# State Analysis of the Water Quality in Rivers in Consideration of Diffusion Phenomenon
## 1 Introduction  
In the age of rapid change and rapid civilisational development, the terms ecology and environmental protection are becoming increasingly important. The environment influences man, and man also influences the place in which he lives, with the difference that our influence is often destructive. However, much of this inappropriate activity can be eliminated by adopting an environmentally friendly attitude. Amongst the many different factors that determine the level of civilisation is water. The requirements for water composition are continually increasing, which is why water purity tests are constantly conducted. This has resulted in the improvement and implementation of highly efficient and often unconventional manufacturing processes that protect the environment. Water is in constant motion, moving on land, in the atmosphere and in the oceans. Rivers play an important role; they form an integral part of water management and are a renewable source of fresh water. Due to the introduction of various biological and chemical substances into the environment, the quality of water has been changing [1,2]. Above all, we humans pose a very great threat to this precious resource. Using mathematical modelling as a tool that can be applied in various areas of research, on modern engineering solutions [3,4], the authors designed an intelligent control andmonitoring system for water quality status in rivers (Figure 1). The use of the above system makes it possible to influence the improvement of water quality, thus preventing the appearance of undesirable water pollution conditions in a river, thereby augmenting the standard of living in the current threatened environmental world. The system combines mathematical modelling and an extensively developed IT tool to monitor the state of water quality and influence its improvement when undesirable conditions arise. The intelligent monitoring and control system is the answer to the demands of Industry 5.0. Its various components, consisting of different types of sensors that monitor the state of water quality and telemetry stations that send real-time data to the intelligent module, enable the monitoring and the prevention of the spread of emerging poor water conditions. A detailed description of the system and the results of research carried out to date, in connection with the intelligent monitoring and control system, are presented in [5, 6, 7]. The paper [6] presents an approach which employs ANN (Artificial Neural Networks) for the real-time monitoring and control of water quality status. The paper [5] presents a spatio-temporal method for analysing the state of river pollution, in the context of application in modern control and measurement systems, for predicting changes. On the other hand, the paper [7] presents an adaptive algorithm to determine the value of the filter amplification factor, which allows for the avoidance of inconveniences, resulting from the need to estimate the characteristics of signals affecting the object under investigation. In this work, the mathematical models used did not make use of the phenomenon of diffusion which, under certain conditions of the river environment, significantly weakened the accuracy of the monitoring process. Theoretical and experimental studies of diffusion in liquids are discussed by many authors in various scientific publications [8, 9, 10]. The paper [11] focuses on discussing the principles, applications and advances in diffusion, thermal diffusion and thermal conductivity in liquid systems. The presented experimental methods, for studying diffusion processes in liquids, systematise the theoretical interpretation of diffusion coefficients. In explaining the control of the specific gravity of an air-water mixture, the authors [12] use the partial differential equation of convective diffusion at a constant state.