Stokes flow through a rigid porous medium is analyzed in terms of the method of volume averaging. The traditional averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The equation of motion contains integrals involving spatial deviations of the pressure and velocity, the Brinkman correction, and other lower-order terms. The analysis clearly indicates why the Brinkman correction should not be used to accommodate ano slip condition at an interface between a porous medium and a bounding solid surface.

Flow in porous media I: A theoretical derivation of Darcy's law

Hot air and freeze-drying of high-value foods: a review.

https://doc.rero.ch/record/9768/files/Renard_Ph.-_Calculating_equivalent_permeability_20080903.pdf

Calculating equivalent permeability: a review

http://paginas.fe.up.pt/~sereno/publ/2004/JFE_ShrinkReview.pdf

Modelling shrinkage during convective drying of food materials: a review

Size, Shape, Volume, and Related Physical Attributes.- Rheological Properties of Foods.- Thermal Properties of Foods.- Electromagnetic Properties.- Water Activity and Sorption Properties of Foods.- Surface Properties of Foods.

Physical properties of foods

Dependable data on bulk density, volumetric shrinkage due to water loss and porosity are needed to model processes such as drying, packaging and storing. Experimental data are presented for all three properties. It is possible to model the water-loss-based bulk shrinkage coefficient to obtain a predictive equation based on composition of the foodstuff. From this, a generalized correlation is obtained which predicts bulk shrinkage coefficient knowing only the initial moisture content of the food. Porosities for the foodstuffs considered can be predicted through suitable correlations, but there is no generalized equation spanning all foods.

Shrinkage, Porosity and Bulk Density of Foodstuffs at Changing Moisture Contents

Pipeline Design Calculations for Newtonian and Non-Newtonian Fluids, James F. Steffe and R. Paul Singh Sterilization Process Engineering, Hosahilli S. Ramaswamy and R. Paul Singh Prediction of Freezing Time and Design of Food Freezers, Donald J. Cleland and Kenneth J. Valentas Design and Performance Evaluation of Dryers, Guillermo H. Crapiste and Enrique Rotstein Design and Performance Evaluation of Membrane Systems, Jatal D. Mannapperuma Design and Performance Evaluation of Evaporation, Chin Shu Chen and Ernesto Hernandez Material and Energy Balances, Brian E. Farkas and Daniel F. Farkas Food Packaging Materials, Barrier Properties, and Selection, Ruben J. Hernandez Kinetics of Food Deterioration and Shelf-Life Prediction, Petros S. Taoukis, Theodore P. Labuza, and I. Sam Saguy Temperature Tolerance of Foods during Distribution, John Henry Wells and R. Paul Singh Definition,Measurement, and Prediction of Thermophysical and Rheological Properties, Martin J. Urbicain and Jorge E. Lozano Dough Processing Systems, Leon Levine and Ed Boehmer Cost and Profitability Estimation, J. Peter Clark Simulation and Optimization, Enrique Rotstein, Julius Chu, and I. Sam Saguy CIP Sanitary Process Design, Dale A. Seiberling Process Control, David Bresnahan Food Chemistry for Engineers, Joseph J. Warthesan and Martha R. Meuhlenkamp Index Catalog no. 8694, 1998, 736 pp., ISBN: 0-8493-8694-2 $134.95 / GBP90.00 Short TOC

Handbook of Food Engineering Practice

A simple procedure has been implemented to measure porosity of apples as a function of moisture contents. The method has been applied to apples with change in moisture contents by conventional air drying. It is shown that the pores, which for biological reasons are open, i.e. connected to the outside, at the onset of dehydration, remain so until X = 1.5 g/g. As dehydration proceeds the pores are split into two families of pores: externally connected pores and locked-in bores. Both total and open pore porosity can be predicted from experimental correlations. Alternatively, the total porosity can be estimated from data on bulk volume shrinkage and the average composition of the tissue by means of equations presented. The interpretation of experimental data using this approach confirms that there is a significant change in the three-dimensional arrangement of the cellular tissue below X = 1.5 g/g. The two approaches lead to the conclusion that, probably due to cellular collapse, the open structure that characterizes the fresh foodstuff changes into a structure with locked-in pores. This fact may help to explain the slow and difficult re-hydration which characterizes air-dried foodstuffs. This hypothesis will be followed up in future work. The information developed should be of help in qualitative and quantitative modeling of processes involving moisture changes.

Enrique Rotstein

Papers

Shrinkage, Porosity and Bulk Density of Foodstuffs at Changing Moisture Contents

Handbook of Food Engineering Practice

Total porosity and open-pore porosity in the drying of fruits

A general closure scheme for the method of volume averaging

Drying of cellular material—I. A mass transfer theory