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Polymers have interesting physicochemical characteristics such as charge density, functionalities, and molecular weight. Such attributes are of great importance for use in industrial purposes. Understanding how these characteristics are affected is still complex, but with the help of molecular dynamics (MD) and quantum calculations (QM), it is possible to understand the behavior of polymers at the molecular level with great consistency. This study was applied to polymers derived from polyacrylamide (PAM) due to its great use in various industries. The polymers studied include hydrolyzed polyacrylamide (HPAM), poly (2-acrylamido-2-methylpropanesulfonate) (PAMPS), polyacrylic acid (PAA), polyethylene oxide polymer (PEO), and guar gum polysaccharide (GUAR). Each one has different attributes, which help in understanding the effects on the polymer and the medium in which it is applied along a broad spectrum. The results include the conformation, diffusion, ion condensation, the structure of the water around the polymer, and interatomic polymer interactions. Such characteristics are important to selecting a polymer depending on the environment in which it is found and its purpose. The effect caused by salinity is particular to each polymer, where polymers with an explicit charge or polyelectrolytes are more susceptible to changes due to salinity, increasing their coiling and reducing their mobility in solution. This naturally reduces its ability to form polymeric bridges due to having a polymer with a smaller gyration radius. In contrast, neutral polymers are less affected in their structure, making them favorable in media with high ionic charges.

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Due to the increase in the amount of copper sulphide minerals processed through concentration processes and the need to improve the efficiency of these production processes, the development of theoretical models is making an important contribution to generating a better understanding of their dynamics, making it possible to identify the optimal conditions for the recovery of minerals, the impact of the independent variables in the responses, and the sensitivity of the recovery to variations in both the input variables and the operational parameters. This paper proposes a method for modeling, sensitizing, and optimizing the mineral recovery in rougher cells using a discrete event simulation (DES) framework and the fitting of analytical models on the basis of operational data from a concentration pilot plant. A sensitivity analysis was performed for low, medium, and high levels of the operative variables and/or parameters. The outcomes of the modeling indicate that the optimum mineral recovery is reached at medium levels of the flow rate of gas, bubble size, turbulence dissipation rate, surface tension, Reynolds number of bubble, bubble–particle contact angle, superficial gas velocity and gas hold-up in the froth zone. Additionally, the optimal response is reached at maximum levels of particle size and density and at minimum levels of bubble speed, fluid kinematic viscosity and fluid density in the sampled range. Finally, the recovery has an asymptotic behavior over time; however, the optimum recovery depends on an economic analysis, examining the marginalization of the response over time in an operational context.

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