Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Multiphase porous media model for Intermittent Microwave Convective Drying (IMCD) of food

Intermittent microwave convective (IMCD) drying is an advanced drying technology that improves both energy efficiency and food quality during the drying of food materials. Despite numerous experimental studies available for IMCD, there is no complete multiphase porous media model available to describe the process. A multiphase porous media model considering liquid water, gases and the solid matrix inside the food during drying can provide in depth understanding of IMCD. In this article, firstly a multiphase porous media model was developed for IMCD. Then the model is validated against experimental data by comparing moisture content and temperature distributions after each heating and tempering periods. The profile of vapour pressures and evaporation during IMCD are presented and discussed. The relative contribution of water and vapour fluxes due to gas pressure and diffusion demonstrated that the fluxes due are relatively higher in IMCD compared to convection drying and this makes the IMCD faster.