Limitations of mathematical modelling and numerical simulation of industrial and laboratory high-pressure processes

High pressures up to several hundreds of MPa are utilised in a wide range of applications in chemical engineering, bioengineering, and food engineering, aiming at selective control of (bio-)chemical reactions. Non-uniformity of process conditions may threaten the safety and quality of the resulting products as the process conditions such as pressure, temperature, and treatment history are crucial for the course of (bio-)chemical reactions. Therefore, thermofluid dynamical phenomena during the high-pressure process have to be examined, and tools to predict process uniformity and to optimise the processes have to be developed. Recently, mathematical models and numerical simulations of laboratory and industrial scale high-pressure processes have been set up and validated by experimental results. This contribution deals with the assumption of the modelling that relevant (bio-)chemical compounds are ideally dissolved or diluted particles in a continuum flow. By considering the definition of the continuum hypothesis regarding the minimum particle population in a distinct volume, limitations of this modelling and simulation are addressed.