Drying of Polymeric and Solid Materials

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.