Theoretical and experimental investigations were conducted to predict particle deposition and layer growth during formation of a dynamic membrane using cross-flow microfiltration. A critical particle size model was developed and solved in radial, circumferential and axial directions by analyzing the forces acting on a single particle. The model accounted for the normal drag, lateral lift, shear-induced and Brownian diffusion forces in the depositional direction, the van der Waals force in the circumferential direction, and the cross-flow drag and van der Waals forces in the axial direction. Cross-flow velocity and feed temperature were selected as representative influencing factors to examine variations of the critical particle sizes with permeate flux. Experiments were then conducted with carbon tubes as the support and zirconium dioxide particles as the coating material to verify the model. Results showed that a dynamic layer with non-uniform thickness along the circumferential direction was formed within the horizontal tube due to gravity. The layer thickness decreased as the cross-flow velocities were increased under a given trans-membrane pressure difference and feed concentration. An appropriately large cross-flow velocity was beneficial to achieve thickness uniformity during formation. The effect of the feed temperature on the critical particle size and layer thickness can be ignored. Comparisons between the theoretical predictions and experimental data of the layer thicknesses displayed good agreements. The effects of trans-membrane pressure differences and feed concentrations were finally examined in the present work.

Freeze-drying of the initially porous frozen material with pre-built pores from liquid material was found experimentally to save drying time by over 30% with an initial saturation being 0.28 compared with the conventional operation with the initial saturation being 1, using mannitol as the solid material. In order to understand the mass and heat transfer phenomena of this novel process, a two-dimensional mathematical model of coupled mass and heat transfer was derived with reference to the cylindrical coordinate system. Three adsorption–desorption equilibrium relationships between the vapour pressure and saturation value namely, power-law, Redhead's style and Kelvin's style equation, were tested. Kelvin's style in exponential form of adsorption equilibrium relation gave an excellent agreement between the model prediction and experimental measurement when the equation parameter, γ, of 5000 was applied. Analyses of temperature and ice saturation profiles show that additional heat needs to be supplied to increase the sample temperature in order to promote the desorption process. Simulation also shows that there is a threshold initial porosity after which the drying time decreased with the increase in the initial porosity. Enhanced freeze-drying is expected to be achieved by simultaneously enhancing mass and heat transfer of the process.Download full-size image