Scale-up of Processes Using Material Systems with Variable Physical Properties

M. Zlokarnik

Abstract
According to the theory of similarity, two processes are similar to one another if they take place in a similar geometrical space, and if all the dimensionless numbers necessary to describe the process, have the same numerical value. A complete similarity requires a geometrical, material and process-related similarity. This contribution aims at problems concerning material similarity. In many industrial tasks this problem presents no difficulties. In order to find an alternative fluid for model measurements, the model experiments are performed with Newtonian fluids of different viscosities to achieve the flow range in question on industrial scale, or one sticks to the same material system because it cannot be specified physically (slurries, slimes, foams, etc.) A problem arises when model (laboratory, bench-scale) measurements are to be performed in a so-called “cold model”, but the industrial plant operates at high temperatures (petrochemicals; T
800 – 1000 °C). How can we ascertain that the laboratory model system behaves hydrodynamically similarly to that in the industrial plant? Here, different temperature dependence of physical properties (viscosity, density) can cause problems. A problem arises when laboratory measurements are to be performed with cheap and problem-free model fluids to gain information about scaling-up of an apparatus for the treatment of cell cultures in biotechnology (mammal and plant cells, aerobic cultures, yeasts), the rheological behaviour of which is very complex (non-Newtonian: pseudoplactic and viscoelastic). Which model system may we choose? These are only two of the many problems which will be addressed and treated in this paper. The answer will be clear and unambiguous: We may choose any model material system whose dimensionless material function in question is similar to that of the original material system. It will be shown how to proceed to arrive at it.

This work is licensed under a Creative Commons Attribution 4.0 International License

Keywords
Dimensionless material functions, variable physical properties, rheological properties