Mathematical modelling of the drying of sol gel microspheres

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

Mixing and drying mud and ash at Tully Mill

Disposal of mud and ash, particularly in wet weather conditions, is a significant expense for mills. This paper reports on part of a process to pelletise mud and ash, aimed at making mud and ash more attractive to growers across entire mill districts. The full process and the re-constituting and centrifuging rotary vacuum filter mud part of the process were described in two papers to the 2011 conference. The component described in this paper involves aspects of mixing mud and ash with subsequent drying using boiler exit gas. The mud material needs to mix easily with boiler ash and the mixture has to feed easily into and be pneumatically conveyed by a flue gas dryer. The performance of a pilot flue gas dryer for drying mud and ash was evaluated. The mud and ash mixture was found to dry much faster than final bagasse, provided the mud and ash material was broken up into individual particles. A previously developed computer model of bagasse drying was updated to take into account the smaller particle size of the mud and ash mixture. This upgraded model predicted the performance of the pilot flue gas dryer well.

The hygienic efficacy of different hand-drying methods : a review of the evidence

The transmission of bacteria is more likely to occur from wet skin than from dry skin; therefore, the proper drying of hands after washing should be an integral part of the hand hygiene process in health care. This article systematically reviews the research on the hygienic efficacy of different hand-drying methods. A literature search was conducted in April 2011 using the electronic databases PubMed, Scopus, and Web of Science. Search terms used were hand dryer and hand drying. The search was limited to articles published in English from January 1970 through March 2011. Twelve studies were included in the review. Hand-drying effectiveness includes the speed of drying, degree of dryness, effective removal of bacteria, and prevention of cross-contamination. This review found little agreement regarding the relative effectiveness of electric air dryers. However, most studies suggest that paper towels can dry hands efficiently, remove bacteria effectively, and cause less contamination of the washroom environment. From a hygiene viewpoint, paper towels are superior to electric air dryers. Paper towels should be recommended in locations where hygiene is paramount, such as hospitals and clinics.

Intermittent drying of food products : a critical review

Drying is very energy intensive process and consumes about 20-25% of the energy used by food processing industry. The energy efficiency of the process and quality of dried product are two key factors in food drying. Global energy crisis and demand for quality dried food further challenge researchers to explore innovative techniques in food drying to address these issues. Intermittent drying is considered one of the promising solutions for improving energy efficiency and product quality without increasing the capital cost of the drier. Intermittent drying has already received much attention. However, a comprehensive review of recent progresses and overall assessment of energy efficiency and product quality in intermittent drying is lacking. The objective of this article is to discuss, analyze and evaluate the recent advances in intermittent drying research with energy efficiency and product quality as standpoint. Current available modelling techniques for intermittent drying are reviewed and their merits and demerits are analyzed. Moreover, intermittent application of ultrasound, infrared (IR) and microwave in combined drying technology have been reviewed and discussed. In this review article the gaps in the current literature are highlighted, some important future scopes for theoretical and experimental studies are identified and the direction of further research is suggested.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Influence of atmospheric sublimation and evaporation on the heat pump fluid bed drying of bovine intestines

Experiments on atmospheric two-stage fluidized bed drying of bovine intestines with heat pump were carried out. The investigation covers innovative fluidized bed heat pump drying of bovine intestines. The two-stage drying consists of atmospheric moisture sublimation immediately followed by evaporation. Studies were done to establish the influence of the drying condition on the drying characteristics and product quality of bovine intestines and properties focusing on kinetics, diffusion, and color. The investigation of the drying characteristics has been conducted during moisture removal by evaporation and combined sublimation and evaporation. The effect of drying temperature on the drying constants was determined by fitting the experimental data using regression analysis techniques. The investigation revealed that the drying kinetics is most significantly affected by temperature. Correlations expressing the drying constants and effective moisture diffusivity dependence on the drying conditions are reported.

Modeling heat and mass transfer process during convection drying of fruit

Fruit drying is a process of removing moisture to preserve fruits by preventing microbial spoilage. It increases shelf life, reduce weight and volume thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. But, it is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the material. In this background, the aim of this paper to develop a mathematical model to simulate coupled heat and mass transfer during convective drying of fruit. This model can be used predict the temperature and moisture distribution inside the fruits during drying. Two models were developed considering shrinkage dependent and temperature dependent moisture diffusivity and the results were compared. The governing equations of heat and mass transfer are solved and a parametric study has been done with Comsol Multiphysics 4.3. The predicted results were validated with experimental data.

A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying

A coupled SPH-DEM based two-dimensional (2-D) micro-scale single cell model is developed to predict basic cell-level shrinkage effects of apple parenchyma cells during air drying. In this newly developed drying model, Smoothed Particle Hydrodynamics (SPH) is used to model the low Reynolds Number fluid motions of the cell protoplasm, and a Discrete Element Method (DEM) is employed to simulate the polymer-like cell wall. Simulations results reasonably agree with published experimental drying results on cellular shrinkage properties such as cellular area, diameter and perimeter. These preliminary results indicate that the model is effective for the modelling and simulation of apple parenchyma cells during air drying.

A particle-based micromechanics approach to simulate structural changes of plant cells during drying

This paper is concerned with applying a particle-based approach to simulate the micro-level cellular structural changes of plant cells during drying. The objective of the investigation was to relate the micro-level structural properties such as cell area, diameter and perimeter to the change of moisture content of the cell. Model assumes a simplified cell which consists of two basic components, cell wall and cell fluid. The cell fluid is assumed to be a Newtonian fluid with higher viscosity compared to water and cell wall is assumed to be a visco-elastic solid boundary located around the cell fluid. Cell fluid is modelled with Smoothed Particle Hydrodynamics (SPH) technique and for the cell wall; a Discrete Element Method (DEM) is used. The developed model is two-dimensional, but accounts for three-dimensional physical properties of real plant cells. Drying phenomena is simulated as fluid mass reductions and the model is used to predict the above mentioned structural properties as a function of cell fluid mass. Model predictions are found to be in fairly good agreement with experimental data in literature and the particle-based approach is demonstrated to be suitable for numerical studies of drying related structural deformations. Also a sensitivity analysis is included to demonstrate the influence of key model parameters to model predictions.

Multiphysics modelling of convective drying of food materials

Currently, 1.3 billion tonnes of food is lost annually due to lack of proper processing and preservation method. Drying is one of the easiest and oldest methods of food processing which can contribute to reduce that huge losses, combat hunger and promote food security. Drying increase shelf life, reduce weight and volume of food thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. However, drying is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the food material. Modelling of this process is essential to optimize the drying kinetics and improve energy efficiency of the process. Since material properties varies with moisture content, the models should not consider constant materials properties, constant diffusion .The objective of this paper is to develop a multiphysics based mathematical model to simulate coupled heat and mass transfer during convective drying of fruit considering variable material properties. This model can be used predict the temperature and moisture distribution inside the food during drying. Effect of different drying air temperature and drying air velocity on drying kinetics has been demonstrated. The governing equations of heat and mass transfer were solved with Comsol Multiphysics 4.3.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.