CFD (computational fluid dynamics) modelling has gained a lot of momentum throughout the last decade and also becomes a valuable tool in biopharma. Taking the example of mixing in Single Use System (SUS) Mixers as an example, this paper discusses the huge advantages that CFD modelling brings for gaining deeper insights into mixing in these novel mixers but also shows the downsides of CFD modelling in general and its environmental impact under sustainability aspects and how Super-Designed Modelling can help significantly.

Mixing liquids is a basic operation frequently performed in the biopharmaceutical sector for both small-scale (beakers or flasks) and large-scale, e.g. bioreactors. In bioreactors, upstream as well as downstream processes are key when compounding, pooling, mixing and filling from large tanks.

So far, smooth-walled stainless-steel containers with standardized lapper bottoms have mostly/ widely been used on a larger scale together with common mixing impellers (located usually around the lower third of the container) For these set-ups mixing processes are well established, characterized extensively and generally scaled using P/V (energy input as a power to volume ratio).

For various business and regulatory reasons, efforts have recently been made to switch to Single Use Systems (SUS) for mixing as well/additionally. Here, specially sized three-dimensional plastic bags are hooked into a support cover. To minimize shear stress on biopharmaceuticals, the SUS impellers have entirely different shapes compared to those that were previously common; they sit floating in cup-shaped recesses at the bottom of the bag and are usually also eccentrically displaced. In addition, even when carefully inserted into the support cover and being filled, the bags do not form a smooth wall but have a creased or wrinkled surface.

When submitting new drugs for approval, the authorities require comprehensive knowledge of the product not only regarding the pharmacological, toxicological and clinical aspects, but also regarding the formulation and manufacturing process, which includes mixing.

Accordingly, the characterization of mixing processes in SUS is of great importance.

While experimental mixer validation is usually unproblematic in small-scale, large-scale experimental mixing tests involving extreme parameters (e.g. different speeds, filling volumes, etc.) present almost insurmountable obstacles, because the products are not only extremely expensive in larger quantities but also are usually not available to a sufficient extent in the early phases of development.

Typically, modelling approaches come into play at such a stage [1].

Computational fluid dynamics (CFD) simulations offer a path forward to gain insights into mixing behavior despite these challenges.

However, CFD simulations require a lot of computational power, especially for high-resolution simulations. Several days of computing are rule rather than exception, even on high performance multi core GPU clusters. The energy consumption of a simple 50L mixing, resembling only minutes of real time operation, might require approx. 43kWh. This equals the power consumption of a fridge/freezer combination operated for 3 months or 2 months of operating a laptop 24/7 under normal load.

Superdesigned modelling (SDM) is an approach to tackle the two downsides of CFD modelling at once: Time and energy consumption. The general questions to be answered by CFD simulation of mixing are usually:

1. What is the required mixer speed for sufficient mixing, while minimizing splashing, foaming, and air incorporation?
2. What is the required mixing time thereof?
3. What is the extent of shear stress on a biologic drug substance?

This means that from the vast amount of three-dimensional data, which are generated over tiny high resolution timesteps, only three(!) computed numbers make up/comprise the relevant output. As inputs there are mainly fill level, proportion of liquids to be mixed, their densities and viscosities.

Developing Design of Experiments (DOEs) around simulations by using these inputs as factors for a DOE and conducting the appropriate simulations forms the foundation for SDM.

Although the number of required simulations for a given mixer/impeller combination is kept to a minimum, the performed and analyzed DOE allows for an interpolation of data for any given input combination. As a result, the model can predict output parameters without running additional CFD simulations. Since the model also serves as an analytical equivalence of the simulations, it could be used to derive underlying functional dependencies and uncover even more knowledge around mixing.