for a Cylinder.- 6.1 Solid Cylinder of Infinite Length with Infinite Rate of Evaporation.- 6.1.1 Constant Diffusivity.- 6.1.2 Concentration-Dependent Diffusivity.- 6.2 Solid Cylinder of Infinite Length with Finite Rate of Evaporation.- 6.2.1 Constant Diffusivity.- 6.2.2 Concentration-Dependent Diffusivity.- 6.3 Solid Cylinder of Finite Length with Infinite Rate of Evaporation.- 6.3.1 Constant Diffusivity.- 6.3.2 Concentration-Dependent Diffusivity.- 6.4 Solid Cylinder of Finite Length with Finite Rate of Evaporation.- 6.4.1 Constant Diffusivity.- 6.4.2 Concentration-Dependent Diffusivity.- 6.5 Liquid-Filled Hollow Cylinder of Infinite Length with Infinite Rate of Evaporation.- 6.5.1 Constant Diffusivity.- 6.5.2 Concentration-Dependent Diffusivity.- 6.6 Liquid-Filled Hollow Cylinder of Infinite Length with Finite Rate of Evaporation.- 6.6.1 Constant Diffusivity.- 6.6.2 Concentration-Dependent Diffusivity.- 6.7 Liquid-Filled Hollow Cylinder of Finite Length with Infinite Rate of Evaporation.- 6.7.1 Constant Diffusivity.- 6.7.2 Concentration-Dependent Diffusivity.- 6.8 Liquid-Filled Hollow Cylinder of Finite Length with Finite Rate of Evaporation.- 6.8.1 Constant Diffusivity.- 6.8.2 Concentration-Dependent Diffusivity.- 6.9 Conclusions.- Symbols.- 7 Numerical Analysis for a Sphere.- 7.1 Solid Sphere with Infinite Rate of Evaporation.- 7.1.1 Constant Diffusivity.- 7.1.2 Concentration-Dependent Diffusivity.- 7.2 Solid Sphere with Finite Rate of Evaporation.- 7.2.1 Constant Diffusivity.- 7.2.2 Concentration-Dependent Diffusivity.- 7.3 Liquid-Filled Hollow Sphere with Infinite Rate of Evaporation.- 7.3.1 Constant Diffusivity.- 7.3.2 Concentration-Dependent Diffusivity.- 7.4 Liquid-Filled Hollow Sphere with Finite Rate of Evaporation.- 7.4.1 Constant Diffusivity.- 7.4.2 Concentration-Dependent Diffusivity.- 7.5 Conclusions.- Symbols.- 8 Diffusion-Evaporation in Two and Three Dimensions: Isotropic and Anisotropic Media.- 8.1 Introduction.- 8.1.1 Isotropic Medium.- 8.1.2 Anisotropic Medium.- 8.2 Two Dimensions with Infinite Rate of Evaporation.- 8.2.1 Constant Diffusivity.- 8.2.2 Concentration-Dependent Diffusivity.- 8.3 Two Dimensions with Finite Rate of Evaporation.- 8.3.1 Constant Diffusivity.- 8.3.2 Concentration-Dependent Diffusivity.- 8.4 Three Dimensions with Infinite Rate of Evaporation.- 8.4.1 Constant Diffusivity.- 8.4.2 Concentration-Dependent Diffusivity.- 8.5 Three Dimensions with Finite Rate of Evaporation.- 8.5.1 Constant Diffusivity.- 8.5.2 Concentration-Dependent Diffusivity.- 8.6 Conclusions ..- Symbols.- 9 Drying of Paints.- 9.1 Introduction.- 9.2 One Layer.- 9.2.1 Theory.- 9.2.2 Experiment.- 9.2.3 Results.- 9.3 Two Layers.- 9.3.1 Theory.- 9.3.2 Experiment.- 9.3.3 Results.- 9.4 Conclusions.- Symbols.- 10 Drying of Wet Earth for Adobe Construction.- 10.1 Introduction.- 10.2 Modelling the Drying of Wet Earth.- 10.2.1 Theory.- 10.2.2 Experiment.- 10.2.3 Results.- 10.3 Conclusions.- Symbols.- 11 Drying of Rubbers.- 11.1 Introduction.- 11.2 Thin Sheets.- 11.2.1 Theory.- 11.2.2 Experiment.- 11.2.3 Results.- 11.2.4 Conclusions.- 11.3 Cylinders of Finite Length.- 11.3.1 Theory.- 11.3.2 Experiment.- 11.3.3 Results.- 11.3.4 Conclusions.- 11.4 Tubes of Infinite Length.- 11.4.1 Theory.- 11.4.2 Experiment.- 11.4.3 Results.- 11.4.4 Conclusions.- 11.5 Annuli.- 11.5.1 Theory.- 11.5.2 Experiment.- 11.5.3 Results.- 11.5.4 Conclusions.- 11.6 Conclusions of the Drying of Rubbers.- Symbols.- 12 Drying of Plasticised PVC.- 12.1 Introduction.- 12.2 Drying Process.- 12.2.1 Theory.- 12.2.2 Experiment.- 12.2.3 Results for Immersion.- 12.2.4 Results for Drying.- 12.3 Conclusions.- Symbols.- 13 Drying of Wood.- 13.1 Introduction.- 13.2 Thin Sheets.- 13.2.1 Theory.- 13.2.2 Experiment.- 13.2.3 Results for Moisture Content Below FSP.- 13.2.4 Results for Moisture Content Above FSP.- 13.2.5 Conclusions.- 13.3 Diffusion-Evaporation in Two Dimensions.- 13.3.1 Theory.- 13.3.2 Experiment.- 13.3.3 Results for Transverse-Transverse Drying.- 13.3.4 Results for Longitudinal-Radial Drying.- 13.3.5 Conclusions.- 13.4 Diffusion-Evaporation in Three Dimensions.- 13.4.1 Theory.- 13.4.2 Experiment.- 13.4.3 Results for a Sheet.- 13.4.4 Results for a Block.- 13.4.5 Conclusions.- Symbols.- 14 Drying of Thermosetting Coatings.- 14.1 Introduction.- 14.2 Drying Process.- 14.2.1 Theory.- 14.2.2 Experiment.- 14.2.3 Results.- 14.3 Conclusions.- Symbols.- 15 Drying of Dosage Forms for Medical Applications.- 15.1 Introduction.- 15.2 Drying in an Infinite Atmosphere.- 15.2.1 Theory.- 15.2.2 Experiment.- 15.2.3 Results.- 15.2.4 Effect of Temperature.- 15.3 Drying in an Finite Atmosphere.- 15.3.1 Theory.- 15.3.2 Experiment.- 15.3.3 Results.- 15.4 Drying Under Controlled Vapour Pressure.- 15.4.1 Theory.- 15.4.2 Simulation Using a Numerical Model.- 15.5 Conclusions.- Symbols.- 16 Drying of a Polymer Sphere with Shrinkage.- 16.1 Introduction.- 16.2 Theory.- 16.3 Experiment.- 16.4 Results.- 16.5 Conclusions.- Symbols.