Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.

Multiscale hydrodynamics in line contacts were analyzed from the newly developed ‎multiscale flow equations by respectively considering the weak, medium and strong fluid-‎contact interactions. In the studied line contact, the surface separation is on the same scale ‎with the thickness of the adsorbed layer on the contact surface, and between the coupled ‎adsorbed layers occurs the continuum fluid flow. The present study shows that when using ‎the developed multiscale flow equations to calculate the surface separation for the weak or ‎medium fluid-contact interactions, the value of the parameter k, which is in the important ‎formulation ‎ ‎, should be taken as about 5. 0, different from its value 1. 0 for the ‎strong fluid-contact interaction. The study also shows that owing to the adsorbed layer effect, ‎for a given operating condition, stronger the fluid-contact interaction, greater the surface ‎separation. The results show the significant effect of the fluid-contact interaction in ‎hydrodynamic line contacts in a quite wide range of the surface separation because of the ‎multiscale hydrodynamic effect‎.