The absolute majority of modern studies dealing with the interpretation of experimental data on the basis of the Freundlich isotherm ignore the fact that the data obtained for regions of low and moderate adsorbate concentration/pressure can be analytically continued within the Freundlich adsorption model to the adsorptive saturation area with coverages tending to 100%. Needless to say, this would give valuable extended information about the corresponding adsorption process. This message proposes a framework to comprehensively analyse experimental data first recognised as complying with the Freundlich adsorption model. An algorithm-driven method is presented which enables one to translate the data obtained in the area of small and moderate the coverages of the area of adsorptive saturation regime. As examples, three sets of experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on carrier nano-Mg(OH)₂ have been processed and presented according to the framework developed.

A simple SIS-type mathematical model of infection expansion is presented and analysed with focus on the case SARS-Cov-2. It takes into account two processes, namely, infection and recovery/decease characterised by two parameters in total: contact rate and recovery/decease rate. Its solution has a form of a quasi-logistic function for which we have introduced an infection index that, should it become negative, can also be considered as a recovery/decease index with decrease of infected down to zero. Based on the data from open sources for the SARS-Cov-2 pandemic, seasonal influenza epidemics and a pandemic in the fauna world, a threshold value of the infection index has been shown to exist above which an infection expansion pretends to be considered as pandemic. Lean (two-parameter) SIR models affined with the warning SIS model have been built. Their general solutions have been obtained, analysed and shown to be a priori structurally adjusted to the infectives’ peak in epidemiological data.

Using experimental data for the adsorption of phosphates out of wastewater on waste recycled bricks, published independently in MDPI Processes before (2020), this message re-visits the mathematical theory of the Freundlich adsorption model. It demonstrates how experimental data are to be deeper treated to model the saturation regime and to bridge a chasm between those areas where the data fit the Freundlich power function and where a saturation of surface adsorption centers occurs.

Approximate analytical solutions for the overall adsorption functions based on the Fowler-Guggenheim local isotherm with a patchwise topology of adsorption centres location and four different adsorption heat distribution functions have been obtained. The Gaussian, constant, linear (as a particular case of power distribution), and exponential distribution functions have been applied. Overall adsorption functions have been analytically obtained, studied and commented. The Gaussian-related adsorption function reproduces the classic computational result nearly perfectly.