In this work, we aim to determine the dimensions of an axisymmetric crack contained in a non-linear magnetic material. First, we begin to characterize the magnetic material from a modeling of the direct magnetodynamic problem by 2D finite element of the system (magnetic material + sensor) and solved by the Newton Rapheson method. FEMM(Finite Element Method Magnetics, an open source software, was used to validate the model).This direct model is then inverted by a simplex algorithm to determine the dimensions of the crack.

This work includes studying the removal of methylthionine chloride on bridged bentonite, and conducting a batch system adsorption test. The influence of various parameters like the dose of adsorbent, pH, contact time and temperature on the behavior of the MC was studied. The pseudo second order kinetic model seems adequate and correlates with the experimental results. The adsorption isotherm fitted well to the Langmuir model with a maximum adsorption capacity adequate to 45.68 mg g−1. The values of the thermodynamic parameters (∆H◦, ∆G◦, and ∆S◦) are negative indicating that the method of MC removal by the bentonite is exothermic, spontaneous, and with increasing order at the solid-solution interface. The results of the FTIR, XRD, SEM and BET characterizations show that this bentonite may be a mixture of Montmorillonite, Kaolinite, Illite, Quartz and Calcite, with a specific surface estimated at 30,3961 m2 g−1.