ABSTRACT
Material ....................................................................................................... 164 7.2.1 Balance Equations and Assumptions ......................................... 164
7.2.1.1 Momentum Conservation .............................................. 166 7.2.1.2 Mass Conservation ......................................................... 167 7.2.1.3 Preliminary Equation System ....................................... 168
7.2.2 Constitutive and Closure Relations ............................................ 169 7.2.2.1 Solid Components of AGM ............................................ 169 7.2.2.2 Chemical Reactions ......................................................... 172 7.2.2.3 AGM Swelling Process and Solid Strain ...................... 174 7.2.2.4 Liquid Saturation on Capillary Pressure
Dependency ..................................................................... 176 7.2.2.5 Empirical Material Relations ......................................... 177
7.2.3 Final Equation System ................................................................... 177 7.3 Finite-Element Solution ............................................................................. 180
7.3.1 Discretization in Space and Time ................................................ 182 7.3.2 Hysteresis Implementation ........................................................... 186
7.4 Wicking Experiments in Absorbent Swelling Materials ...................... 187 7.4.1 Dynamic Absorption Test ............................................................. 187 7.4.2 Vertical Wicking Experiment ....................................................... 188
7.5 Simulation of Wicking Experiments ....................................................... 190 7.5.1 Determination of Input Parameters for the Core Sample ........ 190 7.5.2 Simulation of Dynamic Absorption Test .................................... 193 7.5.3 Simulation of Vertical Wicking Experiment .............................. 195
7.6 Summary ..................................................................................................... 196 Nomenclature ...................................................................................................... 196
Roman Letters ............................................................................................ 196 Greek Letters ............................................................................................... 198 Subscripts .................................................................................................... 198
Progress in chemical engineering during the last few decades expanded the application of porous media modeling beyond environmental problems in soils to a large variety of arti cial porous materials, such as industrial sponges, packed plastic granulates, hygiene products, and so on. Here, problem scales are reduced to centimeters or even millimeters. However, Darcy’s law for ˆow in saturated porous media as well as Richards’ equation for variably saturated media can still be usefully applied under certain known assumptions.
