Mixing Optimization in Pharmaceutical Manufacturing Processes through CFD 

Introduction: Scale Up from Lab to Large Tanks 

In chemical and pharmaceutical production, mixing processes often play a key role in achieving the required yield and final product specifications, especially in the upstream processing phases. The production of active pharmaceutical ingredients (API), the biopharmaceutical product, generally begins with the culture of living organisms, mammalian cells, or microbial organisms. This phase is called the upstream process, where the cell culture often starts in small batches and is grown to large volumes, also thousands of liters, to obtain several kilograms of the desired API

Mixing processes in production, therefore, spans over a large variety of conditions and systems, literally from laboratory to mass product industrial size. In this article/post it is presented how the mixing process can be optimized by employing computational fluid dynamics (CFD) techniques, resulting in a wide spectrum of benefits.  

As a result, mixing processes in production covers a wide range of conditions and systems, from laboratory to mass product industrial size. This article/post explains how to optimize the mixing process using computational fluid dynamics (CFD) techniques, resulting in a wide range of benefits. 

Mixing Techniques/ Usages 

Mixing is a crucial step in pharmaceutical production and cell growth culture for many reasons; first, it is used to keep substances (cell culture media) and cells in solution or suspension, avoiding precipitations. It allows homogeneity so to keep cell volumetric concentration constant in the tank for the next process phase, dispensations for example.  

In certain cases, cells are grown on carriers (micro-beads), which offer support and anchor for the cells to proliferate on, therefore mixing needs to be designed in accordance to exert sufficient lifting force to keep the carriers in constant agitation/dispersion. Furthermore, generally, more vigorous mixing is necessary to detach the cells from the carriers, therefore optimized impeller design and/or optimal operating conditions have a significant impact on cell growth and product yield.  

As previously said mixing process spans from laboratory magnet mixing to industrial vigorous impellers often ad-hoc built.   

Metrics to eval mixing – is your mixing too aggressive? 

To evaluate the performance of a production process involving mixing stages two major routes are available, experimental testing and CFD simulation. In CFD modelling, the cell growth can be cumbersome to represent physically and accurately, however in the literature well-established correlations have been reported that link certain CFD key outputs to cells behavior,  well-being, and growth. Within these key outputs, the shear stress or shear rate and the Kolmogorov turbulence scale are generally used as performance metrics. Turbulent phenomena are particularly detrimental to cell growth and need to be avoided as much as possible, possibly already in the design phase. This situation is not always accomplishable therefore it is fundamental to evaluate the impact of turbulent phenomena to ensure the selection of optimal operating conditions and CFD together with experimental testing is the only way to accomplish that.  

Shear stress is always present during mixing and in case of turbulent flow can locally reach high, potentially detrimental, values. Turbulent flow happens when the Reynolds number, defined as in equation [1] is higher than a certain critical value (it differs from condition to condition). 

Shear stress is the quantification of the energy applied to the agitated liquid by the generic impeller, while the Kolmogorov turbulence scale, equation [2], is a figure of merit that represents the minimum turbulence eddy formed during an instability turbulence phenomenon.

In this scenario, it becomes useful to consider, together with the shear stress, the size of the turbulent instability. It has been experimentally demonstrated that if the size of the cells or the cell carriers is above 2/3 of the Kolmogorov scale then cell growth is not hindered.

How to use the information from CFD analysis

CFD analysis of fully and partially turbulence flows allows to compare different mixing tanks, impellers geometry and size, and agitation speeds without running experiments. A clear benefit is a selection of correct equipment on the first try, which can save a lot of money. In this paragraph is reported a CFD analysis conducted on laboratory scale mixing equipment, precisely the effect of the magnet length value, L, on the shear stress and turbulence induced in a 5 L cylindrical tank of diameter D. Rotational speed for the magnet is set constant at 150 rpm, while three values of the ratio between the tank diameter and the magnet length are evaluated to show the impact of the latter.

Figure 1

Figure 1 shows the model elements, tank and magnet, and the velocity magnitude profile generated by the rotation.

Figure 2

Figure 2 shows the effect of the ratio L/D, magnet length to tank diameter ratio, when considering the average shear stress fraction in the proximity region of the magnet and the Kolmogorov scale in the entire tank volume.

It can be observed that the average shear stress can be significantly reduced if the ratio L/D is reduced, choosing for example a smaller magnet length. Furthermore, a lower value of the ratio L/D clearly shifts the Kolmogorov scale to larger values, away from critical sizes for cell culture.

The proper choice of the magnet (or impeller) size will depend on several factors, however, the CFD simulation highlights the differences in the designs and potential benefits or defects of a certain choice. Such information is particularly useful for scale-up processes when API production needs to be shifted from lab scales to mass production scales.

Why Evaluate the mixing process through CFD – Yield! & Costs!

CFD techniques together with multi-physical simulations create the possibility to investigate and optimize different aspects of the API manufacturing processes. Mixing stands out as one of the most common and yet essential process phases in downstream processes. Optimization of this step can easily achieve relevant yield increments and consecutive cost reductions. This step’s optimization can easily result in relevant yield increases and subsequent cost reductions. Analysis of mixing processes with CFD techniques allows visualizing precisely potential issues in the mixing tank/batch. For example, the visualization of the flow patterns, and solid particle dispersion together with the evaluation of turbulence phenomena and shear stresses, as shown above.

Another benefit of evaluating mixing processes with CFD analysis is the answer time, for reference, for the example above only a couple of hours are sufficient to generate meaningful output. Therefore, CFD simulations can be used to perform virtual DOE to aid different departments and tasks, guide experimental testing, limiting the number of tests, reducing costs. Furthermore, if CFD analysis is experimentally validated their outputs can be transferred to other domains than just design and validation.


In conclusion, CFD and Multiphysics Simulations provide valuable insights for mixing processes scale-up and optimization. The simultaneous evaluation of multiple factors by the digital representation allows better operating conditions as well as it offers a framework for improved knowledge sharing as design decisions and/or potential issues can be more easily visualized. 


'Day-to-day scripting in Simulation'

by Tore Findsen

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Lene Gottrup Barfod

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